User Guide/Manual for
SANET Standalone
June 14, 2020

Table of Contents

page

1. About SANET
1.1 Functions and Versions
1.2 Copyright
1.3 Use conditions
1.4 Citation in publication
1.5 Contact
1.6 I/O file formats

2

2. How to register and run SANET Standalone
2.1 Hardware and Software requirements
2.2 Unzipping SANET Standalone executable file
2.3 Placing license key to run SANET Standalone5

3. What is SANET?

7

4. Analytical Tools
4.1 Tool 01: Voronoi diagram
4.2 Tool 02: Delaunay diagram
4.3 Tool 03: Kernel density estimation
4.4 Tool 04: Interpolation
4.5 Tool 05: Point clustering method
4.6 Tool 06: Random points generator
4.7 Tool 07: Shortest path distances between points in a set of points
4.8 Tool 08: Shortest path distances between A points to B points
4.9 Tool 09: Network Characteristics: polylines, points and links
4.10 Tool 10: Global auto nearest neighbor distance method
4.11 Tool 11: Global cross nearest neighbor distance method
4.12 Tool 12: Local cross nearest neighbor distance method
4.13 Tool 13: Global auto K function method
4.14 Tool 14: Global cross K function method
4.15 Tool 15: Local cross K function method
4.16 Tool 16: Voronoi cross K function method
4.17 When SANET claims “The network is disconnected”

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36
39
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5. Visualize the SANET sample results on ArcMap, R and QGIS
5.1 Visualize the results on ArcMap and ArcScene
5.2 Visualize the results on R
5.3 Visualize the results on QGIS

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65
73

 About Handling SANET Setup Wizard

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6. Manuals
6.1 Procedure for generating ‘buffer sub-networks’ of a generator point set
6.2 Procedure for counting the number of points on ‘buffer sub-networks’ of agenerator point set
6.3 Procedure for computing the total length of ‘buffer-ring sub-networks’ of agenerator point set
6.4 Exact statistical test for network Voronoi cross K function method

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104
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1. About SANET
1.1 Functions and Versions
SANET Standalone statistically analyzes spatial patterns of events that occur
on/alongside networks.
Current version of SANET Standalone Version 1.0 is a licensed program.
The effective license period for SANET Standalone Version 1.0 is one year.
SANET is developed by the SANET Team (Leader: Atsu Okabe).
SANET Version 3.1 is for ESRI ArcGIS Ver.9.1 & 9.2 with Windows XP.
SANET Version 4.0 is for ESRI ArcGIS Ver.9.3 with Windows Vista and Windows XP.
SANET Version 4.1 is for ESRI ArcGIS Ver.10 with Windows 7, Vista and Windows XP.
1.2 Copyright
The program is copyrighted by PASCO and is intended for the use of students,
academic researchers, non-profit researchers and educators.
SANET can be distributed freely on educational and research purposes, but cannot
be re-sold.
1.3 Use conditions
SANET Team distributes the program only to those who agree on the following
conditions
 The user will use SANET for nonprofit purposes only.
 The authors will not bear responsibility for any trouble that the user may
meet in the use of SANET.
 When the user uses SANET, he/she will report to the authors his/her
name, affiliation, address and e-mail address.
 When the user publishes any results obtained by using SANET, he/she will
explicitly state in the paper that he/she used SANET. Also, he/she will senda reprint of the paper to the authors.
 The authors appreciate the reports of users which help us discover andisolate bugs within SANET.
1.4 Citation in publication
SANET must be cited correctly in any papers or publication that use results
obtained from SANET. Also it should be acknowledged the use of SANET, Spatial
Analysis along Networks developed by the SANET Team (leader: Atsu Okabe),
Tokyo, Japan. In addition, in case any correspondence exists between specificmembers, his/her name is most preferably being cited.
3

1.5 Contact
SANET team contact information is as follows.
Request for distribution of SANET Program and sending papers should contact toAtsu Okabe [atsu@csis.u-tokyo.ac.jp]
Technical questions relating to the SANET software and manual should contact toAtsu Okabe [atsu@csis.u-tokyo.ac.jp]
1.6 I/O file types
The current Version is SANET Standalone 1.0.
The SANET program inputs spatial data (e.g. accident incidence spots data, retail store
location data) with ESRI Shapefile.
The SANET program computes various spatial factors and gives results in forms of
Shapefile, CSV file or R file for chart the result.

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2. How to resister and run SANET Standalone
2.1 Hardware and Software requirements
Concerning the interface either ESRI ArcMap or QGIS Desktop is required tovisualize the results obtained from running the SANET Standalone.
GNU R is also preferably installed for the better performance of the results.
2.2 Unzipping SANET Standalone executable file
Firstly, download the SANET Standalone executable file (zip).
Secondly, unzip the file and put it in your preferable place.
Thirdly, double click setup.exe. Since the setup wizard appears in Japanese, pleaserefer to pp.77-78 for an illustration.
2.3 Placing license key to run SANET Standalone
Once you launched the SANET Standalone, below window will appear. On thebottom you will find the resister button.

Click the button and the license register window appears.

Place the license number which the SANET team have sent to you after receiving
5

your registration form.
To obtain the license number, download a registration form, fill up the form andemail it to the SANET contact person (see the section 1.5 above). Having qualified
as an eligible user, the license key will be sent to you via email.

AB6666-5555-4444-3333-2222

Input your license key to your SANET License Register.
Click the SET button and you will find all SANET tools in your window.

Enjoy SANET until your license expires.

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3. What is SANET?
In the real world, there are many and various kinds of network events. Those events may
be classified into two types: the events occurring exactly on networks, termed on-network
events and those occurring alongside networks, termed alongside-networks (Figure 1.1).
network (constrained) events

on-network events

alongside-network events
SANET
Store

Source: Figure 1.1 in Okabe and Sugihara (2012). Network (constrained) events
consisting of on-network events and alongside-network events.
Typical examples of on-network events are: traffic accidents (shown in Figure 1.2), roadkills of animals, street crimes, beaver lodges in watercourses, leakages in gas pipe lines
and river contamination. Alongside-network events include advertisement agencies (Figure1.3), fast-food shops, convenience stores, fashionable boutiques and other kinds offacilities locating alongside streets in urbanized areas. Almost all facilities in urbanizedareas are regarded as alongside-network events because their entrances are adjacent tostreets.

Tokyo Bay

Source: Figure 1.2 in Okabe and Sugihara (2012). Sites of traffic accidents around Chiba
station, Japan (private roads are not shown).
7

0

0.5

1.0 kmSource: Figure 1.3 in Okabe and Sugihara (2012). The distribution of advertisement
agency sites (the black points) alongside streets (the gray line segments) in Shibuya ward,
one of the sub-central districts in Tokyo.
Traditionally, network events are analyzed with spatial methods assuming Euclidean
distance on a plane, referred to as planar spatial analysis. However, this assumption isdifficult to accept in practice when analyzing network events, in particular, in urbanizedareas, because Euclidean distances and their corresponding shortest-path distances are
significantly different. As a matter of fact, an empirical examination shows that thedifference is more than 20% when Euclidean distances are less than 400 meters.
Alternatively, network spatial analysis assumes the shortest-path distance on networks.
This analysis potentially enables more practical investigation of network events than planar
spatial analysis, but it requires heavy geometrical and topological computations. Thisdifficulty hindered its development. To overcome this difficulty, SANET, a GIS toolbox has
been developed. Using this toolbox, application-oriented GIS scientists, who are notalways skilled in programming, can now easily perform network spatial analysis withdetailed data (not spatially aggregated data, but such as objects in Figures 1.2 and 1.3).
Network spatial analysis is not only practical but also theoretically sound because it can
avoid misleading statistical inference when network events are examined. A clear example
is provided in Figure 1.4. Having observed the distribution of points in panel (a), nobody
would consider that points are randomly distributed. This is true when a plane is assumed
but this becomes false when a network is assumed. In fact, the points in panel (b) are
randomly generated according to the uniform distribution over the network (theconfiguration of points in panel (a) and that in panel (b) is the same). This shows that8

planar spatial analysis is likely to lead to false conclusions when applied to network
events.

(a)(b)

Source: Figure 1.4 in Okabe and Sugihara (2012). Point distributions: (a) nonrandomly
distributed points on a bounded plane, (b) randomly distributed points on a network (notethat the point distributions in (a) and (b) are the same).
As is noticed from the above discussion, tools in SANET are practically as well as
theoretically useful for examining network events.

94. Analytical Tools
SANET Toolbox includes the following tools: The following sections show how to operatethese tools using the sample data downloadable from the SANET website. Note that eachsection is self-contained; therefore, the user can directly go to any section you want to
read.
4.1 Tool 01: Voronoi diagrams
This tool generates the ordinary Voronoi diagram and the additively weighted
Voronoi diagram for a given generator set of points placed on a given network. Detailsof this diagram are described in Chapter 4 of Okabe and Sugihara (2012).
Click the “Voronoi diagram” in the SANET menu.

Then the following window appears.

10Clickto choose a file of network (e.g. orgroad.shp: street network in thesample data set).
Click

to choose a set of points that generates Voronoi diagrams (e.g.

store_pts.shp: 3 shop locations in the sample data set).
If you use the ordinary Voronoi diagram, leave the ‘Additively Weighted Field” blank.
If you use the additively weighted Voronoi diagram, choose ▼ to set the field of thefile of the generation point set where weights are given.
Click

to store the resulting output files, andClick “OK”.
If the following window does not appear, the network is completely connected.
Proceed to the next step marked by *** below.

If this window appears, the given network is not completely connected. In that case,see p.55 to find out your next step to proceed.
***
When the network is completely connected or if you click “Yes” in the warning
window, the program begins to run. Having no trouble such as memory overflows,
you may obtain the following files as the output.

The attribute table of the output is as follows.

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Shape: polylines
SgtID: link ID (a polyline ID).
FromX, FromY, From Z: from the node (x, y, z).
ToX,ToY, ToZ: to the node (x, y, z).}.
Length: the length of a link.
AcsID: the Voronoi subnetwork ID to which a link belongs.
To visualize the result, please see section 5.1 / section 5.3.
Reference
Okabe, A. and K. Sugihara (2012) Spatial Analysis along Networks: Statistical andComputational Methods, Chichester: John Wiley, a volume in the Wiley series of
Statistics in Practice.
4.2 Tool 02: Delaunay diagram
Originally, a Delaunay triangulation (a diagram on a plane) is defined as the reciprocal
figure of the corresponding Voronoi diagram on a plane. Stated explicitly, generate line
segment between the generators whose Voronoi polygons share the same Voronoiedge. The resulting line segments form a triangular network, termed the Delaunay
triangulation of the given Voronoi diagram. Delaunay diagrams on a network are similar
to Delaunay triangulations on a plane in spirit. Given a Voronoi diagram on a network,
generate the shortest-path between two generators whose Voronoi sub-networks are
adjacent. The resulting shortest-paths form a Delaunay diagram on a network.
Click the “Delaunay diagram” in the SANET menu.

Then the following window appears.
12Clickto choose a file of network (e.g. orgroad.shp: street network in the sample

data set).
Click

to choose a set of points that generates Delaunay diagrams (e.g.

store_pts.shp: 3 shop locations in the sample data set. Ignore Weight field.).
Click

to store the resulting output files, and click “OK”.

If the following window does not appear, the network is completely connected.
Proceed to the next step marked by *** below.

If this window appears, the given network is not completely connected. In that case,see p.55 to find out your next step to proceed.
***
When the network is completely connected or if you click “Yes” in the warning
window, the program begins to run. Having no trouble such as memory overflows,13

you may obtain the following files as the output.
To visualize the result, please refer section 5.1 / section 5.3.
4.3 Tool 03: Kernel density estimation
For a given set of points on a given network, this tool estimates the density of points
on the network. For details, see Chapter 9 and Section 12.2.5 in Okabe and Sugihara(2012).
Click “Kernel density estimation”. Then the following window appears.

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Choosethe file of a network (e.g., orgroad.shp: street network in the sample

data set.).
Choosethe file of a set of points (e.g., rsd_pts.shp: location of points in thesample data set.).
Choose ▼ one of the two estimation methods: “equal split continuous at nodes” or“equal split discontinuous at nodes”.
Fill in a band width and a cell width. 50 and 10 are put respectively in this example.
Note that if you use a large band width and a small cell width, computation time
becomes long. Try to use a fairly small band width and a large cell size satisfyingthat the former is larger than the latter. If the computation time is within your timeallowance, change those values. Our experience says [band size] = 10*[cell size].
We also note that you are supposed to use the same grid coordinates system as thatof the network.
Chooseto store the resulting output files, andClick “OK”.
If the following window does not appear, the network is completely connected.
Proceed to the next step marked by *** below.

If this window appears, the given network is not completely connected. In that case,see p.55 to find out your next step to proceed.
***
When the network is completely connected or if you click “Yes” in the warning
window, the program begins to run. If you do not have any trouble such as memory
overflows, you may obtain the following files as the output.

15

To visualize the result, please see section 5.1 / section 5.3.
Reference
Okabe, A. and K. Sugihara (2012) Spatial Analysis Along Networks: Statistical andComputational Methods, Chichester: John Wiley, a volume in the Wiley series of
Statistics in Practice.
4.4 Tool 04: Interpolation
For a given set of known attributes values at sample points on a given network, thistool interpolates unknown attribute values at arbitrary points on the network using theinverse distance weighting method. Stated explicitly, the tool predicts the value ẑ0 at
p0 as the weighted average of the known attribute z j values at the points p j of aneighborhood PN ( p0 ) of p0 , i.e.:
zˆ0 

w z

i
pi PN ( p0 )i,where the weight wi is given by:wi d S ( p 0 , p i ) 
p j PN

d S ( p0 , p j ) ,

where  is a positive predetermined parameter.
For details, see Chapter 9 and Section 12.2.5 in Okabe and Sugihara (2012).
Click “Interpolation”. Then the following window appears.

16Choosethe file of a network (e.g., orgroad.shp: street network in the sample

data set.).
Choosethe file a set of points at which their attribute values are known (e.g.,

location points in the sample data set.).
Choose ▼ the field in which weights are given.
Choose ▼ “Inverse distance weighting method”.
17Fill in cell width (This determines the resolution of the resulting figure; default is 10,
but might require much memory; you may start a larger value, say 10).
 value of  , say 0.5.


number of points in the neighborhood PN ( p0 ) , say 10.

Chooseto store the resulting output files, andClick “OK” .
If the following window does not appear, the network is completely connected.
Proceed to the next step marked by *** below.

If this window appears, the given network is not completely connected. In that case,see p.55 to find out your next step to proceed.
***
When the network is completely connected or if you click “Yes” in the warning
window, the program begins to run. If you do not have any trouble such as memory
overflows, you may obtain the following six files as the output.

To visualize the result, please see section 5.1 / section 5.3.
Reference
Okabe, A. and K. Sugihara (2012) Spatial Analysis Along Networks: Statistical andComputational Methods, Chichester: John Wiley, a volume in the Wiley series of
Statistics in Practice.

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4.5 Tool 05: Point clustering method
This tool clusters points in a given point set on a given network by the closest-pairclustering method. For details, see Sections 8.1.2.1 and 12.2.4 in Okabe andSugihara (2012).
Click the “Point clustering method” in the SANET menu.

Then the following window appears.

Choosethe file name of a network (e.g., orgroad.shp: street network in thesample data set).
Choosethe file name of a set of points (e.g., location points in the sample data

set.).
19

Chooseto store the resulting output files, andClick “OK” .
If the following window does not appear, the network is completely connected.
Proceed to the next step marked by *** below.

If this window appears, the given network is not completely connected. In that case,see p.55 to find out your next step to proceed.
***
When the network is completely connected or if you click “Yes” in the warning
window, the program begins to run. If you do not have any trouble such as memory
overflows, you may obtain the following “SANETClustering.R” file as the output.

To visualize the result, please see section 5.2.
Reference
Okabe, A. and K. Sugihara (2012) Spatial Analysis Along Networks: Statistical andComputational Methods, Chichester: John Wiley, a volume in the Wiley series of
Statistics in Practice.
4.6 Tool 06: Random points generator
This tool generates random points on a given network according to the uniform
distribution over the network. The resulting points are a realization of the complete
spatial randomness (CSR) often used for a null-hypothesis. For details, see Sections
2.4.2 3.4.5 and 12.1.4 in Okabe and Sugihara (2012).
Click the “Random points generator” in the SANET menu.

20Then the following window appears.

Choosethe file name of a network (e.g., orgroad.shp: street network in thesample data set).
Fill in a number of random points, say 200.
Chooseto store the resulting output files, andClick “OK”.
If the following window does not appear, the network is completely connected.
Proceed to the next step marked by *** below.

21

If this window appears, the given network is not completely connected. In that case,see p.55 to find out your next step to proceed.
***
When the network is completely connected or if you click “Yes” in the warning
window, the program begins to run. If you do not have any trouble such as memory
overflows, you obtain the following files in the output file.

To visualize the result, please see section 5.1 / section 5.3.
Reference
Okabe, A. and K. Sugihara (2012) Spatial Analysis Along Networks: Statistical andComputational Methods, Chichester: JonWiley, a volume in the Wiley series of
Statistics in Practice.
4.7 Tool 07: Shortest-path distances between points in a point set
This tool computes the shortest-path distances between any pair of points in a given
set of points placed on a given network. For details, see Section 12.1.3 in Okabe andSugihara (2012).

Click the “Shortest-path distances between points in a point set” in the SANET menu.

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Then the following window appears.

Choosethe file name of a network (e.g., orgroad.shp: street network in thesample data set).
Choosethe file name of a set of points (e.g., store_pts.shp: store location

points in the sample data set)
Chooseto store the resulting output file, andClick “OK”.
If the following window does not appear, the network is completely connected.
Proceed to the next step marked by *** below.

If this window appears, the given network is not completely connected. In that case,see p.55 to find out your next step to proceed.
***
When the network is completely connected or if you click “Yes” in the warning
window, the program begins to run. If you do not have any trouble such as memory
overflows, you obtain the following file.

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The contents of the file are as follows.

The first column indicates “from the i-th point of the point set”.
The second column indicates “to the j-th point of the point set”.
The last column indicates the shortest-path distance between those points. For
instance, the shortest-path distance from the 0th point to the first point is 313.0112
and so forth.
AVERAGE of the last row shows the average of all the distances.
Reference
Okabe, A. and K. Sugihara (2012) Spatial Analysis Along Networks: Statistical andComputational Methods, Chichester: John Wiley, a volume in the Wiley series of
Statistics in Practice.
4.8 Tool 08: Shortest path distances from type A points to type B points
This tool computes the shortest-path distance from each point in a given set of type A
points to each point in a given set of type B points, where those points are on a given
network. For details, see Section 12.1.3 in Okabe and Sugihara (2012).
Click the “Shortest-path distances between type A points and type B points” in the
SANET menu. Then the following window appears.

24Choosethe file name of a network (e.g., orgroad.shp: street network in thesample data set).
Choosethe file name of a set of type A points (e.g., rsd_pts.shp: location points

in the sample data set).
Choosethe file name of a set of type B points (e.g., store_pts.shp: store location

points in the sample data set).
Chooseto store the resulting output file, and click “OK”.

If the following window does not appear, the network is completely connected. Proceed
to the next step marked by *** below.

If this window appears, the given network is not completely connected. In that case,see p.55 to find out your next step to proceed.
***
When the network is completely connected or if you click “Yes” in the warning window,
the program begins to run. If you do not have any trouble such as memory overflows,
you obtain the following file.
25

The contests are as follows.

The first column indicates “from the i-th point of the type A point set.
The second column indicates “to the j-th point of the type B point set.
The last column indicates the shortest-path distance between those points. For
instance, the shortest-path distance from the 0th point of the type A to the 0th point of
the Type B is 76.3664.
Reference
Okabe, A. and K. Sugihara (2012) Spatial Analysis Along Networks: Statistical andComputational Methods, Chichester: John Wiley, a volume in the Wiley series of
Statistics in Practice.
4.9 Tool 09: Network Characteristics: polylines, points and links
This tool shows the characteristics of polylines, points and links forming a given
network.

26

Click the “Network characteristics: polylines, points and links” in the SANET menu.
Then the following window appears.

Choosethe file name of a network (e.g., orgroad.shp: street network in the sample

data set).
Chooseto store the resulting output files, and click “OK”.

If the following window does not appear, the network is completely connected. Proceed
to the next step marked by *** below.

If this window appears, the given network is not completely connected. In that case, seep.55 to find out your next step to proceed.
***
When the network is completely connected or if you click “Yes” in the warning window,
the program begins to run. If you do not have any trouble such as memory overflows,
you obtain the following three files.

27



SANETNetworkLink.csv

This table shows that:
SgtID: line segment ID;
PntID and AdjacentPntID are end nodes of a line segment;



FromToFlg:
From: from PntID to AdjacentPntID;
To: from AdjacentPntID to PntID.
SANETNetworkPnt.csv

This table shows that the (x, y, z) coordinates of a point specified by PntId.
 SANETNetworkSgt.csv

This table shows that the length of a link specified by SgtID.
28

Reference
Okabe, A. and K. Sugihara (2012) Spatial Analysis along Networks: Statistical andComputational Methods, Chichester: John Wiley, a volume in the Wiley series of
Statistics in Practice.
4.10 Tool 10: Global auto nearest neighbor distance method
This tool tests the complete spatial randomness (CSR) hypothesis in terms of theshortest-path distance from every point in a given set of points placed on a given
bounded network to its next nearest point in the set. Note that in the literature, the global
auto nearest neighbor distance method is simply referred to as the nearest neighborhood
distance method. The CSR hypothesis means that points are independently andidentically distributed according to the uniform distribution over the network, or points
follow the homogeneous binomial point process on the bounded network. A generaldescription about the nearest neighbor distance method is provided in Chapter 5 inOkabe and Sugihara (2012); specifically, the global auto nearest neighbor distancemethod is shown in Section 5.1.2 and its application in Section 12.2.2.1.
Click the “Global auto nearest neighbor distance method” in the SANET menu.

Then the following window appears.

29

Choosethe file name of a network (e.g., orgroad.shp: street network in thesample data set).
Choosethe file name of a set of points (e.g., rsd_pts.shp: location points in thesample data set).
Fill in: a number of iterations for Monte Carlo simulation (a default values is 1000), a bin width (a continuous distance is divided by the equal bin width; a default
value is 10; in this case, the resulting intervals are 0-10, 10-20, 20-30,…..) , one-sided statistical significance level (the default value is 5%).
Chooseto store the resulting output files. If you want to have intermediate data,
check “Output logs”, which may require much memory. Click “OK”.
If the following window does not appear, the network is completely connected. Proceed
to the next step marked by *** below.

30

If this window appears, the given network is not completely connected. In that case,see p.55 to find out your next step to proceed.
***
When the network is completely connected or if you click “Yes” in the warning window,
the program begins to run. If you do not have any trouble such as memory overflows,
you obtain the following three files.

The contents of the resulting files are as follows.
 SANETNNDObservedValue.csv- - - - -The first column indicates “from the i-th point”.
The second column indicates “to its nearest neighbor point”. Note that the same ID
points mean different points are placed at the same location.
The last row “AVERAGE” indicates the average nearest neighbor distance. Note thatthe same FromPtId implies that those points are placed at the same location.


SANETNNDExpectedValue.csv

31

The first column indicates the i-th iteration of Monte Carlo simulation.
The second column indicates “from the j-th point” in a given point set.
Third column indicates “to its nearest neighbor point”.
The last column indicates the shortest-path distance between them.
The last row of the last (1000) iteration (AVERAGE) indicates the average of the nearest
neighbor distance for the j-th iteration.
At the end of this file, “Lower” indicates the lower critical value for the one-sided
significance level is 5 %, while “Upper” indicates the upper critical value for the onesided significance level is 5 %“ALL AVERAGE” indicates the average nearest neighbor distances for 1000 iterations.
The Clark-Evans index is given by AVERAGE in the table of
SANETObservedValue.csv divided by ALL AVERAGE in the table of
SANETExpectedValue.csv. In the above example, the value of the index is23.70/16.52=1.43.
 SANETNNDExpectedValue.R.
To visualize SANETNNDExpectedValue.R, please see section 5.2.
Reference
Okabe, A. and K. Sugihara (2012) Spatial Analysis Along Networks: Statistical andComputational Methods, Chichester: John Wiley, a volume in the Wiley series of
Statistics in Practice.
4.11 Tool 11: Global cross nearest neighbor distance method
This tool tests the complete spatial randomness (CSR) hypothesis in terms of theshortest-path distance from each point in a given set of type B points to its nearest point
in a given set of type A points. In the literature, the global cross nearest neighbor distancemethod is sometimes referred to as the conditional nearest neighborhood distancemethod. In general, it is assumed that type B points are temporal, while type A points arestable over time; for instance, the former points are restaurants and the latter points arerailway stations. This method tests the effect of railway stations on the distribution ofrestaurants in comparison with the CSR hypothesis. The CSR hypothesis means that32

points are independently and identically distributed according to the uniform distribution
over the network, or points follow the homogeneous binomial point process on thebounded network. A general description about the nearest neighbor distance method isprovided in Chapter 5 in Okabe and Sugihara (2012); specifically, the global crossnearest neighbor distance method is shown in Section 5.2.2 and its application in Section
12.2.2.2.
Click the “Global cross nearest neighbor distance method” in the SANET menu.

Then the following window appears.

33

Choosethe file name of a network (e.g., orgroad.shp: street network in the sample dataset).

Choosethe file of type A points (e.g., store_pts.shp: store location points in the sample

data set); and the file of type B points (e.g., rsd_pts.shp: location points in the sample data set).

Fill in: a number of iterations for Monte Carlo simulation (a default values is 1000), a bin width (a continuous distance is divided by the equal bin width; a default value
is 10; in this case, the resulting intervals are 0-10, 10-20, 20-30,…..) , a statistical significance level (the default value is 5%; one-sided).
Chooseto store the output resulting files, and click OK.
If the following window does not appear, the network is completely connected. Proceed
to the next step marked by *** below.

If this window appears, the given network is not completely connected. In that case, seep.55 to find out your next step to proceed.
***
When the network is completely connected or if you click “Yes” in the warning window,
the program begins to run. If the memory is enough, the following three files are obtained
as the output.

The contents of the resulting files are as follows.
 SANETCNNDObservedValue.csv

34

- - - - -The first column indicates “from the i-th point in the type B point set”.
The second column indicates “to its nearest neighbor point in the type A point set”.
The third column indicates the shortest-path distance between those points.
The last row “AVERAGE” indicates the average nearest neighbor distance from all type
B points to their nearest type A points.


SANETCNNDExpectedValue.csv- - - - -The first column indicates the i-th iteration of Monte Carlo simulation.
The second column indicates “from the j-th point of type B”.
Third column indicates “to its nearest neighbor point of type A”.
The last column indicates the shortest-path distance between those points. The lastrow of the i-th iteration, AVERAGE, indicates the average distance of from each type B
point to its nearest type A point.
At the bottom, ALL AVERAGE indicates the average of AVERAGEs, and ALL
VARIANCE indicates the variance of AVERAGEs.
“Lower” and “Upper” indicate the lower and upper critical values for a given
significance level, say, 5 % (one-sided).
35

These numbers indicate: the lower critical value is 104.1329, the upper critical value is187.033(the significance level is 5 %) and the average of the average nearest
neighbor distances for 1000 iterations is 135.6321.
The Clark-Evans index is given by AVERAGE in the table of
SANETCNNDObservedValue.csv (119.5153 in this case) divided by the last ALL
AVERAGE in the table of SANETECNNDExpectedValue.csv (135.6321 in this case);consequently, 0.88.
If the observed AVERAGE is outside the range “Lower” and “Upper”, the CSR
hypothesis is rejected with, say 95% confidence level.
 SANETCNNDExpectedValue.R
To visualize SANETCNNDExpectedValue.R, please see section 5.2.
Reference
Okabe, A. and K. Sugihara (2012) Spatial Analysis along Networks: Statistical andComputational Methods, Chichester: John Wiley, a volume in the Wiley series of
Statistics in Practice.
4.12 Tool 12: Local cross nearest neighbor distance method
Given two sets of points: the set of type A points, denoted by A and the set of type B
points by B, consider a subset, Bi , of set B satisfying that the nearest point from every
point in Bi is a specific point in set A, e.g., the i-th point in set A. This tool tests thecomplete spatial randomness (CSR) hypothesis in terms of the shortest-path distancesfrom points in subset Bi to the i-th point in set A. In general, it is assumed that type B
points are temporal, while type A points are stable over time; for instance, the former
points are restaurants and the latter points are railway stations. This method tests theeffect of railway stations on the distribution of restaurants in comparison with the CSR
hypothesis. The CSR hypothesis means that points are independently and identically
distributed according to the uniform distribution over the network, or points follow thehomogeneous binomial point process on the bounded network. A general description
about the nearest neighbor distance method is provided in Chapter 5 in Okabe andSugihara (2012); specifically, the local cross nearest neighbor distance method is shownin Section 5.2.1.
Click the “Local cross nearest neighbor distance method” in the SANET menu.

36

Then the following window appears.

Choosethe file name of a network (e.g., orgroad.shp: street network in thesample data set).
37

Choosethe file name of a set of type A points (e.g., store_pts.shp: store location

points in the sample data set).
Choosethe file name of a set of type B points (sd_pts.shp: location points in thesample data set).
Chooseto store the resulting output file, and click “OK”.

If the following window does not appear, the network is completely connected. Proceed
to the next step marked by *** below.

If this window appears, the given network is not completely connected. In that case,see p.55 to find out your next step to proceed.
***
When the network is completely connected or if you click “Yes” in the warning window,
the program begins to run. If you do not have any trouble such as memory overflows,
you obtain the following six files, three for the observed values and three for the
expected values.

The contents of the resulting files are as follows.
 SANETLocalCNNDObservedValue0.csv >> table below left
 SANETLocalCNNDObservedValue1.csv >> table below middle
 SANETLocalCNNDObservedValue2.csv >> table below right

38





SANETLocalCNNDExpectedValue0.csv >> table below left
SANETLocalCNNDExpectedValue1.csv >> table below middle
SANETLocalCNNDExpectedValue2.csv >> table below right

Reference
Okabe, A. and K. Sugihara (2012) Spatial Analysis along Networks: Statistical andComputational Methods, Chichester: John Wiley, a volume in the Wiley series of
Statistics in Practice.
4.13 Tool 13: Global auto K function method
This tool tests the complete spatial randomness (CSR) hypothesis in terms of thenumber of points in a given point set satisfying that the shortest-path distance from every
point to another point is less than a parametric shortest-path distance. The CSR
hypothesis means that points are independently and identically distributed according to
the uniform distribution over the network, or points follow the homogeneous binomial
point process on the bounded network.

39

To state it explicitly, for a set of n points placed on a network, letof points that are within shortest-path distancefrom point

be the number
andbe the densityof points on the network. Then the K function is given.
In the literature, the global auto K function method is simply referred to as the K function
method. A general review of the K function method is illustrated in Chapter 5 in Okabeand Sugihara (2012); specifically, the global auto K function method is described in
Section 6.1.2, and its application in Section 12.2.3.1.
Click the “Global Auto K function Method” in the SANET menu.

Then the following window appears.

40

Choosethe file name of a network (e.g., orgroad.shp: street network in the sample

data set)
Choosethe file name of a set of points (e.g., rsd_pts.shp: location points in thesample data set).
Fill in: a number of iterations for Monte Carlo simulation (a default values is 1000), a unit interval (a continuous distance is divided by the equal unit interval; adefault value is 10) , a statistical significance level (the default value is 5%).
Chooseto store the output files.
If you want to obtain intermediate files, check “Output log”. Please note that the output
file requires much memory.
Click “OK”.
If the following window does not appear, the network is completely connected. Proceed
to the next step marked by *** below.
41

If this window appears, the given network is not completely connected. In that case, seep.55 to find out your next step to proceed.
***
When the network is completely connected or if you click “Yes” in the warning window,
the program begins to run. If you do not have any trouble such as memory overflows,
you obtain the following three files.
The contents of the resulting files are as follows.
 SANETObservedValue.csv…

The first column indicates “from the i-th point”.
The second column indicates “to the j-th point ” ().

The third column indicates the shortest-path distance between those points.
The last row “AVERAGE” indicates the average of shortest-path distances between any
pair of points.
42

 SANETExpectedValue.csv
This file has two tables.
The first one is as shown below.

The first row indicates that the unit interval is 50 and the resulting intervals are 50, 100,
150, and so on.
Each column indicates the numbers of points within the distance given by the unit
interval ×i for 1000 Monte Carlo iterations, and those numbers are ordered from thesmallest to the largest. For instance, 101 points are independently and identicallygenerated according to the uniform distribution over the street network for 1000 times;
then the points whose nearest neighbor points within 150 are 4, 8, 8, , .
The second table is as shown below. Note that the file size of this example may be toolarge to fit for Excel. Access may be a better choice.

…

43

The first column indicates the i-th iteration of Monte Carlo simulation.
The second column indicates “from the j-th point” in the point set.
Third column indicates “to the k-th point in the point set.
For instance, the above table shows part of the output of the 0-th iteration, where theshortest-path distances are from the 0-th point to the k-th point (k =1, 2, …., 100).
At the end of this file, AVERAGE appears, e.g., AVERAGE 2824.017907. This implies
that the average of theshortest-path distances between any pair of points inthe point set.
 SANETGraphics.R
To visualize SANETGraphics.R, please see section 5.2.
Reference
Okabe, A. and K. Sugihara (2012) Spatial Analysis Along Networks: Statistical andComputational Methods, Chichester: John Wiley, a volume in the Wiley series of
Statistics in Practice.
4.14 Tool 14: Global cross K function method
Given two sets of points, a set of type A points and that of type B points, placed on agiven network, this tool tests the complete spatial randomness (CSR) hypothesis. The
CSR hypothesis means that points are independently and identically distributed
according to the uniform distribution over the network, or points follow the homogeneous
binomial point process on the bounded network, implying that the configuration of type
A points does not affect the distribution of type B points.
To state this test explicitly, consider a set of n A type A points and that of nB type B
points, and let n (t | pA i ) be the number of type B points that are within shortest-path
distance t from the i-th type A point pA i , and B be the density of type A points on
the network. Then the local cross K function is given by
1 i 1 n(t | p A i ).
K AB (t | p A i ) 
B
nA
nA

In the literature, the global cross K function method is simply referred to as the cross K
function method. A general review of the cross K function method is illustrated in Chapter
6 in Okabe and Sugihara (2012); specifically, the global cross K function method is
44described in Section 6.2.2, and its application in Section 12.2.3.2..
Click the “Global Cross K function Method” in the SANET menu.

Then the following window appears.

45

Choosethe file name of a network (e.g., orgroad.shp: street network in the sample

data set).
Choose.

The file of type A points (e.g., store_pts.shp: store location points in the sample data
set; type A points are supposed to be structural points)
The file of type B points (e.g., rsd_pts.shp: location points in the sample data set; type
B points are supposed to be temporal points).
Fill in: the number of iterations for Monte Carlo simulation (a default values is 1000), a unit interval (a continuous distance is divided by the equal unit interval; a default
value is 10; in this case, the resulting intervals are 10, 20, 30,…..),
 a statistical significance level (the default value is 5%; one-sided).
Choosethe out file where the resulting files are stored

If you want to obtain intermediate files, check “Output log”. Please note that the output
file requires much memory.
Click “OK”.
If the following window does not appear, the network is completely connected. Proceed
to the next step marked by *** below.

If this window appears, the given network is not completely connected. In that case, seep.55 to find out your next step to proceed.
***
When the network is completely connected or if you click “Yes” in the warning window,
the program begins to run. If you do not have any trouble such as memory overflows,
you obtain the following three files.

46



SANETCKFuncObservedValue.csv…

The first column indicates “from the i-th point of type B”.
The second column indicates “to the j-th point of type A”.
The third column indicates the shortest-path distance between those points.
The last row “AVERAGE” indicates the average shortest-path distance.


SANETCKFuncExpectedValue.csv

The first row indicates that the unit interval is 10 and the resulting intervals are 10, 20,
30 and so on.
Each column indicates the numbers of points within the distance given by the unit
interval×i for 1000 Monte Carlo iterations, and those numbers are ordered from thesmallest to the largest.
 SANETCKFuncGraphics.R
To visualize SANETCKFuncGraphics.R, please see section 5.2.
47

Reference
Okabe, A. and K. Sugihara (2012) Spatial Analysis Along Networks: Statistical andComputational Methods, Chichester: John Wiley, a volume in the Wiley series of
Statistics in Practice.
4.15 Tool 15: Local cross K function method
Given two sets of points, a set of type A points and that of type B points, placed on agiven network, this tool tests the complete spatial randomness (CSR) hypothesis. The
CSR hypothesis means that points are independently and identically distributed
according to the uniform distribution over the network, or points follow the homogeneous
binomial point process on the bounded network, implying that the configuration of type
A points does not affect the distribution of type B points.
To state this test explicitly, consider a set of n A type A points and that of nB type B
points, and let n (t | pA i ) be the number of type B points that are within shortest-path
distance t from the i-th type A point pA i , and B be the density of type A points on
the network. Then the local cross K function is given by1
K AB (t | pA i ) n(t | pA i ).
B
A general review of the cross K function method is illustrated in Chapter 6 in Okabe andSugihara (2012); specifically, the local cross K function method is described in Section
6.2.1, and its application in Section 12.2.3.4 (note that type A and type B are reversedin their book).

48

Click the ‘Local cross K function method’ in the SANET menu.
Then the following window appears.

Choosethe file name of a network (e.g., orgroad.shp: street network in the sample

data set).
Choose: the file of type A point set (e.g., store_pts.shp: location points in the49

sample data set), the file of type B point set (e.g., rsd_pts.shp: store location points inthe sample data set). Recall that the local cross K function deals with the number of type
B points within a parametric shortest-path distance from the i-th point in the type A point
set.
Fill in: a number of iterations for Monte Carlo simulation (a default values is 1000), a unit interval (a continuous distance is divided by the equal unit interval; a default
value is 10; in this case, the resulting intervals are 10, 20, 30,…..; in the example,
10 was used) , a statistical significance level (the default value is 5%; one-sided).
ChooseClick “OK”.

to store the resulting output files, andIf the following window does not appear, the network is completely connected. Proceed
to the next step marked by *** below.

If this window appears, the given network is not completely connected. In that case, seep.55 to find out your next step to proceed.
***
When the network is completely connected or if you click “Yes” in the warning window,
the program begins to run. Note that for 2 type A points and 47 type B points on the street
network in the sample data set. Also note that this computation requires much output
space, and so your computer memory might be overflowed. When you use the local cross
K function, you are interested in particular type A points, and so you are supposed to use
a small number of type A points. To shorten computational time, you may choose a longunit interval, say 100 (the default is 10).

50

If the memory is enough, the following files are obtained in the output file. The number offiles is the number of A points multiplied by three. In the example, the number is nine
(three multiplied by three).



SANETLocalCKFuncObservedValue.csv…

The first column indicates the i-th point in the type A point set.
The second column indicates the j-th point in the type B point set.
The last column indicates the shortest-path distance between those points.
The last row indicates the average distance fom the i-th A point to evey B point.
 SANETLocalCKFuncExpectedValue.csv
This file has two tables.
The first table is shown below.

51

…

…

The first column indicates the i-th iteration of Monte Carlo simulation.
The second column indicates “from the j-th point of type A”.
Third column indicates “to the k-th point of type B”.
The last column indicates the shortest-path distance between those points.
The last row “AVERAGE” of each simulation indicates the average of those shortestpath distances (e.g., the 9th row is the average for the first (denoted by 0) simulation.
The last row of the last simulation (e.g., 999) indicates the average of the averages ofall simulations.
The second table is shown below.

The row indicates intervals (with a chosen unit interval). For instance, 100, 200, 300,
and so on.
The column indicates the numbers of type B points within the unit interval for 1000
iterations, and those numbers are ordered from the smallest to the largest. For instance,52

in the 900 column, the numbers of the type A points within 900 are: 0, 0, 1, 1, … (anumber of these numbers is 1000) for 1000 iterations.
 SANETLocalCKFuncGraphics.R
To visualize SANETLocalCKFuncGraphics.R, please see section 5.2.
Reference
Okabe, A. and K. Sugihara (2012) Spatial Analysis along Networks: Statistical andComputational Methods, Chichester: John Wiley, a volume in the Wiley series of
Statistics in Practice.
4.16 Tool 16: Voronoi cross K function method
Given two sets of points placed a network: a set of type A points (its number is n A ; a
network Voronoi network is generated by A points; an example a network Voronoi
diagram is shown in Figure 1 in Section 6.1) and that of type B points (its number is nB ),this tool tests the complete spatial randomness (CSR) hypothesis in terms of the numberof type B points that are within a parametric shortest-path distance t from their nearest
type A points. To state it a little more explicitly, consider the shortest-path distance fromevery type B point to its nearest type A point. Note that if a type B point is placed in theVoronoi subnetwork of the i-th type A point, the nearest type A point from the type B pointis the i-th type A point. The number of the resulting shortest-path distances is nB . Next
consider a function, K(t), that indicates the number of type B points satisfying that theassociated shortest-path distances are less than t. The tool tests the CSR hypothesis
with K(t).
Click the “Voronoi Cross K function Method” in the SANET menu.

53

Then the following window appears.

Choosethe file name of a network (e.g., orgroad.shp: street network in thesample data set).
Choose: the file of type A point set (e.g., store_pts.shp: location points in thesample data set), and the file of type B point set (e.g., rsd_pts.shp: store location
54

points in the sample data set).
Fill in: a number of iterations for Monte Carlo simulation (a default values is 1000), a unit interval (a continuous distance is divided by the equal unit interval; adefault value is 10; in this case, the resulting intervals are 10, 20, 30,…..),
 a statistical significance level (the default value is 5%).
Chooseto store the resulting output files, andClick “OK”.
If the following window does not appear, the network is completely connected.
Proceed to the next step marked by *** below.

If this window appears, the given network is not completely connected. In that case,see p.55 to find out your next step to proceed.
***
When the network is completely connected or if you click “Yes” in the warning window,
the program begins to run. If you do not have any trouble such as memory overflows,
you obtain the following three files.



SANETVCKFuncObservedValue.csv…
55

The first column indicates “from the i-th point of type A”.
The second column indicates “to the j-th point of type B”.
The third column indicates the shortest-path distance between those points.
The last row “AVERAGE” indicates the average distance.

 SANETVCKFuncExpectedValue.csv
The row indicates bin lengths. For instance, 10 means the bin length is 0-10; 20
means the bin length is 10-20; and so on. While the column indicates the numbers of
points in the i-th bin for 1000 iterations, and those numbers are ordered from thesmallest to the largest.
 SANETVCKFuncGraphics.R
To visualize SANETVCKFuncGraphics.R, please see section 5.2.
Reference
Okabe, A. and K. Sugihara (2012) Spatial Analysis Along Networks: Statistical andComputational Methods, Chichester: John Wiley, a volume in the Wiley series of
Statistics in Practice.

56

4.17 When SANET claims “The network is disconnected”
As you run SANET, you may occasionally come up with the below window;

If this window appears, the given network is not completely connected.
If you say “Cancel”, the SANET do nothing.
If you say “Yes”, the SANET chooses the largest connected network included in thegive network.
If you say “No”, the SANET gives you following six file.

When you add this Shapefile on ArcGIS, for example, you will be provided with the
below warning map which indicates disconnected parts by color.

The attribute table shows disconnected links by numbers on the AcsID column.

57

If you think that the disconnected parts should be connected, click “Setting” in the
SANET menu. Then the following window appears.

The “Vertex tolerance” means that if the distance between two nodes (vertexes) is lessthan 0.001(the unit depends on the scale of the map you are using, default is 0.00001),
then two vertices are regarded as the same. You change the tolerance distance and try
again. If your network is still disconnected, you are supposed to connect disconnectedparts using tools in ArcGIS or QGIS.

58

5Visualize the SANET sample results on ArcGIS, R and QGIS
5.1 Visualize on ArcGIS and ArcScene
Launch ArcMap and add the Shapefile which the SANET yielded. Open the layer
properties window and set “Value Field” and add values at the symbology tab to makethe layer look properly. The below is an example of setting “Symbology”.

Tool 01:Voronoi diagram59



Tool 02:Delaunay diagram

Tool 03: Kernel density estimation

60

Above figure is classified as below;

Launch ArcScene, and you can present the figure in 3D.
Add the SHAPEFILE;SANETKDensitySgt.shp using

Go to layer properties to set the extrusion information.
61

button.

Base Heights : Set the elevation value such as 2.0 to exaggerate a bit.



Extrusion :Finally, you get the below 3D presentation of Kernel Density62

Tool 04: Interpolation

ArcScene will give you the 3D presentation of Interpolation in the same manner as63

you did with Tool 03 ; Kernel Density Estimation.

Here, the elevation value is set to 1.5.


Tool06:Random points generator

645.2 Visualize the results on R
Launch R program, and click “Files”.
Then the following window appears.

Click “Source R code”, select the resulting output file, and open it.
 Tool 05: Point clustering method
SANETClustering.R
Selecting the SANET yielded R file, the following dendrogram is obtained.

65 Tool 10: Global auto nearest neighbor distance method
SANETNNDExpectedValue.R
Selecting the SANET yielded R file, the following graph is obtained.

The curves are: the observed curve; the upper and lower envelop curves for the
one-sided significance level 5%; and the expected curve under the CSR
hypothesis. If the observed curve is in between the upper and lower envelop curves,
we cannot reject the CSR hypothesis with 0.95 confidence level.
 Tool 11: Global cross nearest neighbor distance method
SANETCNNDExpectedValue.R
Selecting the SANET yielded R file, the following graph is obtained.

66

The curves are: the observed curve; the upper and lower envelop curves for
significance level 5%; and the expected curve under the CSR hypothesis. If theobserved curve is in between the upper and lower envelop curves, we cannot
reject the CSR hypothesis with 0.95 confidence level.
 Tool 13: Global auto K function method
SANETKFuncGraphics.R
Selecting the SANET yielded R file, the following graph is obtained.

67

The blue curve indicates the observed curve;
the red curve indicates the mean value under the CRS hypothesis;
the green and pink curves are, respectively, the upper and lower envelop curves
under the CSR hypothesis.
 Tool 14: Global cross K function method
SANETCKFuncGraphics.R
Selecting the SANET yielded R file, the following graph is obtained.

68The blue curve indicates the observed curve;
The red curve indicates the mean value under the CRS hypothesis;
The green and pink curves are, respectively, the upper and lower envelop curves
under the CSR hypothesis.
 Tool 15: Local cross K function method
SANETLocalCKFuncGraphics.R
Selecting the SANET yielded R file, the following graph is obtained.

69

70

The blue curve indicates the observed curve;
the red curve indicates the mean value under the CRS hypothesis;
the green and pink curves are, respectively, the upper and lower envelop curves
under the CSR hypothesis.
 Tool 16: Voronoi cross K function method
SANETVCKFuncGraphics.R
Selecting the SANET yielded R file, the following graph is obtained.

71

The blue curve indicates the observed curve;
the red curve indicates the mean value under the CRS hypothesis;
the green and pink curves are, respectively, the upper and lower envelop curves
under the CSR hypothesis.

725.3 Visualize the results on QGISHow to view SANET results on QGIS is shown here using SANETVoronoi Shapefile
as an example.
If you have already downloaded and installed QGIS on your PC, just launch QGIS
desktop and add the Shapefile which the SANET yielded.
To add SANETVoronoiSgt file is as follows.
 Select the file in the directory window and right click your mouse button. Then
you will find “Add Layer” in you pull-down menu to select.



After selecting the coordinate reference system of your Shapefile, you will get
below image.

73

In order to view the SANET results of voronoi diagram, open the ”Properties”
window.



In your Layer Properties window, select “Categorized”.

As for Column, choose AcsID as below

74



Press “Classify” button and press OK in the property window as below.

75Then, you will view the voronoi diagram of the SANET output.

76 About Handling SANET Setup Wizard
1. Unzip the SANET_standalone10_32.zip / SANET_standalone10_64.zip
2. Double click the executable SANET file.
3. Welcome to SANET Setup Wizard

Welcome to SANET Setup Wizard
This Setup Wizard guides
you the necessary steps
to install SANET
This product is protected by law
and international treaties on
copyright. Duplicate all or part ofthis product without priorpermission, and to distributecopies without permission, please
note that it is a violation of
copyright.

NEXT

Cancel
4. Select a folder to install SANET

Select a folder to install SANET
If you use a folder besides thisdefault one, put the address below
BrowseFor all users (E)For only this user (M)Cancel

Back

NEXT
77

5. Click to start installing SANET
6.

Confirm installation
Prepared to install SANET_WIN32
Please click NEXT to start the installation

Back

NEXT
7. Installing SANET

Installing SANET
Please wait

Cancel8. Completed installation
Completing installation on yourcomputer
SANET_WIN32 has been successfully installed
Click CLOSE to finish theWizard

CLOSE
78

6 Manuals
6.1 Procedure for generating ‘buffer sub-networks’ of a generator point set using
QGIS with GRASSThe ‘buffer subnetworks’ of a generator point set on a network means: for a given network(the gray and red line segments in Figure 1) and a given generator point set (the orange
circles in Figure 1), the shortest path distance from any points on ‘buffer subnetworks’ (redline segments in Figure 1) to the nearest point in the generator point set is less than or equal
to a given shortest path distance x (x=200m in Figure 1). An example is illustrated in Figure
1.

Figure 1: Buffer subnetworks (the red line segments; the orange circles are generator
points)791) Open QGIS 3.x with GRASS 7.x (x represents any number of the version of thesoftware).

Figure 22) Click “New Project” icon (Ctrl+N for short-cut).

Figure 3
Then the window in Figure 4 appears.
803) Click “Open Data Source Manager” (Ctrl+L).

Figure 4
Then the window in Figure 5 appears.

Figure 5814) Select “Vector” in Figure 5.
Then the window in Figure 6 appears.

Figure 65) Click “Browse” icon,in Figure 6.

Choose a shp file of network.
“Add” a shp file of a set of points that generates buffers.
Click “Add”.
If you see the files on the map canvas, click “Close” in Figure 6.
The map in Figure 7 is a sample of the screenshot after adding the files.

82

Figure 76) Select “Processing” > “Toolbox” indicated by the arrow in Figure 7.
Then, Processing Toolbox window in Figure 8 appears.
Enter v.net.iso in the search box and double click the tool name appeared in the
result of search as in Figure 8.

Figure 87) Select a network data to “input vector line layer” (in Figure 9) anda set of generator points data to “centers point layer” (in Figure 9).

83Set the value of “threshold for connecting centers to the network”
and ”costs for isolines” (in Figure 9).
The costs for isolines means the list of buffer distances that you want to create;
noted that you should use a comma to separate values (e.g., 100, 200, 300).
After entering those parameters, click “Run” (the arrow in Figure 9).

Figure 98) Completed the task, click “Close” (in Figure 9) to close the v.net.iso window.
9) Right click the output temporary file (the orange arrow in Figure 10), andclick “Property” (the green arrow in Figure 10).

84

Figure 1010) Select “Symbology” tab (the orange arrow in Figure 11), and choose “Categorized”
from the box on the top (the green arrow in Figure 11).

Figure 1111) Set “cat” in Value (Figure 12).
85

Click “Classify” (the orange arrow in Figure 12).
Set the rules for symbols (e.g., color and width) as you like.
Click “OK” (the green arrow in Figure 12).
Note that “cat = 1” represents line segments form the buffer subnetwork in which
the shortest path distance from the nearest generator point is less than 100 m; “cat= 2” is between 100 m and 200 m; “cat =3” is more than 200 m.

Figure 12
You obtain the map in Figure 13, showing multi-distance buffer subnetwork.

86

Figure 1312) If you want to save the temporary file as a permanent shape file, right click theoutput temporary file (the orange arrow in Figure 14), andclick “Make Permanent” (the green arrow in Figure 14).

87

Figure 1413) Click “Browse” icon,in Figure 15.

Specify the destination to save and click “OK”.

88Figure 15

6.2 Procedure for counting the number of points on ‘buffer sub-networks’ of agenerator point set
Note that from the resulting 𝑛 𝑥

𝑃, the number of points on the line segments between xi andxi+1 is obtained.
To state the above computation precisely, let 𝑁(𝑥 , 𝑥) denote the ‘buffer-ring sub-networks’ of a

network 𝑁 in which the shortest path distance from any points on 𝑁(𝑥 , 𝑥
generator point (Type A) is between 𝑥 and 𝑥, where 𝑥 < 𝑥, 𝑥) to the nearest− 𝑥 = 𝑐 for 𝑖 = 0, 1, 2, …

Note that 𝑐 is a parameter determined by a user. In an illustrative example here, 𝑐 = 10m. Visually,𝑁(0, 𝑥) is obtained from the ‘buffer sub-networks’ in Figure 1 in Section 6.1, where 𝑥

Therefore, ‘buffer-ring sub-networks’ 𝑁(𝑥 , 𝑥) is obtained from 𝑁(0, 𝑥compliment of 𝑁(0, 𝑥 ) with respect to 𝑁(0, 𝑥).

89= 200.

)¥ 𝑁(0, 𝑥 ), i.e., theTo state the above computation precisely, given a set of generator points on a given network 𝑁,
let 𝑁(𝑥 , 𝑥) denote the sub-network of 𝑁 in which the shortest path distance from any pointsin 𝑁(𝑥 , 𝑥) to the nearest generator point in given generator points is between 𝑥 and 𝑥

where 𝑥 < 𝑥𝑥,− 𝑥 = 𝑐 for 𝑖 = 0, 1, 2, … Note that 𝑐 is a parameter determined by a user.

In an illustrative example here, 𝑐 = 10m.
Let 𝐿(𝑥 , 𝑥) be the total length of line segments constituting the sub-network 𝑁(𝑥 , 𝑥), and 𝐿

is the total length of line segments constituting the whole network 𝑁.
In terms of the above notations, this manual describes the procedure for computing 𝐿(𝑥 , 𝑥).

Let 𝑙 be link 𝑗 of a given network, and 𝑑(𝜕𝑙 ) refers to the shortest path distance between thestart node of link j and the nearest generating point from link j; 𝑑(𝜕𝑙 ) is the shortest pathdistance between the end node of link 𝑗 and the nearest generating point.
Step 1Run the “Voronoi diagram” tool of SANET. In more detail, see Section 4.1 Tool 01: Voronoi
diagrams in User Guide/Manual for SANET Standalone.
Step 2
Copy “SANETVoronoiPnt.dbf” and “SANETVoronoiSgt.dbf” on one folder.
Step 3
Open these files in Excel.
* You may follow the four steps described below, or you may use an alternative method as you
like.
3-1)

Open Excel.

3-2)

Select File, “Open” (the orange arrow in Figure 1).

90

3-3)

Click “Browse” and select the folder in which you saved the files (the green arrow in
Figure 1).

3-4)

In the “Files of Type” drop down box, select: “All Files” (the blue arrow in Figure 1),
and then choose “SANETVoronoiPnt.dbf” and “SANETVoronoiSgt.dbf”, and click “Open”.

Figure 1
Step 4
Copy these two sheets on a new book (for instance, Book1). Figure2 is a sample of the screenshot
after step 4).

Figure 291

Step 5In the cell Q2 (column Q and row 2) of “SANETVoronoiSgt” sheet, enter the formula to compute
distance from the generator to “FromPnt” of the segment:=VLOOKUP(H2,SANETVoronoiPnt!$A:$J,8, FALSE)
Hit the enter.

Figure 3
Step 6
Copy the formula to the other segments by left-clicking and dragging the small dot at the lower
right corner of Q2 down column Q to the end row of the data.

Figure 4

Step 7
In cell R2 of SANETVoronoiSgt, enter the formula to compute distance from the generator to“ToPnt” of the segment:=VLOOKUP(I2,SANETVoronoiPnt!$A:$J,8, FALSE)
92

Hit the enter.

Figure 5

Step 8
Copy the formula to the other segments by left-clicking and dragging the small dot at the lower
right corner of R2 down column R to the end row of the data.

Figure 6
Step 9Copy the values of columns Q and R, and paste them to a new sheet.

93

Figure 7
Step 10
Delete Cell A1 and B1 (blank spaces). Note that choosing “Shift cells up” as the option and thenclicking “OK”.

Figure 8

Step 11
Hit Alt + F11 to open Excel VBA editor.
94

Step 12
Add a new module in VBA editor by clicking on VBAProject (Book1), right click, Insert > Module.

Figure 9
Step 13
Copy the following scripts and paste it into the window of Module1. The code sorts out the data.
Column D will have 𝑑(𝜕𝑙 ): the shortest path distance between the start node of link j and thenearest generating point from link j; and column E will have 𝑑(𝜕𝑙 ): the shortest path distance
between the end node of link 𝑗 and the nearest generating point.
Sub Transformation()
MaxRow = Rows.CountFor i = 1 To MaxRow
If Cells(i, 1) > Cells(i, 2) Then
Origin = Cells(i, 2)
Destination = Cells(i, 1)
95

Else
Origin = Cells(i, 1)
Destination = Cells(i, 2)
End IfCells(i, 4).Value = Origin
Cells(i, 5).Value = Destination
Next iEnd Sub

Figure 1096

Step 14
Run the module by clicking “Run Sub” icon (see Figure 11).

Figure 12 is an output example. You

would see that each value of Column D must be smaller than each one next to it (Column E).

Figure 11

Figure 1297

Step 15
Create another module in the VBA editor (Module2), and copy the following scripts and paste it into
the window. This code is for calculating 𝐿(𝑥 , 𝑥
the sub-network 𝑁(𝑥 , 𝑥): the total length of line segments constituting). Note that this code assumes that the bin width 𝑐 = 10m.

Sub Classification()
MaxRow = Rows.Count
MaxVal = WorksheetFunction.Max(Range(Cells(1, 5), Cells(MaxRow, 5)))
MaxBin = MaxVal ¥ 10 + 1
For j = 0 To MaxBin
For i = 1 To MaxRow
If Cells(i, 4) <= j * 10 And Cells(i, 5) > (j + 1) * 10 Then
Cells(j + 1, 10) = Cells(j + 1, 10) + 10
ElseIf Cells(i, 4) <= j * 10 And Cells(i, 5) >= j * 10 And Cells(i, 5) <= (j + 1) * 10 Then
Cells(j + 1, 10) = Cells(j + 1, 10) + (Cells(i, 5) - j * 10)
ElseIf Cells(i, 4) > j * 10 And Cells(i, 4) <= (j + 1) * 10 And Cells(i, 5) > (j + 1) * 10 Then
Cells(j + 1, 10) = Cells(j + 1, 10) + ((j + 1) * 10 - Cells(i, 4))
ElseIf Cells(i, 4) > j * 10 And Cells(i, 4) <= (j + 1) * 10 And Cells(i, 5) <= (j + 1) * 10 Then
Cells(j + 1, 10) = Cells(j + 1, 10) + (Cells(i, 5) - Cells(i, 4))
End IfNext iNext jFor k = 1 To MaxBin
98

Cells (k,9) = k*10
Next kEnd Sub

Step 16
Run the module by clicking “Run Sub” icon. Note that this macro takes a lot of time (about several
hours depending on data size) to complete the calculation. Figure 13 is an example of outputs.

Figure 13

Let 𝑃 = {𝑝 , ⋯ , 𝑃 } be type B points and 𝑛 𝑥
in the sub-network within distance 𝑥

𝑃

be the number of type B points included

from 𝑃 .

In terms of the above notations, this manual describes the procedure for computing 𝑛 𝑥

𝑃.

Note that this computation uses the output of the Voronoi cross K function tool in SANET software
package.

991) Run the “Voronoi cross K function method” tool of SANET. See the Section 4.16 in the
SANET manual.
2) Copy “SANETVCKFuncObservedValue.csv” to another folder.
3) Open these files in Excel.

* You may follow the steps below, or you may use an alternative method as you like.
a)Open Excel.

b)

Select File, “Open” (the orange arrow in Figure 1).

c)

Click “Browse” and select the folder in which you saved the files (the green arrow in
Figure 1).

d)

In the “Files of Type” drop down box, select: “All Files” (the blue arrow in Figure 1), andthen choose “SANETVCKFuncObservedValue.csv”, and click “Open”.

Figure 11004) In cell E2, enter 𝑥 : the minimum value (meters) of bin 𝑐 (e.g., 10). Next, in cell E3, enter𝑥 : a double value of E2 (e.g., 20).

Figure 25) Highlight cells E2:E3. When we drag the fill handle to the below (by left-clicking anddragging the small dot at the lower right corner: AutoFill function), Excel will fill in the next
cells with values having same intervals (e.g., 30, 40, 50, and so on… as shown in Figure 3).

101

Figure 3
6) In cell F2, enter the formula that counts 𝑛 𝑥𝑃: the number of point-like facilities

located within a specific range from generating points=COUNTIFS($C$2:$C$131,"<”&E2)*Note that “131” (the number of type B points) in the formula change appropriately.
Hit the enter.

102

Figure 47) Copy the formula to the rest of bins by using AutoFilll function.

Figure 51038) If you want to obtain the number of points on the line segments between xi and xi+1, enter
the following formula in cell G2.
=COUNTIFS($C$2:$C$131,"<"&E2, $C$2:$C$131,">="&E2-10)
Hit the enter and copy the formula to the rest of bins by using AutoFilll function.

Figure 6

6.3 Procedure for computing the total length of “buffer-ring sub-networks” of agenerator point set
To state the above computation precisely, let 𝑁(𝑥 , 𝑥) denote the ‘buffer-ring sub-networks’ of a

network 𝑁 in which the shortest path distance from any points on 𝑁(𝑥 , 𝑥) to the nearest

generator point (Type A point) is between 𝑥 and 𝑥− 𝑥 = 𝑐 for 𝑖 =, where 𝑥 < 𝑥, 𝑥0, 1, 2, … Note that 𝑐 is a parameter determined by a user. In an illustrative example here, 𝑐 = 10m.
Visually, 𝑁(0, 𝑥𝑥= 200 .

𝑁(0, 𝑥Therefore,the‘buffer-ring

sub-networks’𝑁(𝑥 , 𝑥)¥ 𝑁(0, 𝑥 ), i.e., the compliment of 𝑁(0, 𝑥 ) with respect to 𝑁(0, 𝑥

Let 𝐿(𝑥 , 𝑥𝑁(𝑥 , 𝑥) is obtained from the ‘buffer sub-networks’ in Figure 1 in Section 6.1, where)isobtainedfrom).

) be the total length of line segments constituting the buffer-ring sub-networks), and 𝐿 is the total length of line segments constituting the whole network 𝑁.

104

In terms of the above notations, this manual describes the procedure for computing 𝐿(𝑥 , 𝑥).

Let 𝑙 be link 𝑗 of a given network, and 𝑑(𝜕𝑙 ) refers to the shortest path distance between thestart node of link j and the nearest generating point from link j; 𝑑(𝜕𝑙 ) is the shortest path distance
between the end node of link 𝑗 and the nearest generating point.
Step 1Run the “Voronoi diagram” tool of SANET. In more detail, see Section 4.1 Tool 01: Voronoi
diagrams in User Guide/Manual for SANET Standalone.

Step 2
Copy “SANETVoronoiPnt.dbf” and “SANETVoronoiSgt.dbf” on one folder.
Step 3
Open these files in Excel.
* You may follow the four steps described below, or you may use an alternative method as you
like.
3-1)

Open Excel.

3-2)

Select File, “Open” (the orange arrow in Figure 1).

3-3)

Click “Browse” and select the folder in which you saved the files (the green arrow in
Figure 1).

3-4)

In the “Files of Type” drop down box, select: “All Files” (the blue arrow in Figure 1),
and then choose “SANETVoronoiPnt.dbf” and “SANETVoronoiSgt.dbf”, and click “Open”.

105Figure 1

Step 4
Copy these two sheets on a new book (for instance, Book1). Figure2 is a sample of the screenshot
after step 4).

Figure 2

Step 5In the cell Q2 (column Q and row 2) of “SANETVoronoiSgt” sheet, enter the formula to compute
distance from the generator to “FromPnt” of the segment:=VLOOKUP(H2,SANETVoronoiPnt!$A:$J,8, FALSE)
Hit the enter.

106Figure 3
Step 6
Copy the formula to the other segments by left-clicking and dragging the small dot at the lower
right corner of Q2 down column Q to the end row of the data.

Figure 4

Step 7
In cell R2 of SANETVoronoiSgt, enter the formula to compute distance from the generator to“ToPnt” of the segment:=VLOOKUP(I2,SANETVoronoiPnt!$A:$J,8, FALSE)
Hit the enter.

107

Figure 5

Step 8
Copy the formula to the other segments by left-clicking and dragging the small dot at the lower
right corner of R2 down column R to the end row of the data.

Figure 6

Step 9Copy the values of columns Q and R, and paste them to a new sheet.

108

Figure 7
Step 10
Delete Cell A1 and B1 (blank spaces). Note that choosing “Shift cells up” as the option and thenclicking “OK”.

Figure 8

Step 11
Hit Alt + F11 to open Excel VBA editor.
109

Step 12
Add a new module in VBA editor by clicking on VBAProject (Book1), right click, Insert > Module.

Figure 9
Step 13
Copy the following scripts and paste it into the window of Module1. The code sorts out the data.
Column D will have 𝑑(𝜕𝑙 ): the shortest path distance between the start node of link j and thenearest generating point from link j; and column E will have 𝑑(𝜕𝑙 ): the shortest path distance
between the end node of link 𝑗 and the nearest generating point.
Sub Transformation()
MaxRow = Rows.CountFor i = 1 To MaxRow
If Cells(i, 1) > Cells(i, 2) Then
Origin = Cells(i, 2)
Destination = Cells(i, 1)
110

Else
Origin = Cells(i, 1)
Destination = Cells(i, 2)
End IfCells(i, 4).Value = Origin
Cells(i, 5).Value = Destination
Next iEnd Sub

Figure 10111

Step 14
Run the module by clicking “Run Sub” icon (see Figure 11).

Figure 12 is an output example. You

would see that each value of Column D must be smaller than each one next to it (Column E).

Figure 11

Figure 12112

Step 15
Create another module in the VBA editor (Module2), and copy the following scripts and paste it into
the window. This code is for calculating 𝐿(𝑥 , 𝑥
the sub-network 𝑁(𝑥 , 𝑥): the total length of line segments constituting). Note that this code assumes that the bin width 𝑐 = 10m.

Sub Classification()
MaxRow = Rows.Count
MaxVal = WorksheetFunction.Max(Range(Cells(1, 5), Cells(MaxRow, 5)))
MaxBin = MaxVal ¥ 10 + 1
For j = 0 To MaxBin
For i = 1 To MaxRow
If Cells(i, 4) <= j * 10 And Cells(i, 5) > (j + 1) * 10 Then
Cells(j + 1, 10) = Cells(j + 1, 10) + 10
ElseIf Cells(i, 4) <= j * 10 And Cells(i, 5) >= j * 10 And Cells(i, 5) <= (j + 1) * 10 Then
Cells(j + 1, 10) = Cells(j + 1, 10) + (Cells(i, 5) - j * 10)
ElseIf Cells(i, 4) > j * 10 And Cells(i, 4) <= (j + 1) * 10 And Cells(i, 5) > (j + 1) * 10 Then
Cells(j + 1, 10) = Cells(j + 1, 10) + ((j + 1) * 10 - Cells(i, 4))
ElseIf Cells(i, 4) > j * 10 And Cells(i, 4) <= (j + 1) * 10 And Cells(i, 5) <= (j + 1) * 10 Then
Cells(j + 1, 10) = Cells(j + 1, 10) + (Cells(i, 5) - Cells(i, 4))
End IfNext iNext jFor k = 1 To MaxBin
113

Cells (k,9) = k*10
Next kEnd Sub

Step 16
Run the module by clicking “Run Sub” icon. Note that this macro takes a lot of time (about several
hours depending on data size) to complete the calculation. Figure 13 is an example of outputs.

Figure 13

6.4 Exact statistical test for Voronoi cross K function method on networks
using outputs of the tools in SANET software package
This manual instructs a procedure for achieving the exact statistical test of global Voronoi cross K
function method. The global Voronoi cross K function method is explained in detail in Section 6.2.3
in Chatper 6 of Okabe and Sugihara (2012).

114

To begin with, let us introduced a few notations. We consider a network 𝑁, on which two types ofpoints are placed, i.e., Type A points (generator points of the network Voronoi) and Type B points(activity points).
Note that the notations conform to the SANET software. Okabe and Sugihara (2012) treated theterms in the opposite (i.e., Type A: activity points, Type B: generator points).
Let 𝑁(𝑥 , 𝑥𝑁(𝑥 , 𝑥)denote the sub-network of 𝑁 in which the shortest path distance from any points on) to the nearest point in Type B points is between 𝑥 and 𝑥, where 𝑥 < 𝑥, 𝑥−

𝑥 = 𝑐 for 𝑖 = 0, 1, 2, … Note that 𝑐 is a parameter determined by a user. In an illustrative example
in Figure 1, 𝑐 = 10 m.
Let 𝐿(𝑥 , 𝑥) be the total length of line segments constituting the sub-network 𝑁(𝑥 , 𝑥), and 𝐿

is the total length of line segments constituting the whole network 𝑁.
Let 𝑚(𝑥 , 𝑥) be the number of type B points on the sub-network 𝑁(𝑥 , 𝑥).

Suppose that Type B points are distributed on 𝑁 according to the complete spatial randomness,
CSR. Then the probability that a Type B point is located on 𝑁(𝑥 , 𝑥𝐿(𝑥 , 𝑥)/𝐿, and 𝑚(𝑥 , 𝑥

The data of 𝐿(𝑥 , 𝑥) is given by 𝑝 =) follows the binomial distribution with parameter 𝐿(𝑥 , 𝑥)/𝐿.

) are obtained from running the Voronoi diagram tool in SANET. This task is

explained by the manual “A procedure for computing the length of line segments of a network
satisfying that the shortest path distance from a point on the line segments of a network to its nearest
generator point among given generator points placed on the network is between 𝑥 and 𝑥”.

Step 1
Compute the total length 𝐿 of network 𝑁 by summing 𝐿(𝑥 , 𝑥
AutoSum function as shown in Figure 1.

115) for 𝑖 = 0, 1, 2, …. You may use

========[Omit]========

Figure 1

Step 2
To compute, first, type in the equation in cell K2 (Figure2) and drag as shown in Figure3.

Figure 2116

Figure 3

Step 3Create a new sheet and set the framework shown in Figure 4.

117

Figure 4
Step 4
In cell B2, type in the following formula to calculate the probabilities of the binomial distribution
for 𝑖 = 10, 20, …
=BINOM.DIST($A2, 131, Sheet1!$K$2, FALSE)*Note that “131” (the number of type A points) and “Sheet1” (the sheet name storing theprobabilities of each bin width) in the formula change appropriately. In this case, the resulting value
in cell B2 of Figure 5 represents the probability to locate no type A points within 10m from theirnearest type B points under CSR hypothesis.

118

Figure 5

Step5
Copy the formula to the rest of rows (Column B) by using AutoFilll function. And, in cell C2, type in
the following formula to calculate the probability.
=BINOM.DIST($A2, 131, Sheet1!$K$3, FALSE)* Change the value from $2 in the formula described at Step 4 to $3 (colored in Red).

Figure 6
119Repeat Step 5 until all bins and counts are filled.
* The value colored in Red in Step 5 should be added one by one every time changing the column.
Figure 7 shows the sample output.

Figure 7

Step 6
In order to visualize the magnitude of probabilities, you may want to use "data bars" withconditional formatting. Select the cells which you would like apply the rules. On the home tab, click“Conditional Formatting”. Point to Data Bars, and then click “More rules” (Figure 8).

120Figure 8
As Figure 9 shows, select “Number” from type drop down from Maximum and enter 1 in the value.
Click “OK”.

Figure 9121

You obtain the bar charts with values in Figure 10, showing probabilities of a result of the Network
Voronoi Cross K function method.

Figure 10122