1“This is a post-peer-review, pre-copyedit version of an article published in Transportation. The final

2

authenticated version is available online at: https://doi.org/10.1007/s11116-020-10079-y”.

3
4
5

Egocentric social networks and social interactions in the Greater Tokyo
Area

6
7

Giancarlos Parady

8

ORCID iD: 0000-0002-7581-774X

9

Department of Urban Engineering

10

The University of Tokyo, Tokyo, Japan 113-86567

11

Email: gtroncoso@ut.t.u-tokyo.ac.jp

12Phone: +81-3-5841-6234

13
14

Kiyoshi Takami

15

Department of Urban Engineering

16

The University of Tokyo, Tokyo, Japan 113-8656

17

Email: takami@ut.t.u-tokyo.ac.jp

18

Phone: +81-3-5841-6232

19
20

Noboru Harata

21

Department of Urban Engineering

22

The University of Tokyo, Tokyo, Japan 113-8656

23

Email: nhara@ut.t.u-tokyo.ac.jp

24

Phone: +81-3-5841-6233

25
26

Abstract27

This article presents the results of a survey on egocentric social networks in the Greater Tokyo Area.

28

This is, together with our preliminary study, the first study on egocentric social network in Japan that29

uses an unrestricted name generator to elicit personal networks. It is comparable to previous work30

conducted in Europe (Switzerland and The Netherlands) and The Americas (Canada and Chile). In

31

addition to a thorough description of the survey design and execution process, basic results regarding

32

network characteristics and social interaction patterns, and estimation results of a multilevel33

multivariate mixed effect model of social contact frequency by mode are presented and compared

34

against relevant benchmark data. The information provided in this article and the supplementary

35

documents will allow its use as a new benchmark study in the subject of social networks and social

36

interactions research.

37
38

Keywords1

1

Ego-centric social networks, personal networks, social interactions, contact frequency by mode, Japan2

2

Introduction

1

1.

2

In recent years, researchers in the transportation field have started to pay attention to social networks

3

due to the relation between social interactions and socially motivated travel. While the importance of

4

leisure and other socially motivated travel has been widely acknowledged, most of the research in

5transportation planning has focused on work-related trips (Kowald and Axhausen, 2015). To address

6

this gap, several efforts have been conducted in Europe (Frei and Axhausen, 2007; van den Berg,

7

Arentze and Timmermans, 2009; Kowald and Axhausen, 2012) and The Americas (Carrasco et al.,82008; Carrasco and Cid-Aguayo, 2012). One key difference in the way these studies measure social

9

networks, in comparison to more traditional surveys such as the American General Social Survey

10(GSS) is that the name generators are not capped to four or five contacts but are virtually unrestricted

11

allowing with upper limits of more than 40 contacts. In addition, these studies not only gathered

12

information about social contacts in a much finer resolution, but also emphasize the geographic

13

characteristics of the network, whereas traditional social science studies have largely focused on

14

location-agnostic network topology (Axhausen, 2007). This article presents the results of a similar effort

15

in the context of Japan, specifically, of the Greater Tokyo Area.

16

Since the literature on social networks and travel has been recently and thoroughly reviewed elsewhere,17

we refer interested readers to the comprehensive review conducted by Kim, Rasouli and Timmermans

18(2018). Instead (and given the data paper denomination of this article) we will describe the general

19

results of this survey vis-à-vis relevant and comparable studies as we go along.

20

It is worth noting that the social science community has produced a rich literature on social networks

21

in Japan, focusing, among other subjects, on social network characteristics (Harada, 2012; Otani,22

1999; Ishiguro, 2018; Harada and Sugisawa, 2014), and the effect of ICT technologies (in particular23

the internet-capable mobile phones introduced in the Japanese market in the late 90`s) on social

24

networks (Miyata et al., 2004; Iwata, 2014; Igarashi, 2005). In line with the international efforts listed

25

above, key differences between this study and the Japanese literature on social networks are the26collection of information about social contacts in a much finer resolution, via virtually unrestricted name27

generators, and a greater emphasis on the geographic characteristics of the network, which allow for28

analysis and inferences more closely related to travel behavior.

29

The rest of the article is structured as follows. Section 2 describes the survey methodology; Section 3

30

provides a summary of the data characteristics. Section 4 presents the result of a mixed effect31

multivariate model of contact frequency by mode and Section 5 summarizes the main conclusions of32

the article. Supplementary information is provided in the appendix section and the supporting material

33

section of this article.

34

Survey methodology

35

2.

36

Survey objective

37

The main objective of this survey is to measure social network characteristics and social interaction

38

patterns in the Greater Tokyo Area. This survey is part of a larger project which aims at analyzing the3

1

relationship between social networks and travel behavior.

2
3

Sampling strategy

4

The target population were adult residents (over 20 years old) living in the Greater Tokyo Area. For the5

purposes of this study, the Greater Tokyo Area is defined as the combination of the Tokyo Metropolis,

6

and the prefectures of Chiba, Saitama and Kanagawa (often referred to as One Metropolis, Three

7

Prefectures).

89
Figure 1. Target area and location of sampled municipalities

10
11
12

The most comprehensive sampling frame available in the Greater Tokyo Area is the Basic Resident

13

Register. In order to obtain a simple random sample, independent applications would have to be made14

to each of the 184 municipal governments that compose the Greater Tokyo Area, each with different

15

screening criteria, and application procedures, which would increase the sampling costs considerably.

16

As such, given the size of the size of the study, budgetary constraints and practical considerations

17

regarding the sampling frame, the following sampling strategy was adopted:

181.

Stratify the Greater Tokyo Area into generalized accessibility sextiles as defined by Parady, Loder

19

and Axhausen (2017) and illustrated in Figure 1. Accessibility was used as the defining criteria

20

because it is a good indicator of built environment characteristics, in particular of access to activity
41

opportunities, population density, and transport level of service, characteristics that have been2

consistently associated with residential location preferences by households at different life stages.

32.

Sample one municipality per strata. For practical reasons, when municipalities were sampled,

4

consideration was given to factors such as the difficulty associated with obtaining the permit to5

sample the basic resident register, and the time it would take to obtain this permit. Based on these6factors, when deemed necessary, alternative municipalities were sampled from the same strata.

7

In that sense, the sampling at this stage was not purely random, but an approximation limited by

8practical considerations.

93.

Draw a simple random sample from each sampled municipality using the Basic Resident Register10

as sampling frame. The total invited sample size was 1000 and the number of samples per

11municipality was defined based on the population share of each accessibility sextile as shown in

12

Table 1. Table 2 summarizes the general sociodemographic characteristics of the sampled

13

municipalities.

14
15

Table 1. Sampled municipalities given generalized accessibility levels
Municipality Name

Accessibility sextile

Sextile population share

Invited sample size

Shinagawa ward

1

36.2%

362

Matsudo city

2

21.4%

214

Hino city

3

20.0%

200

Kuki city

4

12.2%

122

Odawara city

5

7.0%

70

Kimitsu city

6

3.2%

32

16
17

Table 2. General sociodemographic characteristics of sampled municipalities1
Prefecture

Municipality

Accessibility
level

Population

Area
(km2)

Population density(1/sq.km)

Number ofhouseholds(private)

Tokyo

4.16

386,855

22.84

16,938212,286

Chiba

Shinagawaward
Matsudo city

Meanhouseholdsize(private)
1.81

3.42

483,480

47.73

9,742

215,322

2.21

Tokyo

Hino city

3.28

186,283

27.55

6,762

84,823

2.15

Saitama

Kuki city

2.84

152,311

82.41

1,848

59,035

2.55

Kanagawa

Odawaracity
Kimitsu city

2.20

194,086113.81

1,705

79,0072.41

1.12

86,033318.81

270

34,409

2.44

Chiba

18

1Source: 2015 Population census

19
20

Survey content

21

The survey contained three sections. The first section focused on the respondents’ (hereinafter ego)

22

individual and household characteristics. The second section focused on eliciting ego’s personal
5

1

network using two different methods. The first method is the most widely used in the Japanese literature2(Otani, 1999; Harada, 2012; Iwata, 2014; Ishiguro, 2018) and consists on directly asking respondents

3

to state the number of contacts by relationship type. Following Otani (1999), respondents were asked:

4
5

1.

How many intimate kin, co-workers, neighbors and friends do you have? (People you get together
with frequently)

6
7

The second approach used name generators. In this survey, the name generators used were adapted8

to Japanese from Kowald and Axhausen (2012) as follows:

91.

Name the persons whom you spend your free time with (Examples of free time activities include

10

sports, cultural events, club activities, eating and drinking out, outings during holidays, errands

11

etc.)

12
13

2.

In addition to the persons named in the previous question, please name the persons whom you
discuss important issues with.

14

A name interpreter was used to elicit characteristics of the network members (hereinafter alters).

15

Respondents were then asked to create different groups of alters that know each other and usually16

spend their free time together (hereinafter cliques). A maximum of eight cliques could be formed. Alters

17

could belong to more than one clique.

18

The third section focused on measures of trust, namely generalized trust (survey items adapted from19

ESS (2014)) and trust in institutions (survey items adapted from OECD (2017)). Since this section is20

out of the scope of this article, it will not be discussed further. Table 3 summarizes the data collected

21

in the survey. See the supplementary materials for an English version of the paper-based instrument.

22
23

Table 3. Data collected in the final survey
Ego characteristics

Alter and relational characteristics

GenderRelationship type

Age

Relationship length

Employment status

GenderMarital status

Age

Household size and structure

Employment status

Education level

Marital status

Mobility tools ownership

Residential location

Household income

Tie strength

Residential location

Contact frequency by mode

Work location

Clique identification

Number of contacts by relationship type
Name generators
Generalized trust
Institutional trust
6

1

Preliminary surveys

2

Two preliminary web surveys were conducted, both using a non-probability quota sampling method

3based on the gender and age distribution of the Greater Tokyo Area. Respondents were sampled from4a monitor panel managed by a marketing research firm in Japan. The first survey was conducted after5

the survey design and interface were completed (effective sample size = 97 egos). The main objective

6

was to evaluate the quality of responses (in particular location data), and to assess the effect of the7

name generator response burden on response quality. Since the survey was conducted in-house, we

8

could observe partial and breakoff responses, which allowed us to test whether respondents with larger

9

networks were less likely to finish the questionnaire. Group comparisons via mean t-test and Wilcox

10

non-parametric tests showed no statistical differences in social network sizes between respondents

11

who completed the survey and respondents who did not but listed at least one name in the name12

generator. A second survey was conducted between February and March of 2018 using the same panel

13

and excluding respondents that participated in the first survey (effective sample size = 347 egos). An

14

exploratory data analysis was conducted and hypotheses from the literature on social networks and15

interaction were evaluated. No major modifications to the survey design resulted from this test, but

16

some questions were dropped to reduce the response burden. See Parady, Takami and Harata (2019)17

for more details.

18
19

Main survey protocol and execution

20

The main survey was conducted using was a combination of web and paper modes. Sampled subjects

21

received an invitation letter by mail between Friday, March 1st and Saturday, March 2nd, 2019 with

22

instructions on how to respond to the web-survey, which was the recommended response medium.

23

For respondents under 60 years (67.5% of the sample), the paper questionnaire was available upon24

request (this group is hereinafter referred to as the web group). For respondents 60 years old or older

25(32.5% of the sample), a paper version of the questionnaire was sent along with the invitation letter

26(this group is hereinafter referred to as the paper group). 7% of the web group respondents requested

27

a paper questionnaire, while 26% of the paper group responded to the questionnaire online. An

28

exclusive toll-free line was set to handle inquiries regarding the survey.

29

A JPY1000 (US$9.24) Amazon.co.jp gift card (digital type, received by e-mail) was offered as an

30

incentive to respondents who completed the questionnaire online. For respondents that chose the31

paper-based version, a gift card of equivalent value was mailed after verifying the return of the survey.

32

The first reminders were sent 2 weeks (web group) and 3 weeks (paper group) after the invitation was

33

sent. The second reminders were sent 3 weeks (web group) and 2 weeks (paper group) after the first34

reminders were sent. As illustrated in Figure 2, the first reminder was very effective in nudging people

35

into responding, especially for the paper group. The second reminder was somewhat effective for the36

web group but had almost no effect on the paper group. The survey was concluded on April 23, 201937

with no further reminders.

725.0%
1st Reminder
sent (web)

1st Reminder
sent (paper)

2nd Reminder
sent (all)

20.0%

15.0%

10.0%

0.0%

1
2

fri-1
sat-2
sun-3
mon-4
tue-5
wed-6
thu-7
fri-8
sat -9sun-10mon-11tue-12
wed-13
thu-14fri-15sat -16
sun-17mon-18tue-19wed-20thu-21
fri-22sat -23
sun-24mon-25tue-26wed-27thu-28fri-29sat -30
sun-31
mon-32tue-33wed-34thu-35fri-36sat-37sun-38mon-39tue-40wed-41
thu-42fri-43sat-44sun-45mon-46tue-47wed-48thu-49fri-50sat-51sun-52mon-53tue-54

5.0%

Web responses

Paper responses

All responses

Figure 2. Cumulative response rate by survey medium (includes all collected responses)

3
4

Response burden and response rates

5

Following Axhausen and Weis (2010) response burden is defined as 𝑅 = ∑𝑘 𝑛𝑘 𝑤𝑘 , where n is the

6number of items in question k and w is the unit response burden for question k. The main reason to7

use this particular system is that several ego-centric social networks surveys have reported these8burden values, thus allowing for comparisons. The ex-ante response burden of this survey was 545

9points (561 for the paper version), compared to 900 (Kowald and Axhausen, 2012), 1482 (Guidon et10al., 2018). Regardless of differences in the response burden score definitions, the difference in total

11

burden score is largely due to the way the response burden for the name interpreter is calculated. The

12burden of individual questions in the name interpreter is a function of the expected average or median13

network size. These values are usually taken from reported values in the literature or from a pre-test.

14

In this study, we used the average network size measured in our preliminary survey (Parady, Takami

15

and Harata, 2019). This study reported an average network size of 4.6 alters, which is considerably

16

smaller than network sizes reported in the literature. For example, if we used an expected network size17

of 14, the response burden would increase to 1175 points (1191 for the paper version).

18

To calculate the response rates, we followed the standards set by the American Association of Public

19

Opinion Research (The American Association for Public Opinion Research, 2011). Complete, partial,

20and breakoff response statuses are defined in Table 4.

21
22
23
8

1
2

Table 4. Criteria to define response status
Status/Section
Complete

Ego
≥ 80%

Name generators

Name Interpreter

Trust

(NG)

(NI)

(T)

∩

-

∩

NG > 0 → NI ≥

∩

≥ 80%

∩

-

60%2

Partial≥ 70%∩

NG > 01∩

Breakoff-

All other cases

3

1Respondent listed at least one name in either name generator.

4

2If respondents listed at least one name in either name generator then the name interpreter must be at least 60%

5complete.

6

For the web survey all responses were mandatory except for the name generators, which could be skipped.

7
8

With an average network size of 9 alters, the ex-post response burden estimate was 825 points (8419

for the paper version) Figure 3 summarizes the ex-post response burden per item of the survey, while

10

Figure 4 plots survey response burden indicators. The left panel shows that the number of named

11

alters is positively associated with response duration, accounting for 65% of the duration variance.

12

Mean survey duration for the web responses was 23.1 minutes (median 19.5). The right panel of Figure

13

4 shows the histogram of the actual individual response burden calculated in seconds/burden points

14

for web respondents.

15

AAPOR response rates RR1 and RR2 were 18.5% and 21.7%, respectively. Final disposition codes16

are reported in Table 5. Effective sample size was 217 respondents.

17
18

Table 5. Final disposition table (Following AAPOR standard definitions)
Code

Final disposition

Frequency

Percentage

1.1

Returned questionnaire

Complete

185

18.5%

Partial32

3.2%

Eligible, "Non-Break-off/too incomplete to

11

1.1%

Interview"process
Nothing ever returned

744

74.4%

Unknown eligibility,

Mailing return undelivered /

23

2.3%

"Non-Interview"

Addressee not known at place of
5

0.5%

1.2
2.12
3.19
3.311

address (Jp-post)
3.23

Refused by addressee (Jp-post)

19

9

1
2

Figure 3. Ex-post survey response burden tabulation
10

1

2

Figure 4. Survey response burden indicators. Left: web survey response duration plotted against

3

number of named alters. Right: Actual response burden of web respondents calculated as

4seconds/burden points (mean: 1.87, median: 1.70, standard deviation: 0.68).

5

Basic data characteristics

6

3.

7

Ego personal characteristics

8

Ego level characteristics are summarized in Table 6. Two types of statistics are reported. The sample

9

statistics, and weighted statistics (weighted by expansion coefficients to get population-level estimates).

10

Throughout this article, unweighted values are presented first, followed by the weighted values in

11parentheses. See Appendix A for a brief summary of how the expansion factors were calculated.

12
13

Table 6. Descriptive statistics of ego characteristics (n=217)
Variable

Ego is male
Age
20-29
30-39
40-49
50-59
60 and over
Civil status
SingleIn a relationship
Married, no children
Married with children
Married with children,with children under 15 in household

Sample Weighted Population
share
share
Share
(%)
(%)
(%)
54.38
49.24
49.24
12.44
13.82
17.51
21.20
35.02

13.53
14.18
16.26
22.83
33.20

13.28
16.56
19.55
14.62
35.99

23.50
4.61
11.52
50.69

23.21
4.71
11.19
51.19

25.241
2
58.42
-

16.13

16.11

16.11

11

Divorced
Widowed
Other
Employment
Full time employee
Freelancer
Part timer
Student
Home maker
Unemployed/retired
Other
Education
High-school and underTechnical degree
University degree and higher
Household income4
Not disclosed/unknown
Under 3 million
3-10 million
Over 10 million

Household size
Network size (name generator)
All
Male
Female
20-29
30-39
40-49
50-59
Over 69
Network size (direct count)All
Male
Female
20-29
30-39
40-49
50-59
Over 69

5.53
2.76
1.38

5.68
2.81
1.21

50.23
0.92
10.60
4.61
11.98
12.90
8.76

50.27
0.87
10.82
5.06
13.12
11.19
8.67

30.88
23.04
46.08

31.44
22.96
45.60

15.67
18.89
48.85
16.59
Sample
mean
2.64

14.96
18.00
49.65
17.39
Sample
SD
1.31

6.40
21.50
60.70
11.40
Wtd.
mean
2.68

Wtd. Min.
SD
1.33
1

8.90
6.95
11.23
10.41
10.27
7.63
7.54
9.79

8.28
6.36
9.64
8.33
9.71
10.24
7.10
7.37

9.07
6.79
11.30
10.22
10.70
7.87
7.30
10.33

8.33
6.18
9.48
8.16
9.70
10.66
6.51
7.43

0
0
0
0
0
0
0
0

15.35
11.83
19.55
21.74
13.40
13.55
14.04
17.03

19.14
12.49
24.26
38.06
11.71
20.74
12.01
14.14

15.50
11.85
19.08
21.56
13.68
12.89
13.26
18.50

19.10
12.59
23.25
36.42
11.26
19.59
10.97
15.21

0 200.00
085.00
0 200.00
1 200.00
0
60.00
0
95.00
0
55.00
1
65.00

4.52
7.26
4.563

1

Population shares from 2015 census unless otherwise stated2

1 Includes both “Single“ and “in a relationship” statuses

3

2 Includes married persons with and without children

4

3 Classed as “unknown” on census

5

4Own calculation Using data from the 2013 Housing & Land Survey. Includes all age cohorts.

Max.
8
52
27
52
27
33
52
29
31

6
7

Compared to the population level data available, the distribution of gender, age and civil status8

reasonably approximates the population distribution. In terms of household size, according to the 2015

9

population census, the average household size in the Greater Tokyo Area is 2.22, while the sample
12

1

average was 2.64 (2.68). This might be due to the fact that sampling from the basic resident register2

was done at the individual level, so larger households are more likely to be sampled.

3

Regarding household income, since the population census does not include related questions, we used4

the 2013 Housing & Land Survey (a probability survey conducted by the Ministry of Internal Affairs and5Communications) to get a population estimate of household income at the individual level (Statistics of6Japan, 2019). However, note that this estimate is calculated including all age cohorts (while our sample

7

is limited to adults (20 years old or older)), and that for 6.4% of individuals household income is8

unknown. Compared to this population estimate, our sample included a higher share of respondents

9in higher income households.

10

As stated above, social networks were measured using two different methods. Given the nature of11each method we expected these to yield different results in terms of social network size, but using both12

methods allowed us to compare our results to the existing literature in Japan that relies mostly on the13

first approach, and with the existing international literature that relies on name generators.

14

Regarding the direct count method results, the average network size in the sample was 15.4 (15.5).

15

When segmenting by gender, women exhibited larger networks than men, with a mean difference of16

7.7 (7.2) alters. When comparing network size against similar studies (see Table 7), the average

17

network size was close to the values reported in the literature. Although survey year and locations of18

most studies differ, the study by Harada (2012) also targeted the Greater Tokyo Area, and reported an

19average network size of 13.6.

20

Regarding the name generator results, to the best of our knowledge there are no similar studies in

21

Japan using an unrestricted name generator, so no comparison is possible. Instead, we compared our

22

results to benchmark data from international studies. Mean network size in the Greater Tokyo sample

23

was 8.9 (9.1) alters. This value includes respondents who named no alters in the name generators,

24

usually referred to as isolates (10.1% of the sample). When excluding isolates the sample mean

25

network size is 9.9. Given that the benchmark studies in the literature also report network sizes

26

excluding isolates, we will use this value in the following comparison.

27

Compared to similar studies in Switzerland, The Netherlands, Canada and Chile, the Greater Tokyo28

sample had the smallest network size with 9.9 (10.0) named alters, followed by Zurich (1) and Zurich29(2), with 12.4, and 15.1 respectively, while the Toronto, Concepcion, Eindhoven and Switzerland

30

samples showed considerably larger networks, with more than 20 alters on average. While31

methodological differences might explain some of these differences, cultural differences might also

32

help explain these results as we hypothesized based on the results of the preliminary survey (see33

Parady, Takami and Harata (2019)). As Nakane (1970) has argued, Japanese social relations are34

characterized by high levels of group consciousness and a vertical structure. Group consciousness

35

strengthens the sense of unity and group solidarity, but also exacerbates the awareness between

36“inside the group” and “outside the group”. Furthermore, we argue that the vertical nature, specifically37

the strong awareness of ranking order in Japanese relationships might impose additional costs to38

creating and maintaining ties. On the other hand, Miyata et al. (2004) argued that greater reticence13

1among Japanese to disclose personal information might make network size comparisons with western2

countries more difficult. While both hypotheses have some plausibility, more research is needed to3validate them.

4
5

Table 7. Average network size comparison against benchmark studies
MethodStudy

Reported

Country / region, survey year

valuesDirectParady et al. (2019)

count

Iwata (2014)11.6 → 9.4

Otani (1999)

13.3

Japan / Hiroshima city, 1989

Harada (2012)

13.6

Japan / Greater Tokyo, 2010

Otani (1999)

14.4

Japan / Matsuyama city, 1989

This study

15.4 (15.5)

Japan / Greater Tokyo, 2019

Ishiguro (2018)

10.9

15.7 → 13.9

Fukuoka city, 2014
Japan, 2001 → 2011

Japan / Yamanashi city, Asaka city,
1993 → 2014

Name

This study

9.9 (10.0)

Japan / Greater Tokyo, 2019

generator2

Frei and Axhausen (2007)

12.4

Switzerland / Zurich (1), 2005-2006

Guidon et al. (2018)

15.1

Switzerland / Zurich (2), 2017

Kowald and Axhausen (2012)

21.6

Switzerland, 2009-2011

Carrasco and Cid-Aguayo

22.2

Chile / Concepcion, 2008-2009

23.3

The Netherlands / Eindhoven, 2008

23.8

Canada / Toronto, 2004-2005(2012)
van den Berg, Arentze andTimmermans (2009)
Carrasco et al. (2008)
6

2These network sizes exclude isolates (respondents who named no alters in the name generators)

78

10.1% (9.7%) of the sample did not report any alter in the name generators (either to spend free time9with or to discuss important matters with). 3.7% (3.4%) reported no social network members with the10

direct count method. Using the 2013 Japan General Social Survey data, Ishida (2011) reported that

11

8.9% of the sample did not report having a person to discuss important problems or having emotional-

12

support-providing relationships. Despite the name generators used in this study being different, the13reported value is similar to the one reported in this study. These values have been used as evidence

14

of social isolation (McPherson, Smith-Lovin and Brashears, 2006; Ishida, 2011), however; we were15

unable to draw a conclusion on such issue, as it is certainly difficult to differentiate between true social

16

isolation and non-response. As such, we limit ourselves to reporting what was observed in the data.

17

Figure 5 plots the weighted network size probability mass (name-generator method).

18

14

1
2

Figure 5. Named network degree probability mass plot (weighted)

3
4

To evaluate whether reported social networks size distribution differed by survey medium and by final

5

survey disposition, we used the non-parametric Mann–Whitney U test, given the non-normal

6

distribution of social network size. As explained above, the survey medium response was highly

7

dependent on the respondent’s age. As such, tests were conducted first using all samples grouped by

8

response medium, and then, using only the 60-years-and-older cohorts. In addition, we tested whether

9

there were differences in the social network size distribution of respondents who fully completed the10survey and those who only did so partially. The tests were conducted for both social network size

11

measures (using the name generator and the direct count methods). Table 8 summarizes the test

12

results.

13

Regarding the survey medium, for networks measured via name generators, the difference in the

14

distribution was statistically significant for the all-age-cohorts test at any significance level, but it was

15

only significant at the 0.1 level for the 60-years-and-older cohort test. This suggests the possible

16

existence of a medium effect, although the evidence is not too strong. However, for the direct count17

case, the medium effect was not observed. A plausible explanation is that the medium difference is

18

exacerbated by the task burden.

19

When looking at the test by final disposition, irrespective of method, the Mann–Whitney U tests were20

statistically significant at any significance level, suggesting that respondents with larger networks were21

less likely to complete the survey. This might be explained by the fact that the larger the number of15

1

elicited names in the name generators, the larger the response burden becomes in the name2interpreter part, as illustrated earlier in Figure 4. This result is different from the one reported by Parady,

3

Takami and Harata (2019) in their non-probability sample. However, as stated earlier, the reported

4

network size in that study was considerable smaller, consequently, so was the response burden.

5
6

Table 8. Mann–Whitney U group tests of reported social networks size
Method

Group

n

test

Test

Min.

Condition

Mean

S.D.

Max.

Test statistic(median)

Name

Web

150

All age0

8.4 (6)

8.6

52

U = 3934

Generator

Paper

67

cohorts010.2 (8)7.4

31p-val. = 0.011

Web

19

60 years0

7.5 (5)

7.4

29

U = 388

Paper

57

and older09.9 (8)7.1

31p-val. = 0.066

Complete

185

All valid data0

8.6 (7)

8.6

11

U = 2130

Partial32

010.7 (9.5)

10.7

14.3

p-val. = 0.011

DirectWeb

150

All age015.2 (11)

21.4

200

U = 4402.5

count

Paper

67

cohorts015.8 (13)

13.0

65

p-val. = 0.145

Web

19

60 years

1

14.6 (12)

14.9

56

U = 484

Paper

57

and older1

15.9 (13)

13.1

65

p-val. = 0.494

Complete

185

All valid data

0

14.4 (10)

19.2

200

U = 2009.5

Partial321

21.1 (16.5)

18.0

85

p-val. = .004

78

Ego-alter relational characteristics

9

Ego-alter relational characteristics are summarized in Table 9. Out of the 1932 alters elicited in the

10

valid sample, the subset of alters with complete information for all the variables presented in the11following section was used (n=1448).

12

In terms of the spatial distribution of ego and alters, the average geodesic distance was 102km (105km),

13

and median distance 9.2km (9.5km). Many studies in the literature have reported that ego-alter

14

distance patterns follow a power law distribution (Latané et al., 1995; Lambiotte et al., 2008; Backstrom,

15

Sun and Marlow, 2010; Onnela et al., 2011; Illenberger, Nagel and Flӧtterӧd, 2013; Kowald et al.,162013), but with the exception of Onnela et al. (2011), these studies used a log-log regression of the17histogram of distances to support the power-law distribution argument. This approach; however, has

18been shown to generate significant and systemic large errors, and a more adequate method has been

19

proposed using a maximum likelihood (ML) method (Clauset, Shalizi and Newman, 2009).

20

We tested both the OLS and the ML approach in our data. Following the results reported by Kowald et21

al. (2013), which uses similar data, we used the OLS method with a 100km cutoff (that is, only using

22

data from alters within a 100km distance range), and obtained a significant exponent coefficient of 1.24

23

(p value <0.01) which is in line with the range of values reported by Kowald et al. (1.08 ~ 1.58) in their

24

comparative analysis. However, when using the more adequate ML method proposed by Clauset,16

1

Shalizi and Newman (2009), not only did the exponent coefficient estimate differs considerably from2

the OLS estimate (4.11 and 4.16 for discrete and continuous fit, respectively), but goodness of fit test3

results suggested that the power law distribution was not a plausible fit for the data.

4
5

Table 9. Descriptive statistics of ego-alter relational characteristics (n=1448)
Variable
Homophily
Gender
Occupation typeAge cohort
Civil status
Relationship length
1 year or less
1-5 years
5-10 years
over 10 years
Relationship type
Immediate family
Extended family
Work
SchoolNeighbor
Club or circle friend
Other
Tie strength
Tier 1 (Would discuss
important problems with)
Tier 2 (Would ask forhelp in an emergency)

Tier 1 & 2

All

Share (%)
Ego is Ego ismale female

Weighted Share (%)
All
Ego is Ego ismale female

71.69
47.31
36.95
47.31

65.53
47.78
34.98
49.32

75.87
46.98
38.28
45.94

72.25
48.24
37.24
46.59

65.59
49.93
35.34
48.72

75.88
47.32
38.27
45.43

3.94
15.19
17.27
63.60

1.02
16.38
17.58
65.02

5.92
14.39
17.05
62.65

4.45
15.24
17.27
63.03

1.06
16.76
16.95
65.24

6.30
14.42
17.45
61.83

21.82
11.33
14.09
14.71
5.11
12.22
20.72

26.96
7.34
16.55
9.56
6.83
9.04
23.72

18.33
14.04
12.41
18.21
3.94
14.39
18.68

22.00
11.52
13.58
15.37
4.35
12.74
20.43

28.53
7.72
15.18
10.47
5.67
10.03
22.40

18.44
13.59
12.71
18.04
3.63
14.22
19.36

32.18

31.06

32.95

31.74

30.77

32.26

26.93

29.35

25.29

25.79

28.14

24.51

37.98
Mean

38.91
Median

37.35
S.D.

36.94
Wtd.
Mean

38.10
Wtd.
Median

36.30
Wtd.
SD

Min.

Max.

9.20
10.16

674.05390.63

9.46
11.72

686.74413.90

0
0

10876
8793

8.78

811.32

105.4
6
67.80
125.9
7

8.90

796.21

0

10876

18.00
2.00
0.00
0.00

122.19
77.30
84.43
98.47

73.76
28.03
30.82
43.86

18.00
2.00
0.00
0.00

122.57
78.23
84.05
98.40

0
0
0
0

365
365
365
365

Geodesic distance (km)All
Male
FemaleContact frequency(1/year)Face to face
Phone
Email/SMS
SNS

102.2
4
64.06
128.1
9

73.76
27.66
30.97
43.71

6
7

We also tested the ML method using different distance cutoffs and got similar results. Also using the8

ML method and at the 100km cutoff, the lognormal distribution was found to be a plausible fit. While9also a fat-tailed distribution, this distribution decays faster than the power law distribution. However, for17

1different distance cutoffs, the lognormal distribution was not a plausible fit (See Appendix B for results,

2and Appendix C for a brief summary of the ML method to test power-law distributions).

3

Contact frequency by mode was measured for four modes: face-to-face, phone, e-mail/short message

4

service (SMS), and social networking services (SNS). The email and SMS categories were combined

5

because in Japan, e-mail services were provided on feature phones at a very early stage and are very

6

similar in nature to SMS messages. Frequency was measured as an ordinal variable with 8 levels:

7"Never","1-3 times/year","4-11 times/year","1-2 times/month","3-4 times/month","1-3 times/week","4-7

8times/week", "Several times a day". To convert to a continuous measure of annual contact frequency,

9the midpoint of each frequency range was set as the frequency value. For the never case, frequency

10

was set at 0.5, and for the several times per day case the frequency was set at 365. Figure 6 illustrates

11

the weighted average contact frequency by mode, and its modal share over distance. When looking at

12average contact frequencies, all modes except SNS decrease with distance, with face-to-face contact

13

showing the steepest decline, reflecting its increasing marginal cost as distance increase. This is

14

consistent with findings reported by Kowald et al. (2013).

15

When looking at the contact modal share by distance, SNS acts as a substitute for face-to-face

16

interactions as distance increase and becomes the largest share at around the 50km threshold. No

17clear trend was observed for phone and e-mail/SMS modes, highlighting the market dominance of SNS

18

for remote communications.

19

20

Figure 6. Average contact frequency and contact mode share as a function of ego-alter distance21(weighted)

22
23

Tie strength was measured by asking respondents to specify (i) which alters they would discuss

24

important problems with (32% of all alters) and (ii) which alters they would ask for help in an emergency

25(27% of all alters). Hereinafter we define a strong tie as an alter that falls into either one of these18

1categories, which averaged on the sample 38% of all alters.

2
3

Clique characteristics

4

For the purpose of this study, we define a clique as a sub-community of persons that often meet.

5

Respondents were not asked to identify all members of such communities, but the ones they most6

frequently meet and contact.

7

74% of the sample reported at least one clique, and 53% reported at least one clique of size larger

8than 2.

9

Among those who reported at least one clique, the average clique size (when including ego) was 4.35

10

(4.31), and the median was 4 (4). When excluding dyads (ego-alter pairs) and considering only

11

reported cliques of size larger than 2, the average clique size was 6.01 (5.93) and median 5 (5). the12mean number of cliques reported (excluding dyads) was 3.37 (3.39) with a median of 3 (3).

13

A mixed effect multivariate model of contact frequency by mode

14

4.

15

To evaluate the statistical association between contact frequencies by mode, socio-demographics and16

relational characteristics, a linear mixed-effect multivariate model was estimated. Such a model

17

allowed for the joint estimation of multiple dependent variables as well as to account for the hierarchical18

structure of the data, which included both ego-level and ego-alter relational characteristics. The model

19

was estimated using the restricted maximum likelihood method approach (REML) in R (v.3.5.1) with20

the lme4 package (Bates et al., 2007). Dependent variables were log-transformed for estimation, and21

weights were applied to the model. Random effects were assumed to be normally distributed.

22

Estimation results are summarized in Table 10.

23

The significance of random effects was tested via a single-term-deletion likelihood ratio test. That is,24

for each test, one random effect is eliminated from the model and the likelihood ratio test calculated.

25

The statistical significance of both random effects and intraclass correlations of 0.10 and 0.35 for the26“Ego:Contact mode” and “Ego:Alter” intercepts, respectively, justify the use of the multilevel structure.

27

Regarding fixed effects, a clear pattern between age and ICT contact frequency can be observed.

28

Being 60 years or older was positively associated with higher phone contact frequencies, the most29

orthodox of all ICT contact modes. For e-mail/SMS, the biggest effect was observed for the 50-5930

cohort. This cohort already exhibited heavy use of both web-phones and PC-based e-mail in Japan in

31

the early 2000s (Miyata et al., 2004), when they belonged to the 30-39 cohort. On the other hand, the32

20-29 cohort in the early 2000s (40-49 cohort at present), which exhibited the highest share of web-33

phone e-mail use at that time, likely transitioned to new technologies such as SNS when they became

34

available. The effect of being 60 years old on e-mail/SMS contact frequency was also positive but of a35

smaller magnitude. Finally, in terms of SNS, it can be seen that from cohorts 40 years and older, the36

coefficients become progressively larger in magnitude (i.e. more negative) with age, showing less37

willingness to adopt new technologies.

38

Network size (as measured by the name generators) was not significant for face-to-face or phone191contact but was negatively associated with e-mail/SMS contact frequency, and positively associated2with SNS contact frequencies. This reflects the convenience of SNS services as compared to other3

ICT modes, which allow people to keep in touch with a larger number of contacts in a relatively

4effortless manner and at low costs.

5
6

Table 10. Estimation results of mixed-effect multivariate model of annual contact frequency by

7

mode
Face to face
Fixed effects

coef.

Intercepts

t-value

Phone

Email/SMS

SNS

coef.

t-value

coef.

t-value

coef.

t-value

3.63

9.73 -0.05

-0.14

0.21

0.57

1.81

4.85

0

0

Personal level variables
Age
20-29 (reference)

0

0

30-39

-0.58

-1.39

0.08

0.19

0.30

0.70

-0.51

-1.22

40-49

-0.74

-1.90 -0.06

-0.16

0.62

1.60

-0.70

-1.81

50-59

-0.47

-1.24

0.50

1.31

1.48

3.91

-1.31

-3.45

60 and over

-0.36

-1.05

1.27

3.71

0.85

2.48

-2.55

-7.44

Social network size

0.00

0.08 -0.01

-1.00

-0.03

-2.33

0.03

1.92

0

0

Relational level variables
Relative
No (reference)
Yes

0.70

2.78

1.04

0
4.16

0.20

0
0.81

-0.67

-2.68

Immediate family
No (reference)
Yes

0
0.60

0
3.78

1.08

0
6.74

0.59

0
3.66

0.80

5.01

Tie strength
Other (reference)

0

0

0

0

Strong tie (non-relative)

0.06

0.59

0.28

2.58

0.17

1.58

0.03

0.30

Strong tie (relative)

0.09

0.68

0.29

2.05

0.44

3.19

0.31

2.21

Age (non-relative)

-0.33

-2.89

0.01

0.05

-0.16

-1.38

0.03

0.25

Age (relative)

-0.26

-1.74

0.01

0.05

-0.01

-0.04

0.06

0.42

Gender (non-relative)

-0.34

-2.58

0.12

0.95

0.06

0.46

0.14

1.04

Gender (relative)

-0.08

-0.55

0.24

1.72

-0.17

-1.27

0.10

0.74

Family status (non-relative)

0.19

1.65

0.21

1.87

0.29

2.53

0.00

0.03

Family status (relative)

-0.01

-0.06

0.32

2.17

0.15

1.03

0.54

3.66

Occupation (non-relative)

0.30

2.73

0.24

2.18

0.27

2.43

0.07

0.66

Homophily20

Occupation (relative)

0.12

0.78

0.07

0.46

0.46

2.92

0.38

2.45

Log of geodesic distance (non-relative) -0.28-9.86 -0.02

-0.58

0.04

1.59

0.04

1.59

Log of geodesic distance (relative)-0.56-21.57 -0.17

-6.38

-0.13

-4.87

-0.07

-2.49

Random effects

Var

S.D

Likelihood ratio test (p-value)

Ego:Contact mode (intercept)

1.64

1.28

1842 (<0.01, df=1)

Ego:Alter (intercept)

0.43

0.66

382 (<0.01, df=1)

Residual

2.68

1.64

Intraclass correlation (Ego:Contact mode )0.35

Intraclass correlation (Ego:Alter )0.10

Marginal R2

0.26

Conditional R2

0.58

n Alters

1448

n Egos167n Contact modes

4

1
2

Coefficients statistically significant above the .10 level in bold.

3
4

In terms of ego-alter relational characteristics, irrespective of mode, being immediate family was

5associated with higher contact frequencies. Tie strength was positively associated with ICT contact6frequency, but the significance of the coefficients differed by relationship type, that is, between relatives

7

and non-relatives.

8

Homophily effects were rather mixed. Age homophily was negatively associated with face-to-face

9

contact frequency irrespective of relationship type, while gender homophily was negatively associated10with non-relative face-to face contact. On the other hand, positive associations were observed for ICT

11contact frequency and civil status and occupational homophily for both relatives and non-relatives, with12

significance and magnitude differing by mode. A positive association was also observed for family

13

status homophily and occupational status homophily with non-relative face-to-face contact. The adage

14

that “birds of one feather fly together” seems to be truer for characteristics more closely associated15with life stage such as civil and occupational status than basic demographics such as gender and age.

16

Consistent with finding from the literature, ego-alter distance was negatively associated with face-to-

17

face contact frequencies with magnitudes twice as large for contact with relatives. It is interesting to18

note that the effect of distance on ICT contact frequency actually differed by relationship type. While19

distance was significant and negatively associated with ICT-based contact frequencies irrespective of20

mode for relatives (with SNS showing the smallest effect magnitude), distance effects were not21

significant for non-relatives contact frequencies.

22

Table 11 summarizes effect directions reported in the literature for the variables used in our model.

23

Some of the differences in effect directions might be explained by cultural differences, as well as

24

methodological and model specification differences among studies. Other differences, such as the age
21

1effects in phone and email/SMS might be a result of the time of execution of these surveys, which go2

as far back as 2005, implying not only different levels of technological development and market

3

penetration but also upward movement in age cohorts.

4
5

Table 11. Comparison of significant effect directions reported in the literature

Face to face
Age

Network

Phone

Email

SMS

Young (+)1,3,7●Old (+)1

Young (+)2

Young (+)1,2,7

Old (+)1

Old (-)7

Old (-)7

Old (-)7(-)2,5(-)2,5(-)2(+)5●(-)5,7●(-)2,7(-)2,3

Internet
/SNS
●(-)5

(-)5

(-)7

size
Relation●Relative (+)2,3●Relative (+)1,2,7●Relative (+)2

●Relative (+)2,7

type

Relative (-)1

Friend (+)7

Relative (-)1

Friend (+)7

Friend (+)3

Neighbor (-)7

Friend (+)7

Neighbor (-)7

Friend (-)7

Colleague (+)2,7

Neighbor (-)7

Colleague (+)2,7

Neighbor (+)3,7

Colleague (+)2,7

Colleague (-)2
Tie strength(+)1,3

Gender●(+)3

homophily

●(-)9

Age

●(-)3,9

●(+)1

●(+)1

●(+)1

●(+)1

●(-)1,7,8(+)1,2,7,8●(-)1,2,7,8●(-)6

homophily
Distance●(-) 1,2,3,4,6,7,8,9

●(-)6
6

●Indicates same effect directions as in this study.

7

1van den Berg, Arentze and Timmermans (2012);2Frei and Ohnmacht (2015); 3Sharmeen, Arentze and8

Timmermans (2014); 4Carrasco and Cid-Aguayo (2012); 5van den Berg, Arentze and Timmermans (2013);

9

6Mok, Wellman and Carrasco (2010); 7van den Berg, Arentze and Timmermans (2009); 8Larsen, Axhausen

10

and Urry (2006); 9Parady et al. (2019)11

Conclusion

12

5.

13

This article presented the results of a survey on egocentric social networks in the Greater Tokyo Area,

14

comparable to previous work conducted in Europe (Switzerland and The Netherlands) and The

15

Americas (Canada and Chile). It is to the best of our knowledge the first study on egocentric social

16

network in Japan that uses an unrestricted name generator to elicit personal networks. The survey

17

methodology and data characteristics were thoroughly described.

18

The descriptive analysis showed that compared against benchmark data form similar international22

1

studies, the Greater Tokyo sample exhibited the smallest network size. Analysis of contact modal share2

as a function of distance showed a substitution pattern between face-to-face contact and social

3

networking services (SNS) contact given increasing distances, becoming the dominant contact mode

4

after 50 km. Regarding contact frequency, a transition towards SNS as a preferred ICT contact was5also observed, being the mode with the second highest average frequency after face-to-face contact.

6

SNS preference, however, was dependent on age cohorts, with older cohorts less willing to adopt new

7

technologies.

8

In addition, a multilevel multivariate mixed effect model of social contact frequency by mode was

9estimated. Results showed significant associations between contact frequency by mode and (i)10personal and network attributes, (ii) relational attributes, and (iii) ego-alter spatial distances. The reader

11

is directed to the work of Parady et al. (2020) for a more in-depth comparative analysis of contact

12frequencies by mode across different socio-cultural contexts using this and similar datasets.

13

Finally, the information provided in this article and the supplementary documents will allow its use as

14

a new benchmark study in the subject of social networks and social interactions research.

15
16

Data availability statement

17

The survey data is available as of publication for collaborative research projects. The data homepage

18

can be accessed via the UTokyo Academic Archives collection: https://da.dl.itc.u-

19

tokyo.ac.jp/dalink/index_en.html, or by directly visiting http://www.ut.t.u-tokyo.ac.jp/en/sndatatokyo.

20

To protect the privacy of respondents, data will be deidentified before sharing. Disaggregate

21

information on locations, names or any other type of personal information shall not be provided.

22
23

Acknowledgments

24This study was funded by JSPS Grant-in-Aid, Grant 17K14737. The authors would like to thank Mr.

25

Yuki Tamura, Mr. Ryo Sakuramoto, Mr. Masahiro Araki and Mr. Yo Kamijo for their help in tabulating26

the paper-based responses of the survey. The authors have no competing interests to declare.

27
28

Author contributions:

29

GP conceived the study, built the web-survey interface, processed the results, conducted the data

30

analysis and wrote the first article draft. GP, KT and NH designed and tested the survey instrument,

31

provided comments and revisions to the drafts and approved the final version.

32
33

Biography

34

Giancarlos Parady is Assistant Professor at the Department of Urban Engineering, Graduate School

35

of Engineering, the University of Tokyo. His research interests include the relation between social

36

networks, the built environment and travel behavior, and the effects of new transport technologies on

37

urban form.

38
23

1

Kiyoshi Takami is Associate Professor at the Department of Urban Engineering, Graduate School of

2

Engineering, the University of Tokyo. His research focuses on integrated transportation and land use

3planning.

45Noboru Harata is Professor at the Department of Urban Engineering, Graduate School of Engineering,6

the University of Tokyo. His research interests include disaggregate travel demand models and7

sustainable transport planning.

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1

APPENDIX A

2Regarding the expansion coefficient calculation:

3

When calculating expansion coefficients, in addition to adjusting by accessibility strata, we controlled

4for ego sociodemographic characteristics statistically associated with social network characteristics, in5this particular case, with social network size (as measured by the name generators).

6

Table A summarizes the OLS estimation results of social network size against sociodemographic

7

characteristics of ego. There were three statistically significant variables in the model, gender, income

8and being married with children under 15 in the household.

9
10

Table A. OLS regression of social network size on sociodemographic characteristics of ego
Variable(Intercept)
Female
Age
30-39
40-49
50-59
over 60
Education
High-school and under (reference)
Technical degree
University degree and higher
Worker
IncomeUnder 3 million (reference)
3-10 million
Over 10 million
SingleMarried with children under 15 in HH
Residual standard error:
R square:Adjusted R square:

Coef.
6.594
3.963

S.E.
2.956
1.261

t-stat2.231
3.143

p-value
0.027
0.002

0.704
-3.546-3.387-1.038

2.636
2.599
2.551
2.568

0.267
-1.365-1.328-0.404

0.790
0.174
0.186
0.687

1.257
-0.122
0.691

1.663
1.469
1.592

0.756 0.451-0.083 0.934
0.434 0.665

F-statistic:

2.90 (p-value: 0.001)

2.813
1.604
5.663
2.222
-0.9671.731-5.5201.929
7.729 (170 d.f.)
0.17
0.11

1.754
2.549
-0.559-2.862

0.081
0.012
0.577
0.005

11
12

Since the population census does not include information on household income, expansion coefficients13

were calculated to match the population distribution in terms of (i) gender by accessibility sextile and14(ii) nuclear households with children under 15 years old. The sample was divided in mutually exclusive

15

classes based on these categories and expansion coefficients calculated as the inverse of the sampling

16

probability for each class1. When classes were empty in the sample they were merged with similar
1

Although as stated in the sampling strategy subsection, for practical reasons the sampling ofmunicipalities per strata was not a purely random process. However, for the purposes of the expansion
coefficient calculation, to calculate the inverse of sampling probabilities a random sampling process was29

1classes. Table B shows the class definition used. Expansion coefficients were estimated at the2individual level.

3
Table B. Mutually exclusive classes used to estimate expansion coefficients

4

Accessibility sextile

1

2

3

4

5

6

GenderMarried with children
U15 in householdAllothersFemale

1

7

Male

2

8

Female

3

9

Male

4

10

Female

5

11

Male

6

12

Female

5

13

Male

6

14

Female

5

15

Male

6

16

Female

5

17

Male

6

18

Population size: 29,657,771 (The whole Greater Tokyo Area).
Ratio of maximum to minimum weight: 6.14.
No weight trimming used.

5
6

assumed.

30

1

APPENDIX B

2Table C. Goodness of fit statistics for power law and lognormal fits using different fitting

3

methods
Power law
Distance

Lognormal

Lower bound γ

p-value Lower bound μσp-value--

MethodCutoff (km)

OLS

100

-

1.24 <0.01

-

-

100

36

4.11 <0.01

14

3.29 0.52 0.083

ML

500

19

2.07 <0.01

2

2.43 1.56 <0.01

discrete

1000

181.91 <0.01

2

2.39 1.77 <0.01

50000

16

1.78 <0.01

1

1.10 2.57 <0.01

100

35.72

4.16 <0.01

13.26

3.29 0.52 0.106

ML

500

19.03

2.08 <0.01

0.55

2.36 1.62 <0.01

continuous

1000

17.29

1.90 <0.01

0.11

2.27 1.86 <0.01

50000

15.40

1.77 <0.01

0.24

2.19 2.10 <0.01

4Note that In the ML method a statistically significant p-value suggests the data does not fit the power law

5

assumption. See Appendix C for a detailed description of the ML fitting method.

6
7

Figure A. Power law and lognormal plots using different fitting methods

31Upper-left: Power law fit using the OLS method (100km cutoff); Upper-right: Power law and lognormal fit
using the ML method (100km cutoff) – discrete fit; Bottom-left: Power law and lognormal fit using the ML
method (all distances) – discrete fit
1

32

1

APPENDIX C

2This section describes the estimation procedure for the exponent coefficient of a power-law distributed

3

variable and its goodness of fit evaluation as defined in Clauset, Shalizi and Newman (2009), and4

Barabási (2016):

5
6

1.

For a given ego-alter distance set of data k choose a value k 𝑚𝑖𝑛 < 𝐾𝑚𝑖𝑛 < 𝑘𝑚𝑎𝑥 and estimate thedegree exponent γ given 𝐾𝑚𝑖𝑛 as

7

−1

𝑁

γ = 1 + N [∑ 𝑙𝑛

8

𝑖=1

9

2.

𝑘𝑖
1
𝐾𝑚𝑖𝑛 − 2]

For the calculated pair of values (γ, K 𝑚𝑖𝑛 ), assume a probability distribution function PDF for k of
the form

10

𝑝𝑘 =

11

1
𝑘 −𝛾
𝜁(γ, K 𝑚𝑖𝑛 )

12
13

3.

Estimate the respective cumulative distribution function CDF of k as
Pk = 1 −14𝜁(γ, k)𝜁(γ, K 𝑚𝑖𝑛 )15
where 𝜁(∙) is the Hurwitz-zeta function.

16
17
18

4.

For the pair of values (γ, K 𝑚𝑖𝑛 ), use the Kolmogrov-Smirnov test to get the maximum distance D

19

between the observed data CDF S(k) and the fitted model described in the previous step, where20

D is defined as
𝐷 = max |𝑆(𝑘) − 𝑃𝑘 |21

𝑘≥𝐾𝑚𝑖𝑛22
23

5.

Find the value that minimizes D by scanning the whole range of k. The optimal fit for γ is that
where D is minimized, Dmin.

24
25
26

6.

Use the estimated optimal values of γ, K 𝑚𝑖𝑛 to generate a sequence of values ksynth following theprobability distribution function defined in step 2 and calculate Dsynth for the generated sequence.

27
28
29

7.

Repeat step 6 M times and get the distribution of Dsynth, p(Dsynth). (Note that each generated
sequence is fit to its own power law model, against which each Dsynth is calculated)

30
31
32
33

8.

A visual way to evaluate goodness of fit is to plot p(Dsynth) and plot Dmin as a vertical line. If this line
falls within the distribution p(Dsynth) then the power law is a reasonable model fit.
33

1
2

9.

A p-value can be estimated to obtain a quantitative estimate of goodness of fit. This p-value is the3

fraction of cases Dsynth that are larger than the value for the empirical data Dmin. Large p-values

4close to 1 indicate that the difference between synthetic and empirical data can be attributed to5statistical fluctuations alone. Small p-values close to 0 suggest that the fit is not plausible. Barabási

6(2016) suggests the threshold p>0.01 (that is, a share larger than 1%) to establish a plausible fit

7

for the data, while Clauset, Shalizi and Newman (2009) suggests a stricter threshold of p>0.108(that is, a share larger than 10%).

34