Synthetic Geosocial
Network Generation
Ketevan Gallagher, Taylor Anderson,
Andrew Crooks, Andreas Züfle

1Background: Synthetic Social Networks◎ Representations of people connect to one another◎ Real world data diﬀicult to find◎ Three classical models: Erdős-Rényi, Barabási-Albert,
Watts-Strogatz

2

Background: Spatial Social Network Models◎ Real-world social networks exhibit spatial homophily◎ Incorporate spatial distances between nodes
Ground TruthErdős-Rényi

Barabási-Albert

3GoalGenerate social networks that exhibit spatial
autocorrelation

4Classical Erdős-Rényi Model◎ Nodes connected randomly

5Classical Barabási-Albert Model◎ Scale free network growth◎ Preferential attachment◎ Nodes are added iteratively

6Classical Watt-Strogatz Model◎ Nodes connect to k nearest neighbors, and then havechance to rewire◎ Exhibits small-world properties

7

Existing Work
◎ Generating and Analyzing Spatial Social Networks[1]○ Assumes that nodes are in a uniform lattice○ When real-world location data is incorporated,large variety of distances leads to sparse graphs orlong runtimes[1] M. Alizadeh, C. Cioﬀi-Revilla, and A. Crooks. Generating and analyzing spatial socialnetworks. Computational and Mathematical Organization Theory, 23:362–390, 2017.

8

Spatial Erdős-Rényi Model◎ 𝑝 (𝑑) = 𝐶𝑑 −𝛼○ 𝑑: distance between nodes○ 𝐶: normalizing coeﬀicient○ 𝛼: distance-decay exponent

9Spatial Barabási-Albert Model◎ Starts with clique of 𝑚 nodes◎ 𝑝 (𝑑) = 𝑘𝑑 −𝛼○ 𝑘: degree of node being considered for connection◎ Long runtime

10

Spatial Watts-Strogatz Model◎ Two versions: initially connect based on distance, andrewire based on distance◎ Due to node IDs, random11

Geosocial Erdős-Rényi Model◎ Implemented scaling factor○ 𝑝 (𝑑) = min(1, 𝑠𝑑 −𝛼)○ 𝛼 = 3, average degree 20

12Geosocial Barabási-Albert Model◎ Node processing order◎ Normalize weights from power law◎ 103.1283 seconds vs 49.5471 seconds

13

Geosocial Watts-Strogatz Model◎ Nearest neighbors defined as nodes that are closest
spatially

14Datasets◎ Virginia ZIP code data
○ From Facebook○ Each ZIP code given Social Connectedness Index◎ Fairfax County Census Tracts○ Mobility data
○ Highest estimated population flows for 1/4/2020◎ Average degree 20, 14, 𝛼 = 315Ground Truth Graphs
Virginia ZIP code

Fairfax Census Tracts

16

Qualitative Evaluation (Virginia)

Classical ER

Classical BA

Classical WS

Spatial ER

Spatial WS

Ground Truth Geosocial ER

Geosocial BA

Geosocial WS KNN

16Qualitative Evaluation (Virginia)
Ground Truth

Geosocial Erdős-Rényi

18

Qualitative Evaluation (Fairfax County)

Classical ER

Classical BA

Classical WS

Spatial ER

Spatial WS

Ground Truth Geosocial ER

Geosocial BA

Geosocial WS KNN

20Virginia ZIP Code Statistics

21

Fairfax Census Tract Statistics

22Conclusions and Future Work◎ Geosocial Erdős-Rényi performs well when comparedto other geosocial and spatial graphs◎ Topographical distances instead of Euclidean
distances

23Acknowledgements
This work is supported by National Science Foundation
Grant #2109647 titled “Data-Driven Modeling to Improve
Understanding of Human Behavior, Mobility, and Disease
Spread” and by the Aspiring Scientists Summer Internship
Program (ASSIP) at George Mason University.
Thank you to Dr. Andrew Crooks, Dr. Taylor Anderson, andDr. Andreas Züfle