Structural Aspects of
Massive Social Networks

Outline

Epidemiological Simulation System: EpiSims

Slide 4

Urban Infrastructure Suite

Why Agent Based?

Demand-driven Interdependence

Components of EpiSims

Synthetic Population: Typical Household

Typical Household’s Day

Others Use the Same Locations

Time Slice of a Typical Household’s Day

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Structural Analysis Goals

Structural Analysis Problems

What is “the” social network?

Social Network: bipartite labeled graph

Social Network: bipartite labeled graph

Social Network: bipartite labeled graph

Social Network: bipartite labeled graph

Social Network: bipartite labeled graph

Social Network: bipartite labeled graph

Social Network: explicitly time dependent form

Distance 2 induced graphs

A Social Network: projection onto people

A Social Network: people-people graph

A Social Network: people-people graph

Social Network: location-location graph

Social Network: location-location graph

Social Network: location-location graph

Static graphs

A Social Network: static people-people graph

Social Network: static location-location graph

Measurements on static graphs

Degree distributions for static graphs

Measurements on static graphs

Clustering by degree for static graphs

Measurements on static graphs

Measures of Centrality

Measures of Centrality, cont’d

Measures of Centrality, cont’d

Measurements on static graphs

Local Network Topology

Local Network Topology

Local Network Topology

Local Network Topology

Local Network Topology

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Slide 49

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Local topology variability

Size of giant component vs
degree of people vaccinated

Fraction of people in giant component vs fraction of locations closed

Measurements on static graphs

Dominating Set

Generating Random Social Networks:
The Chung-Lu Model for the Full Bipartite Graph

Chung-Lu vs Episims data

Chung-Lu vs Episims data

Degree Distribution of locations
in Bipartite Graph

Degree Distribution in people-people graph

Clustering Coefficient

Dominating Set

Summary