Social-Affiliation Networks: Patterns and the SOAR Model.

Given a social-affiliation network – a friendship graph where users have many, binary attributes e.g., check-ins, page likes or group memberships – what rules do its structural properties such as edge or triangle counts follow, in relation to its attributes? More challengingly, how can we synthetically generate networks which provably satisfy those rules or patterns? Our work attempts to answer these closely-related questions in the context of the increasingly prevalent social-affiliation graphs. Our contributions are two-fold: (a) Patterns: we discover three new rules (power laws) in the properties of attribute-induced subgraphs, substructures which connect the friendship structure to affiliations; (b) Model: we propose SOAR– short for SOcial-Affiliation graphs via Recursion– a stochastic model based on recursion and self-similarity, to provably generate graphs obeying the observed patterns. Experiments show that: (i) the discovered rules are useful in detecting deviations as anomalies and (ii) SOAR is fast and scales linearly with network size, producing graphs with millions of edges and attributes in only a few seconds. Code related to this paper is available at: www.github.com/dhivyaeswaran/soar.