Exploring Edge Probability Graph Models Beyond Edge Independency: Concepts, Analyses, and Algorithms
Keywords: Random graph models, edge dependency, triangle density, subgraph densities, tractability, variability
TL;DR: We explore edge probability graph models (EPGMs) beyond edge independency, and show that realization beyond edge independence can produce more realistic structures while maintaining high tractability and variability.
Abstract: Desirable random graph models (RGMs) should
*(i)* reproduce *common patterns* in real-world graphs (e.g., high clustering),
*(ii)* generate *variable* (i.e., not overly similar) graphs, and
*(iii)* remain *tractable* to compute and control graph statistics.
A common class of RGMs (e.g., Erd\H{o}s-R\'{e}nyi and stochastic Kronecker) outputs edge probabilities, and we need to realize (i.e., sample from) the edge probabilities to generate graphs.
Typically, each edge's existence is assumed to be determined independently for simplicity and tractability.
However, with edge independency, RGMs theoretically cannot produce high subgraph densities and high output variability simultaneously.
In this work, we explore realization beyond edge independence that can better reproduce common patterns while maintaining high tractability and variability.
Theoretically, we propose an edge-dependent realization framework called *binding* that provably preserves output variability, and derive *closed-form* tractability results on subgraph (e.g., triangle) densities in generated graphs.
Practically, we propose algorithms for graph generation with binding and parameter fitting of binding.
Our empirical results demonstrate that binding exhibits high tractability and well reproduce patterns such as high clustering, significantly improving upon existing RGMs assuming edge independency.
Supplementary Material: zip
Primary Area: learning on graphs and other geometries & topologies
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Submission Number: 8381
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