Equitable random graphs

Abstract

Random graph models have played a dominant role in the theoretical study of networked systems. The Poisson random graph of Erdos and Renyi, in particular, as well as the so-called configuration model, have served as the starting point for numerous calculations. In this paper we describe another large class of random graph models, which we call equitable random graphs and which are flexible enough to represent networks with diverse degree distributions and many nontrivial types of structure, including community structure, bipartite structure, degree correlations, stratification, and others, yet are exactly solvable for a wide range of properties in the limit of large graph size, including percolation properties, complete spectral density, and the behavior of homogeneous dynamical systems, such as coupled oscillators or epidemic models.

5 pages, 2 figures

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• Spectral Planting and the Hardness of Refuting Cuts, Colorability, and Communities in Random Graphs
• A class of network models recoverable by spectral clustering
• Symmetry-driven network reconstruction through pseudobalanced coloring optimization
• Spectral partitioning in equitable graphs
• Sparse Random Block Matrices
• Spectral density of equitable core-periphery graphs
• Reconstruction of evolved dynamic networks from degree correlations
• Uniqueness of communities in regular stochastic block models
• Nonreciprocal random networks and their percolation properties