Minimum entropy stochastic block models neglect edge distribution heterogeneity

Abstract

The statistical inference of stochastic block models as emerged as a mathematicaly principled method for identifying communities inside networks. Its objective is to find the node partition and the block-to-block adjacency matrix of maximum likelihood i.e. the one which has most probably generated the observed network. In practice, in the so-called microcanonical ensemble, it is frequently assumed that when comparing two models which have the same number and sizes of communities, the best one is the one of minimum entropy i.e. the one which can generate the less different networks. In this paper, we show that there are situations in which the minimum entropy model does not identify the most significant communities in terms of edge distribution, even though it generates the observed graph with a higher probability.

References in corpus (13)

• Community structure in social and biological networks
• Finding and evaluating community structure in networks
• Resolution limit in community detection
• Community detection in networks: A user guide
• Modularity from Fluctuations in Random Graphs and Complex Networks
• Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications
• Phase transition in the detection of modules in sparse networks
• The Statistical Physics of Real-World Networks
• Parsimonious module inference in large networks
• Community Detection as an Inference Problem
• Nonparametric Bayesian inference of the microcanonical stochastic block model
• Entropy of stochastic blockmodel ensembles
• Phase transitions in random Potts systems and the community detection problem: spin-glass type and dynamic perspectives

Cited by in corpus (2)

• Edge based stochastic block model statistical inference
• Graph model selection by edge probability sequential inference