# Maximum Entropy

Hub

### The hub of maximum-entropy null models

for network randomization

by J. van Lidth de Jeude

Language: Python 3.5

Last update: 3 December 2018

Networks: binary, directed and undirected

Null-model: hypergeometric for bimodular structures

Paper: J. van Lidth de Jeude et al. (2019) EPL 125, 6

Notes: method to detect statistically significant bimodular structures, i.e. either bipartite or core-periphery ones. It is based on a modification of the so-called "surprise" metric proposed for detecting communities in networks. The present variant allows for bimodular node partitions to be revealed, by letting links to be placed either 1) within the core part and between the core and the periphery parts or 2) just between the (empty) layers of a bipartite network.

The bicm module is an implementation of the Bipartite Configuration Model (BiCM) as described in the article Saracco et al, 2016. The BiCM can be used as a statistical null model to analyze the similarity of nodes in undirected bipartite networks. The similarity criterion is based on the number of common neighbors of nodes, which is expressed in terms of Λ-motifs in the original article Saracco et al, 2016. Subsequently, one can obtain unbiased statistically validated monopartite projections of the original bipartite network.

The construction of the BiCM, just like the related BiPCM and BiRG models, is based on the generation of a grand canonical ensemble of bipartite graphs subject to certain constraints. The constraints can be of different types. For instance, in the case of the BiCM the average degrees of the nodes of the input network are fixed. In the BiRG, on the other hand, the total number of edges is constrained. In general, these models are referred to as entropy-based null models.

The average graph of the ensemble can be calculated analytically using the entropy-maximization principle and provides a statistical null model, which can be used for establishing statistically significant node similarities. For more information and a detailed explanation of the underlying methods, please refer to Saracco et al, 2016.

By using the bicm module, the user can obtain the BiCM null model which corresponds to the input matrix representing an undirected bipartite network. To address the question of node similarity, the p-values of the observed numbers of common neighbors (i.e. of the Λ-motifs) can be calculated and used for statistical verification.

(from the repository description)