Motif Conservation Laws for the Configuration Model

TL;DR

This paper derives conservation laws that relate motif counts within the configuration model, providing a theoretical foundation for understanding motif prevalence in networks.

Contribution

It introduces a novel theoretical framework of conservation laws linking motif counts in the configuration model, advancing network motif analysis.

Findings

Conservation laws relate motif counts in the configuration model.

Provides a theoretical basis for motif detection.

Enhances understanding of motif prevalence in networks.

Abstract

The observation that some subgraphs, called motifs, appear more often in real networks than in their randomized counterparts has attracted much attention in the scientific community. In the prevalent approach the detection of motifs is based on comparing subgraph counts in a network with their counterparts in the configuration model with the same degree distribution as the network. In this short note we derive conservation laws that relate motif counts in the configuration model.