Motif analysis in directed ordered networks and applications to food webs

TL;DR

This paper extends motif analysis to ordered networks, revealing hierarchical structures in food webs and other natural networks by identifying all ordered 3-node substructures and their significance.

Contribution

It introduces a new method for analyzing hierarchical motifs in ordered networks, applicable to empirical food webs and multi-layered networks.

Findings

Hierarchical motifs are significant in food webs.

Ordered motif spectrum provides detailed structural insights.

Method enhances understanding of complex natural networks.

Abstract

The analysis of small recurrent substructures, so called network motifs, has become a standard tool of complex network science to unveil the design principles underlying the structure of empirical networks. In many natural systems network nodes are associated with an intrinsic property according to which they can be ordered and compared against each other. Here, we expand standard motif analysis to be able to capture the hierarchical structure in such ordered networks. Our new approach is based on the identification of all ordered 3-node substructures and the visualization of their significance profile. We present a technique to calculate the fine grained motif spectrum by resolving the individual members of isomorphism classes (sets of substructures formed by permuting node-order). We apply this technique to computer generated ensembles of ordered networks and to empirical food web data, demonstrating the importance of considering node order for food-web analysis. Our approach may not only be helpful to identify hierarchical patterns in empirical food webs and other natural networks, it may also provide the base for extending motif analysis to other types of multi-layered networks.