A New Computationally Efficient Measure of Topological Redundancy of Biological and Social Networks

TL;DR

This paper introduces a new, efficient topological redundancy measure for directed networks, enabling analysis of biological and social networks to reveal differences in redundancy and their relation to network dynamics.

Contribution

It presents a formal, computationally efficient redundancy measure applicable to various directed networks, with insights into biological and social network structures.

Findings

Social networks are more redundant than biological networks.

Transcriptional networks are less redundant than signaling networks.

Redundancy in C. elegans metabolic network is due to currency metabolites.

Abstract

It is well-known that biological and social interaction networks have a varying degree of redundancy, though a consensus of the precise cause of this is so far lacking. In this paper, we introduce a topological redundancy measure for labeled directed networks that is formal, computationally efficient and applicable to a variety of directed networks such as cellular signaling, metabolic and social interaction networks. We demonstrate the computational efficiency of our measure by computing its value and statistical significance on a number of biological and social networks with up to several thousands of nodes and edges. Our results suggest a number of interesting observations: (1) social networks are more redundant that their biological counterparts, (2) transcriptional networks are less redundant than signaling networks, (3) the topological redundancy of the C. elegans metabolic network is largely due to its inclusion of currency metabolites, and (4) the redundancy of signaling networks is highly (negatively) correlated with the monotonicity of their dynamics.