Structure and function in flow networks

TL;DR

This paper introduces an analytical framework linking structure and function in flow networks, enabling the study of network resilience and community detection through voltage solutions and effective topology transformations.

Contribution

It provides a unified analytical approach to relate network structure with flow function, including methods for assessing resilience and community detection.

Findings

Analytical solution for voltages in resistor networks

Transformation of network structure to effective all-to-all topology

Methods for assessing structural resilience and community detection

Abstract

This Letter presents a unified approach for the fundamental relationship between structure and function in flow networks by solving analytically the voltages in a resistor network, transforming the network structure to an effective all-to-all topology, and then measuring the resultant flows. Moreover, it defines a way to study the structural resilience of the graph and to detect possible communities.