Network synchronizability analysis: the theory of subgraphs and complementary graphs

TL;DR

This paper introduces a novel theoretical framework using subgraphs and complementary graphs to analyze and bound the synchronizability of complex networks, especially those with specific subgraph structures.

Contribution

It provides new sharp bounds for the eigenratio of the network's structural matrix, enhancing understanding of network synchronizability with various subgraph configurations.

Findings

Derived sharp bounds for eigenratio related to network synchronizability

Analyzed networks with cycles, chains, bipartite, and product subgraphs

Enhanced theoretical understanding of network synchronization properties

Abstract

In this paper, subgraphs and complementary graphs are used to analyze the network synchronizability. Some sharp and attainable bounds are provided for the eigenratio of the network structural matrix, which characterizes the network synchronizability, especially when the network's corresponding graph has cycles, chains, bipartite graphs or product graphs as its subgraphs.