Sound of Network: Capturing Network Structure by Signal Response

Structural analysis of networks has attracted a lot of attention from researchers. While previous studies have devised structural indices for quantitatively describing network structures, they mostly focus on specific structural characteristics and the structural information provided by them is often fragmental. This paper proposes methods for representing and analyzing structural characteristics of networks that provide a comprehensive understanding of network structure. It describes a new approach for grasping the structural features of networks, wherein a signal is input at a vertex of a given network, and the signal propagates through the network and eventually returns to the input vertex through various routes. The returning signal at the input vertex can be thought of as the response of the network to the input signal and can be used as a representation of the structural characteristics of the network that can be analyzed using existing signal analysis techniques. The paper also describes experiments examining the properties of response signals in artificial networks and presents a method for identifying the structural characteristics of a network by analyzing its response signal.