Abstract
It is well-known that the behavior of many dynamical processes running on networks is intimately related to the eigenvalue spectrum of the network. In this paper, we address the problem of inferring global information regarding the eigenvalue spectrum of a network from a set of local samples of its structure. In particular, we find explicit relationships between the so-called spectral moments of a graph and the presence of certain small subgraphs, also called motifs, in the network. Since the eigenvalues of the network have a direct influence on the network dynamical behavior, our result builds a bridge between local network measurements (i.e., the presence of small subgraphs) and global dynamical behavior (via the spectral moments). Furthermore, based on our result, we propose a novel decentralized scheme to compute the spectral moments of a network by aggregating local measurements of the network topology. Our final objective is to understand the relationships between the behavior of dynamical processes taking place in a large-scale complex network and its local topological properties.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.