Identifying network structure similarity using spectral graph theory

• Main Authors: Ralucca Gera, L. Alonso, Brian Crawford, Jeffrey House, J. A. Mendez-Bermudez, Thomas Knuth, Ryan Miller
• Format: Article
• Language: English
• Published: SpringerOpen 2018-01-01
• Series: Applied Network Science
• Subjects: Network topology; Graph comparison metrics; Laplacian; Eigenvalue distribution; Kolmogorov-Smirnov test
• Online Access: http://link.springer.com/article/10.1007/s41109-017-0042-3

Abstract Most real networks are too large or they are not available for real time analysis. Therefore, in practice, decisions are made based on partial information about the ground truth network. It is of great interest to have metrics to determine if an inferred network (the partial information network) is similar to the ground truth. In this paper we develop a test for similarity between the inferred and the true network. Our research utilizes a network visualization tool, which systematically discovers a network, producing a sequence of snapshots of the network. We introduce and test our metric on the consecutive snapshots of a network, and against the ground truth. To test the scalability of our metric we use a random matrix theory approach while discovering Erdös-Rényi graphs. This scaling analysis allows us to make predictions about the performance of the discovery process.