Graph theory has become a powerful tool in obtaining valuable information in various disciplines such as physics, biology, and engineering. With increasing amount of data, the sizes of graphs/networks range from dozens to millions of nodes resulting in sparse or dense matrices. Graph spectra of matrices can provide local, as well as global perspectives of the system. As will be presented, we have recently developed a method to compare different networks by studying the spectrum of normalized Laplacian matrix. The method is applicable to weighted matrices, thus enabling us to represent realistic edge weights.
The structure-function relationship in proteins is an extensively studied topic. Although several advances are made from experimental and computational front, more insights are needed at various levels. For instance, the protein structures can be very similar when bound to ligands involved in different functions. Or the mechanism of allosteric communication may also be associated with no change in apparent structure of the protein. As will be discussed, the spectral analysis of weighted Laplacian provides some of the elusive information, such as subtle differences in node clustering arising due to small differences in edge weights in different parts of the network.
The talk provides some details of the method and the development of Network Similarity Score (NSS). Further, the application of NSS for protein model validation and the effect of ligand binding in GPCR family of proteins will be discussed.