Reconstructing the Laplacian matrix to estimate social network structure by using compressed sensing

Abstract

For complex large scale networks, like social networks, it is usually impossible to observe complete information about their topology structure or link weight directly. A recent proposal, the network resonance method, can estimate the eigenvalues and eigenvectors of the Laplacian matrix for representing network structure, by using the resonance phenomena of oscillation dynamics on networks. However, it is generally not possible to observe all the eigenvalues and eigenvectors. This paper uses compressed sensing to create a new method of reconstructing the original Laplacian matrix from a partial set of its eigenvalues and eigenvectors. Since very few node pairs in social networks have links, we can expect that compressed sensing will be effective. The estimated Laplacian matrix of a social network enables to us to determine its structure and link weights.