Recursive Node Similarity in Networked Information Spaces

Abstract

The link structure of a networked information space can be used to estimate similarity between nodes. A recursive definition of similarity arises naturally: two nodes are judged to be similar if they have similar neighbours. Quantifying similarity defined in this manner is challenging due to the tendency of the system to converge to a single point (i.e. all pairs of nodes are completely similar).

We present an embedding of undirected graphs into R ⁿ based on recursive node similarity which solves this problem by defining an iterative procedure that converges to a non-singular embedding. We use the spectral decomposition of the normalized adjacency matrix to find an explicit expression for this embedding, then show how to compute the embedding efficiently by solving a sparse system of linear equations.