Neural computation, social networks, and topological spectra

This paper emphasizes some intriguing links between neural computation on graphical domains and social networks, like those used in nowadays search engines to score the page authority. It is pointed out that the introduction of web domains creates a unified mathematical framework for these computational schemes. It is shown that one of the major limitations of currently used connectionist models, namely their scarce ability to capture the topological features of patterns, can be effectively faced by computing the node rank according to social-based computation, like Google's PageRank. The main contribution of the paper is the introduction of a novel graph spectral notion, which can be naturally used for the graph isomorphism problem. In particular, a class of graphs is introduced for which the problem is proven to be polynomial. It is also pointed out that the derived spectral representations can be nicely combined with learning, thus opening the doors to many applications typically faced within the framework of neural computation. (C) 2004 Published by Elsevier B.V.