Ranking influential nodes in networks from partial information

TL;DR

This paper introduces a low-rank approximation method that uses local neighborhood information to accurately estimate node influence in various complex networks, reducing the need for complete interaction data.

Contribution

It presents a novel framework leveraging local information and low-rank approximation to estimate node influence across diverse network types, bypassing full network reconstruction.

Findings

High accuracy in estimating influence in WWW PageRank, ecosystems, and social networks.

Effective when networks are not exceedingly sparse.

Implications for calculating non-linear network observables.

Abstract

Many complex systems exhibit a natural hierarchy in which elements can be ranked according to a notion of "influence". While the complete and accurate knowledge of the interactions between constituents is ordinarily required for the computation of nodes' influence, using a low-rank approximation we show that in a variety of contexts local information about the neighborhoods of nodes is enough to reliably estimate how influential they are, without the need to infer or reconstruct the whole map of interactions. Our framework is successful in approximating with high accuracy different incarnations of influence in systems as diverse as the WWW PageRank, trophic levels of ecosystems, upstreamness of industrial sectors in complex economies, and centrality measures of social networks, as long as the underlying network is not exceedingly sparse. We also discuss the implications of this "emerging locality" on the approximate calculation of non-linear network observables.