The rank convergence of HITS can be slow

TL;DR

This paper demonstrates that the convergence of the HITS algorithm's rank can be extremely slow, requiring exponentially many iterations to accurately rank top nodes in large graphs, even with optimization tricks.

Contribution

It provides a self-contained proof showing the potential exponential slowdowns in HITS convergence without relying on algebraic methods.

Findings

HITS may need exponential iterations to accurately rank top nodes

Convergence speed can be severely limited in large graphs

Even optimized methods like squaring tricks do not guarantee fast convergence

Abstract

We prove that HITS, to "get right" h of the top k ranked nodes of an N>=2k node graph, can require h^(Omega(N h/k)) iterations (i.e. a substantial Omega(N h log(h)/k) matrix multiplications even with a "squaring trick"). Our proof requires no algebraic tools and is entirely self-contained.