Simulating Network Influence Algorithms Using Particle-Swarms: PageRank and PageRank-Priors

A particle-swarm is a set of indivisible processing elements that traverse a network in order to perform a distributed function. This paper will describe a particular implementation of a particle-swarm that can simulate the behavior of the popular PageRank algorithm in both its {\it global-rank} and {\it relative-rank} incarnations. PageRank is compared against the particle-swarm method on artificially generated scale-free networks of 1,000 nodes constructed using a common gamma value, $\gamma = 2.5$. The running time of the particle-swarm algorithm is $O(|P|+|P|t)$ where $|P|$ is the size of the particle population and $t$ is the number of particle propagation iterations. The particle-swarm method is shown to be useful due to its ease of extension and running time.