Collective Influence Algorithm to find influencers via optimal percolation in massively large social media

TL;DR

This paper presents a linear-time implementation of the Collective Influence algorithm for identifying key influencers in large social networks, compares it with extended variants, and discusses their computational feasibility for big data.

Contribution

It introduces a scalable linear-time CI algorithm, extends it with CI_P and CI_BP variants, and analyzes their performance and computational complexity on massive social media data.

Findings

CI algorithm runs in O(N log N) time, suitable for large networks.

CI_P and CI_BP achieve marginally better influence detection but are computationally intensive.

For social networks of hundreds of millions of users, CI is practical while BP variants are infeasible.

Abstract

We elaborate on a linear time implementation of the Collective Influence (CI) algorithm introduced by Morone, Makse, Nature 524, 65 (2015) to find the minimal set of influencers in a network via optimal percolation. We show that the computational complexity of CI is O(N log N) when removing nodes one-by-one, with N the number of nodes. This is made possible by using an appropriate data structure to process the CI values, and by the finite radius l of the CI sphere. Furthermore, we introduce a simple extension of CI when l is infinite, the CI propagation (CI_P) algorithm, that considers the global optimization of influence via message passing in the whole network and identifies a slightly smaller fraction of influencers than CI. Remarkably, CI_P is able to reproduce the exact analytical optimal percolation threshold obtained by Bau, Wormald, Random Struct. Alg. 21, 397 (2002) for cubic random regular graphs, leaving little improvement left for random graphs. We also introduce the Collective Immunization Belief Propagation algorithm (CI_BP), a belief-propagation (BP) variant of CI based on optimal immunization, which has the same performance as CI_P. However, this small augmented performance of the order of 1-2 % in the low influencers tail comes at the expense of increasing the computational complexity from O(N log N) to O(N^2 log N), rendering both, CI_P and CI_BP, prohibitive for finding influencers in modern-day big-data. The same nonlinear running time drawback pertains to a recently introduced BP-decimation (BPD) algorithm by Mugisha, Zhou, arXiv:1603.05781. For instance, we show that for big-data social networks of typically 200 million users (eg, active Twitter users sending 500 million tweets per day), CI finds the influencers in less than 3 hours running on a single CPU, while the BP algorithms (CI_P, CI_BP and BDP) would take more than 3,000 years to accomplish the same task.