[Paper Review] Influence Spread in Large-Scale Social Networks - A Belief Propagation Approach

Huy Nguyen, Rong Zheng|arXiv (Cornell University)|Apr 19, 2012

Bayesian Modeling and Causal Inference10 citations

TL;DR

This paper proposes a belief propagation-based approach to efficiently compute influence spread in large-scale social networks, overcoming computational bottlenecks in greedy influence maximization. By modeling influence diffusion as belief propagation on a directed acyclic graph, the method enables fast, accurate estimation of influence spread without Monte Carlo simulations, achieving high performance with moderate computational cost on real-world networks with up to millions of edges.

ABSTRACT

Abstract. Influence maximization is the problem of finding a small set of seed nodes in a social network that maximizes the spread of influence under a certain diffusion model. The Greedy algorithm for influence maximization first proposed by Kempe, later improved by Leskovec suffers from two sources of computational deficiency: 1) the need to evaluate many candidate nodes before selecting a new seed in each round, and 2) the calculation of the influence spread of any seed set relies on Monte-Carlo simulations. In this work, we tackle both problems by devising efficient algorithms to compute influence spread and determine the best candidate for seed selection. The fundamental insight behind the proposed algorithms is the linkage between influence spread determination and belief propagation on a directed acyclic graph (DAG). Experiments using real-world social network graphs with scales ranging from thousands to millions of edges demonstrate the superior performance of the proposed algorithms with moderate computation costs. 1

Motivation & Objective

• To address the computational inefficiency of greedy influence maximization algorithms that rely on costly Monte Carlo simulations.
• To reduce the number of candidate evaluations per seeding round by enabling fast influence spread estimation.
• To develop a scalable method for influence spread computation that maintains accuracy on large real-world social networks.
• To establish a theoretical and computational link between influence diffusion and belief propagation on directed acyclic graphs.

Proposed method

• The method models influence diffusion as belief propagation on a directed acyclic graph (DAG) derived from the social network structure.
• It leverages the local structure of the DAG to compute influence spread using message-passing updates that propagate influence probabilities forward.
• The influence spread of a seed set is computed by aggregating belief values at the leaf nodes of the DAG, avoiding repeated Monte Carlo simulations.
• The algorithm efficiently identifies the best seed node in each round by ranking candidates based on their computed influence spread via belief propagation.
• The approach exploits the conditional independence properties of the DAG to enable linear-time influence estimation per candidate node.
• The method is designed to scale to networks with thousands to millions of edges, maintaining low computational overhead.

Experimental results

Research questions

• RQ1 Can belief propagation on a DAG accurately approximate influence spread in social networks without Monte Carlo simulations?
• RQ2 How does the proposed method reduce the computational cost of influence maximization compared to greedy algorithms with Monte Carlo evaluation?
• RQ3 To what extent does the belief propagation approach maintain accuracy in influence spread estimation across diverse real-world network topologies?
• RQ4 Can the method efficiently identify high-impact seed nodes with fewer evaluations per round than traditional greedy approaches?
• RQ5 How does the method scale in performance and accuracy when applied to large-scale networks with up to millions of edges?

Key findings

• The belief propagation approach achieves high accuracy in influence spread estimation, closely matching results from Monte Carlo simulations without requiring repeated sampling.
• The method significantly reduces computational cost per influence evaluation, enabling faster seed selection in each round of the greedy algorithm.
• The algorithm scales effectively to large networks, demonstrating moderate computation costs even on graphs with up to millions of edges.
• By replacing Monte Carlo simulations with message-passing on a DAG, the method eliminates the stochastic variance inherent in simulation-based estimation.
• Experiments on real-world social networks show that the proposed approach outperforms existing methods in terms of influence spread while maintaining low computational overhead.
• The linkage between influence diffusion and belief propagation enables efficient, deterministic computation of influence spread, making large-scale influence maximization practical.