Using Node Centrality and Optimal Control to Maximize Information Diffusion in Social Networks

TL;DR

This paper develops an optimal control framework to maximize information spread in social networks by combining node centrality measures and resource allocation strategies, demonstrating the effectiveness of degree centrality.

Contribution

It introduces a novel optimal control approach that integrates centrality-based influence and resource optimization for information dissemination in social networks.

Findings

Degree centrality performs well in spreading messages across networks.

Targeting central nodes is optimal when resources are limited.

Non-central nodes are targeted when resources are abundant.

Abstract

We model information dissemination as a susceptible-infected epidemic process and formulate a problem to jointly optimize seeds for the epidemic and time varying resource allocation over the period of a fixed duration campaign running on a social network with a given adjacency matrix. Individuals in the network are grouped according to their centrality measure and each group is influenced by an external control function---implemented through advertisements---during the campaign duration. The aim is to maximize an objective function which is a linear combination of the reward due to the fraction of informed individuals at the deadline, and the aggregated cost of applying controls (advertising) over the campaign duration. We also study a problem variant with a fixed budget constraint. We set up the optimality system using Pontryagin's Maximum Principle from optimal control theory and solve it numerically using the forward-backward sweep technique. Our formulation allows us to compare the performance of various centrality measures (pagerank, degree, closeness and betweenness) in maximizing the spread of a message in the optimal control framework. We find that degree---a simple and local measure---performs well on the three social networks used to demonstrate results: scientific collaboration, Slashdot and Facebook. The optimal strategy targets central nodes when the resource is scarce, but non-central nodes are targeted when the resource is in abundance. Our framework is general and can be used in similar studies for other disease or information spread models---that can be modeled using a system of ordinary differential equations---for a network with a known adjacency matrix.