A Pressure-Based Diffusion Model for Influence Maximization on Social Networks

TL;DR

This paper introduces the Pressure Threshold (PT) diffusion model, an extension of the Linear Threshold (LT) framework that models reinforcement by amplifying a node’s outgoing influence in proportion to the pressure received at activation. PT preserves monotonicity but is not generally submodular for $\alpha>0$, and it remains NP-hard to optimize the final spread, with LT recovered when $\alpha=0$. The authors implement PT in the CyNetDiff framework and demonstrate through extensive experiments on real and synthetic networks that PT yields seed sets and diffusion outcomes that differ from LT and exhibit stronger amplification in denser graphs. They also show that a small $\alpha$ yields near-LT behavior with approximate submodularity, while larger values reveal pronounced reinforcement effects, underscoring the importance of modeling local reinforcement for realistic diffusion and seed-selection strategies.

Abstract

In many real-world scenarios, an individual's local social network carries significant influence over the opinions they form and subsequently propagate. In this paper, we propose a novel diffusion model -- the Pressure Threshold model (PT) -- for dynamically simulating the spread of influence through a social network. This model extends the popular Linear Threshold (LT) model by adjusting a node's outgoing influence in proportion to the influence it receives from its activated neighbors. We examine the Influence Maximization (IM) problem under this framework, which involves selecting seed nodes that yield maximal graph coverage after a diffusion process, and describe how the problem manifests under the PT model. Experiments on real-world networks, supported by enhancements to the open-source network-diffusion library CyNetDiff, reveal that the PT model identifies seed sets distinct from those chosen by LT. Furthermore, the analyses show that densely connected networks amplify pressure effects far more strongly than sparse networks.

Figures (8)

• Figure 1: Early diffusion stages under PT and LT on the same graph and seed set. Activated nodes are shown in red, newly activated nodes are outlined in black, and amplified edges are highlighted in red.
• Figure 2: Later diffusion stages under PT and LT. PT keeps on amplifying edges and attains full coverage, while LT halts sooner.
• Figure 3: Timeline of seed‑node selection by the CELF algorithm on the Facebook network: PT vs. LT ($k=20$). Horizontal alignment indicates step index; vertical lines connect common seeds appearing in both lists. Early steps overlap strongly; later steps diverge as PT prioritizes nodes positioned to benefit from reinforcement.
• Figure 4: Bitcoin Network: average influence vs. budget. PT’s advantage is present but smaller due to network sparsity and lower local clustering.
• Figure 5: Facebook Network: average influence vs. budget. PT curves exceed LT across budgets; the effect is more pronounced for higher $\alpha$.

Theorems & Definitions (10)

• Theorem 1
• proof
• Remark : Decision vs. optimization
• Corollary 1: Inapproximability inherited at $\alpha=0$
• Theorem 2: Monotonicity of PT
• proof
• Remark
• Proposition 1: PT is not submodular in general
• proof
• Remark