A Community-Aware Framework for Influence Maximization with Explicit Accounting for Inter-Community Influence

Influence Maximization (IM) seeks to identify a small set of seed nodes in a social network to maximize expected information spread under a diffusion model. While community-based approaches improve scalability by exploiting modular structure, they typically assume independence between communities, overlooking inter-community influence$\unicode{x2014}$a limitation that reduces effectiveness in real-world networks. We introduce Community-IM++, a scalable framework that explicitly models cross-community diffusion through a principled heuristic based on community-based diffusion degree (CDD) and a progressive budgeting strategy. The algorithm partitions the network, computes CDD to prioritize bridging nodes, and allocates seeds adaptively across communities using lazy evaluation to minimize redundant computations. Experiments on large real-world social networks under different edge weight models show that Community-IM++ achieves near-greedy influence spread at up to 100 times lower runtime, while outperforming Community-IM and degree heuristics across budgets and structural conditions. These results demonstrate the practicality of Community-IM++ for large-scale applications such as viral marketing, misinformation control, and public health campaigns, where efficiency and cross-community reach are critical.

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

In many real-world scenarios, an individual's local social network carries significant influence over the opinions they form and subsequently propagate to others. 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 new model extends the popular Linear Threshold Model (LT) by adjusting a node's outgoing influence proportional to the influence it receives from its activated neighbors. We address the Influence Maximization (IM) problem, which involves selecting the most effective seed nodes to achieve maximal graph coverage after a diffusion process, and how the problem manifests with the PT Model. Experiments conducted on real-world networks, facilitated by enhancements to the open-source network-diffusion Python library, CyNetDiff, demonstrate unique seed node selection for the PT Model when compared to the LT Model. Moreover, analyses demonstrate that densely connected networks amplify pressure effects more significantly than sparse networks.

Fractional Budget Allocation for Influence Maximization under General Marketing Strategies

We consider the fractional influence maximization problem, i.e., identifying users on a social network to be incentivized with potentially partial discounts to maximize the influence on the network. The larger the discount given to a user, the higher the likelihood of its activation (adopting a new product or innovation), who then attempts to activate its neighboring users, causing a cascade effect of influence through the network. Our goal is to devise efficient algorithms that assign initial discounts to the network's users to maximize the total number of activated users at the end of the cascade, subject to a constraint on the total sum of discounts given. In general, the activation likelihood could be any non-decreasing function of the discount, whereas, our focus lies on the case when the activation likelihood is an affine function of the discount, potentially varying across different users. As this problem is shown to be NP-hard, we propose and analyze an efficient (1-1/e)-approximation algorithm. Furthermore, we run experiments on real-world social networks to show the performance and scalability of our method.

CyNetDiff -- A Python Library for Accelerated Implementation of Network Diffusion Models

In recent years, there has been increasing interest in network diffusion models and related problems. The most popular of these are the independent cascade and linear threshold models. Much of the recent experimental work done on these models requires a large number of simulations conducted on large graphs, a computationally expensive task suited for low-level languages. However, many researchers prefer the use of higher-level languages (such as Python) for their flexibility and shorter development times. Moreover, in many research tasks, these simulations are the most computationally intensive task, so it would be desirable to have a library for these with an interface to a high-level language with the performance of a low-level language. To fill this niche, we introduce CyNetDiff, a Python library with components written in Cython to provide improved performance for these computationally intensive diffusion tasks.