Influence maximization (IM) aims to find a group of influential nodes as initial spreaders to maximize the influence spread over a network. Yet, traditional IM algorithms have not been designed with fairness in mind, resulting in discrimination against some groups, like LGBTQ communities and racial minorities. This issue has spurred research on Fair Influence Maximization (FIM). However, existing FIM studies come with some drawbacks. First, most proposed notions of fairness for FIM cannot adjust the tradeoff between fairness level and influence spread. Second, though a few specific notions of fairness allow such balancing, they are limited to a few specific concave functions, which may not be suitable for various real-world scenarios. Furthermore, none of them have studied the deep relations between the features of concave functions and the level of fairness. Third, existing fairness metrics are limited to their corresponding concepts of fairness. Comparing the level of fairness across different algorithms using existing metrics can be challenging. To tackle the above problems, this article first proposes a novel fairness notion named Poverty Reward (PR), which achieves fairness by rewarding the enrichment of groups with low utility. Based on PR, we further propose an algorithmic framework called Concave Fairness Framework (CFF) that allows any concave function that satisfies specific requirements. We also systematically clarify how fairness is improved by applying concave functions and provide an in-depth quantitative analysis of how to select appropriate concave functions for different utility distributions. Moreover, we propose the Reward of Fairness (RoF) metric that evaluates the disparity between groups. Based on RoF, an evaluation system is built to uniformly compare FIM algorithms from different fairness notions. Experiments in real-world datasets have demonstrated the validity of the CFF, as well as the proposed fairness notion.

This paper studies the fair influence maximization problem with efficient algorithms. In particular, given a graph G, a community structure C consisting of disjoint communities, and a budget k, the problem asks to select a seed set S (|S| = k) that maximizes the influence spread while narrowing the influence gap between different communities. This problem derives from some significant social scenarios, such as health interventions (e.g. suicide/HIV prevention) where individuals from racial minorities or LGBTQ communities may be disproportionately excluded from the benefits of the intervention. To depict the concept of fairness in the context of influence maximization, researchers have proposed various notions of fairness, where the welfare fairness notion that better balances fairness level and influence spread has shown promising effectiveness. However, the lack of efficient algorithms for optimizing the objective function under welfare fairness restricts its application to networks of only a few hundred nodes. In this paper, we modify the objective function of welfare fairness to maximize the exponentially weighted sum and the logarithmically weighted sum over all communities' influenced fractions (utility). To achieve efficient algorithms with theoretical guarantees, we first introduce two unbiased estimators: one for the fractional power of the arithmetic mean and the other for the logarithm of the arithmetic mean. Then, by adapting the Reverse Influence Sampling (RIS) approach, we convert the optimization problem to a weighted maximum coverage problem. We also analyze the number of reverse reachable sets needed to approximate the fair influence at a high probability. Finally, we present an efficient algorithm that guarantees 1 − 1/e − ϵ (positive objective function) or 1 + 1/e + ϵ (negative objective function) approximation for any small ϵ > 0. Experiments demonstrate that our proposed algorithm could efficiently handle large-scale networks with good performance.

In this paper, we study the adversarial attacks on influence maximization under dynamic influence propagation models in social networks. In particular, given a known seed set S, the problem is to minimize the influence spread from S by deleting a limited number of nodes and edges. This problem reflects many application scenarios, such as blocking virus (e.g. COVID-19) propagation in social networks by quarantine and vaccination, blocking rumor spread by freezing fake accounts, or attacking competitor's influence by incentivizing some users to ignore the information from the competitor. In this paper, under the linear threshold model, we adapt the reverse influence sampling approach and provide efficient algorithms of sampling valid reverse reachable paths to solve the problem. We present three different design choices on reverse sampling, which all guarantee 1/2 - ε approximation (for any small ε >0) and an efficient running time.

The influence are not linked to any footnote in the text. Please check and suggest. maximization problem aims at selecting the k most influential nodes (i.e., seed nodes) from a social network, where the nodes can maximize the number of influenced nodes activated by a certain propagation model. However, the widely used Independent Cascade model shares the same propagation probability among substantial adjacent node pairs, which is too idealistic and unreasonable in practice. In addition, most heuristic algorithms for influence maximization need to update the expected influence of the remaining nodes in the seed selection process, resulting in high computation cost. To address these non-trivial problems, we propose a novel edge propagation probability calculation method. The method first utilizes the triadic closure structure of social networks to precisely measure the closeness between nodes and assigns different propagation probabilities to each edge, deriving a Triadic Closure-based Independent Cascade (TC-IC) model. Then, we further propose a heuristic influence maximization algorithm named Triadic Closure-based Influence Maximization (TC-IM). The algorithm evaluates the expected influence of a node by integrating the triadic closure weighted propagation probability and the triadic closure weighted degree. Especially, in the seed selection process, only the most influential node that has not been updated in the current round needs to be updated, which significantly improves the efficiency. Besides, we further provide theoretical proofs to guarantee the correctness of this updating strategy. Experimental results on nine real datasets and three propagation models demonstrate that: (1) The TC-IC model can set a proper propagation probability for each node pair, where the IM algorithms could easily identify influential nodes; (2) The TC-IM algorithm can significantly reduce the complexity through an efficient updating strategy with a comparable influence spread to the approximation IM algorithms; (3) Besides, the TC-IM algorithm also exhibits stable performance under other IC models including UIC and WIC, exhibiting good stability and generality.