Individuals may have a range of opinions on controversial topics. However, the ease of making friendships in online social networks tends to create groups of like-minded individuals, who propagate messages that reinforce existing opinions and ignore messages expressing opposite opinions. This creates a situation where there is a decrease in the diversity of messages to which users are exposed ( diversity of exposure ). This means that users do not easily get the chance to be exposed to messages containing alternative viewpoints; it is even more unlikely that they forward such messages to their friends. Increasing the chance that such messages are propagated implies that an individuals’ susceptibility to persuasion is increased, something that may ultimately increase the diversity of messages to which users are exposed. This article formulates a novel problem which aims to identify a small set of users for whom increasing susceptibility to persuasion maximizes the diversity of exposure of all users in the network. We study the properties of this problem and develop a method to find a solution with an approximation guarantee. For this, we first prove that the problem is neither submodular nor supermodular and then we develop submodular bounds for it. These bounds are used in the Sandwich framework to propose a method which approximates the solution using reverse sampling. The proposed method is validated using four real-world datasets. The obtained results demonstrate the superiority of the proposed method compared to baseline approaches.

Influence maximization is a fundamental problem in social network analysis. This problem refers to the identification of a set of influential users as initial spreaders to maximize the spread of a message in a network. When such a message is spread, some users may be influenced by it. A common assumption of existing work is that the impact of a message is essentially binary: A user is either influenced (activated) or not influenced (non-activated). However, how strongly a user is influenced by a message may play an important role in this user’s attempt to influence subsequent users and spread the message further; existing methods may fail to model accurately the spreading process and identify influential users. In this article, we propose a novel approach to model a social network as a fuzzy graph where a fuzzy variable is used to represent the extent to which a user is influenced by a message (user’s activation level). By extending a diffusion model to simulate the spreading process in such a fuzzy graph, we conceptually formulate the fuzzy influence maximization problem for which three methods are proposed to identify influential users. Experimental results demonstrate the accuracy of the proposed methods in determining influential users in social networks.

Centrality measures have been widely used to capture the properties of different nodes in a social network, particularly when the edges are fully deterministic. Various models have also been proposed to calculate nodes’ centrality in graphs where there might be some uncertainty in relation to the edges. Their common characteristic is that graph uncertainty is essentially embedded into the calculation of centrality to compute a single crisp value. However, as the degree of uncertainty may vary, centrality values may also vary. In this paper, making use of fuzzy set theory, we assume that a social network is modelled by a fuzzy graph and a fuzzy variable is used to describe the truth degree of an edge between two nodes. Based on this formulation, appropriate definitions are given to determine the truth degree of different centrality values for a node and thereby centrality as a fuzzy relation. Three well-known centrality measures, degree, h-index and k-shell, are extended to calculate the truth degree for the centrality of a node in a fuzzy graph. Experimental results demonstrate that the proposed centrality measures can determine the importance of nodes in a fuzzy graph more accurately than other fuzzy or deterministic centrality measures.

Network graphs are widely used to model a variety of real-world interactions. In such graphs, nodes do not have the same importance in the graph structure as a result of the graph's topological properties. This may have various implications concerning a network's behaviour as, for example, how different nodes operate (even a node's failure) may not have the same impact for the whole network. The differences in the structural properties of the nodes imply that each node has different importance, which, in turn, gives rise to the notion of importance inequality in a graph. This paper defines and addresses the problem of importance inequality minimization, which may be useful to achieve certain properties in a network. Given a network graph and an integer$k$, the problem aims to identify$k$edges to connect non-adjacent nodes, in a way that minimizes the importance inequality of the graph. The paper provides a formal definition of the problem and proves its NP-hardness. Then, a naive greedy method is proposed, which is enhanced by heuristics that make its use practical. Experiments using 8 real-world networks are conducted to evaluate the proposed methods in terms of effectiveness and efficiency.