Evaluating balancing on social networks through the efficient solution of correlation clustering problems

Abstract

One challenge for social network researchers is to evaluate balance in a social network. The degree of balance in a social group can be used as a tool to study whether and how this group evolves to a possible balanced state. The solution of clustering problems defined on signed graphs can be used as a criterion to measure the degree of balance in social networks and this measure can be obtained with the optimal solution of the Correlation Clustering (CC) problem, as well as a variation of it, the Relaxed Correlation Clustering (RCC) problem. However, solving these problems is no easy task, especially when large network instances need to be analyzed. In this work, we contribute to the efficient solution of both problems by developing sequential and parallel ILS metaheuristics. Then, by using our algorithms, we solve the problem of measuring the structural balance on large real-world social networks.

Multiple partitioning of multiplex signed networks

“…First, by applying our method more systematically to the whole EP dataset. This could cause some computational issues when solving the Correlation Clustering problem, but these could be solved by using an approximate method in lieu of Ex-CC [54]. Second, we observed that when applying k-medoids with an increasing k value, the obtained series of clusterings is almost hierarchical: it might be more appropriate to directly apply a hierarchical clustering algorithm instead.…”

“…there is a weighted link between each pair of nodes. Some authors prefer to extract signed vote similarity networks, which means that a weight can be positive, but also negative [4,34,54,55,58,63]. In their similarity function, they count agreement positively and disagreement negatively.…”

“…Certain authors only consider Abstain-Abstain as agreement, and treat all other abstention situations like absences (by ignoring them) [79] or like disagreements [55,61]. Levorato et al consider Abstain-Abstain as full agreement (+1), whereas Abstain-For and Abstain-Against are half agreement (+0.5) [54]. Reda et al and Macon et al consider all combinations of absences and abstentions (Absent-Absent, Abstain-Abstain, and Absent-Abstain) as agreement [69].…”

“…Crane & Dempsey keep only the links whose weights are above a predefined threshold [12]. For signed networks, it is possible to consider the absolute value of the weights [34,54,80]. In addition to this, Figueiredo & Frota create both positive and negative links between the same two nodes when their agreement and disagreement levels are both above some threshold [34].…”

“…However, when the considered period is particularly long, or dense in terms of voting activity, it is possible to split it in several distinct periods, each one leading to a separated network. In most works, these are considered in a completely independent way [4,34,54,55,58,61,63,76,79], for instance by partitioning separately each network and then studying the evolution of the partition or of some measure of interest. But it is also possible to consider these graphs as time slices constituting a sequence, and therefore a dynamic network.…”