Searching for polarization in signed graphs: a local spectral approach

Abstract

Signed graphs have been used to model interactions in social networks, which can be either positive (friendly) or negative (antagonistic). The model has been used to study polarization and other related phenomena in social networks, which can be harmful to the process of democratic deliberation in our society. An interesting and challenging task in this application domain is to detect polarized communities in signed graphs. A number of different methods have been proposed for this task. However, existing approaches aim at finding globally optimal solutions. Instead, in this paper we are interested in finding polarized communities that are related to a small set of seed nodes provided as input. Seed nodes may consist of two sets, which constitute the two sides of a polarized structure.In this paper we formulate the problem of finding local polarized communities in signed graphs as a locally-biased eigen-problem. By viewing the eigenvector associated with the smallest eigenvalue of the Laplacian matrix as the solution of a constrained optimization problem, we are able to incorporate the local information as an additional constraint. In addition, we show that the locally-biased vector can be used to find communities with approximation guarantee with respect to a local analogue of the Cheeger constant on signed graphs. By exploiting the sparsity in the input graph, an indicator-vector for the polarized communities can be found in time linear to the graph size.Our experiments on real-world networks validate the proposed algorithm and demonstrate its usefulness in finding local structures in this semi-supervised manner.

SSSNET: Semi-Supervised Signed Network Clustering

“…Recommendation systems provide another playground for signed networks; [45] introduced a principled approach to capturing local and global information from signed social networks mathematically, and proposed a novel recommendation framework. Furthermore, there has been a recent growing interest on the topic of polar-ization in social media, mainly fueled by a large variety of speeches and statements made in the pursuit of public good, and their impact on the integrity of democratic processes [52]; our work also contributes to the growing literature of polarization in signed networks.…”

“…These small clusters could strongly influence the public discourse and even threaten the integrity of democratic processes. Detecting such small clusters of polarized agents in a network of ambient nodes is hence of interest [52]. For a network with node set V, [52] introduces the notion of a polarized community structure (C 1 , C 2 ) within the wider network, as two disjoint sets of nodes C 1 , C 2 ⊆ V, such that •(1) there are relatively few (resp.…”

Maximal Multipolarized Cliques Search in Signed Networks

“…Excessive polarized "echo chambers" help users strengthen their beliefs while alienating those who hold different views, which provides a negative user experience and seriously impacts the health of public discourse and information circulation. Therefore, mining polarized structures in social networks is well-motivated for paving the way to further study group polarization [9].…”

“…It should be acknowledged that a signed network can powerfully encode many real-world relations between two entities with positive and negative links, such as proscons opinions in opinion networks and friend-fore relationships between users in social networks [5]. A great deal of recent research has focused on discovering polarized communities in signed networks [1,6,9]. For example, the study [1] has formulated and researched the problem of discovering two polarized communities in signed networks based on graph spectral methods.…”

“…A balance clique is defined as a maximal clique that can be partitioned into two subcliques in which the edges in subclique are positive and the edges between subcliques are negative. However, in the existing works [1,3,9], restricting the number of polarized structures to only two is an unreasonable assumption to make while representing multiple polarized structures in realworld signed networks, which is actually influenced by structural balance theory [2] in signed network analysis. In fact, [4] has already extended structural balance theory and proposed the other fundamental theory, named structural clusterable theory, including a new concept of -clustering graph to relax the strict constraint.…”