Mesoscopic analysis of online social networks: The role of negative ties

Abstract

A class of networks are those with both positive and negative links. In this manuscript, we studied the interplay between positive and negative ties on mesoscopic level of these networks, i.e., their community structure. A community is considered as a tightly interconnected group of actors; therefore, it does not borrow any assumption from balance theory and merely uses the well-known assumption in the community detection literature. We found that if one detects the communities based on only positive relations (by ignoring the negative ones), the majority of negative relations are already placed between the communities. In other words, negative ties do not have a major role in community formation of signed networks. Moreover, regarding the internal negative ties, we proved that most unbalanced communities are maximally balanced, and hence they cannot be partitioned into k nonempty sub-clusters with higher balancedness (k ≥ 2). Furthermore, we showed that although the mediator triad + + − (hostile-mediator-hostile) is underrepresented, it constitutes a considerable portion of triadic relations among communities. Hence, mediator triads should not be ignored by community detection and clustering algorithms. As a result, if one uses a clustering algorithm that operates merely based on social balance, mesoscopic structure of signed networks significantly remains hidden.

Link prediction in multiplex online social networks

“…To this end, instead of computing a meta-path between two users based on the other objects in the layers, they employed clusters to propose a new definition of meta-path. In signed networks, a cluster is referred to a group of nodes for which the intracluster links are positive as much as possible, whereas negative links are placed within cluster as much as possible [44,45]. This is obtained by minimizing intercluster positive links and intracluster negative connections.…”

A memetic algorithm for computing and transforming structural balance in signed networks

“…PRE2014 [17] and SN2013 [25] are two relevant works on the computation of imbalance in signed networks. PRE2014 adopts a classical community detection algorithm Infomap [18] to detect communities in signed networks.…”

“…Here, weighted adjacency matrices A + A − are used to measure the effect of the positive and negative links, respectively, and their items are defined as follows: Based on the knowledge that negative links have little influences on the formation of communities [17] and that the final balance state of signed networks is determined by the number of positive links [8], we define the neighborhoods of node, cluster and partition as follows.…”

“…The energy function proposed by Facchetti et al [7,15] measures the imbalances as the number of unbalanced links in signed networks, and both the gauge transformation [7,15] and memetic algorithms [16] are utilized to minimize the energy function. Besides, some studies evaluate the imbalances as the sum of the positive links across two different communities and the negative links within the same community [15,17], and thereafter they adopt the classical community detection algorithms, such as Infomap [18], FEC [19] and MODPSO [20], to identify the communities in signed networks. Note that, in many cases these studies are constraint to the strong definition of structural balance, and they are worth to be applied to the weak definition of structural balance.…”

Multiple Global Community Detection in Signed Graphs

“…Using (20)- (21) and constraint (9) (for the case of maximization we consider the negative value of P) and the same one-hot encoding approach (3), we can generalize (17) to a k-community formulation and write the penalized modularity M k P as…”