In this paper, we want to study the informative value of negative links in signed complex networks. For this purpose, we extract and analyze a collection of signed networks representing voting sessions of the European Parliament (EP). We first process some data collected by the Vote Watch Europe Website for the whole 7th term (2009-2014), by considering voting similarities between Members of the EP to define weighted signed links. We then apply a selection of community detection algorithms, designed to process only positive links, to these data. We also apply Parallel Iterative Local Search (Parallel ILS), an algorithm recently proposed to identify balanced partitions in signed networks. Our results show that, contrary to the conclusions of a previous study focusing on other data, the partitions detected by ignoring or considering the negative links are indeed remarkably different for these networks. The relevance of negative links for graph partitioning therefore is an open question which should be further explored.
We study the application of spectral clustering, prediction and visualization methods to graphs with negatively weighted edges. We show that several characteristic matrices of graphs can be extended to graphs with positively and negatively weighted edges, giving signed spectral clustering methods, signed graph kernels and network visualization methods that apply to signed graphs. In particular, we review a signed variant of the graph Laplacian. We derive our results by considering random walks, graph clustering, graph drawing and electrical networks, showing that they all result in the same formalism for handling negatively weighted edges. We illustrate our methods using examples from social networks with negative edges and bipartite rating graphs.  We present a reformulation of modularity that allows the analysis of the community structure in networks of correlated data. The modularity preserves the probabilistic semantics of the original definition even when the network is directed, weighted, signed, and has self-loops. This is the most general condition one can find in the study of any network, in particular those defined from correlated data. We apply our results to a real network of correlated data between stores in the city of Lyon (France). The field of complex network clustering has been very active in the past several years. In this paper, a discrete framework of the particle swarm optimization algorithm is proposed. Based on the proposed discrete framework, a multiobjective discrete particle swarm optimization algorithm is proposed to solve the network clustering problem. The decomposition mechanism is adopted. A problem-specific population initialization method based on label propagation and a turbulence operator are introduced. In the proposed method, two evaluation objectives termed as kernel k-means and ratio cut are to be minimized. However, the two objectives can only be used to handle unsigned networks. In order to deal with signed networks, they have been extended to the signed version. The clustering performances of the proposed algorithm have been validated on signed networks and unsigned networks. Extensive experimental studies compared with ten state-of-the-art approaches prove that the proposed algorithm is effective and promising. Modern science of networks has facilitated us with enormous convenience to the understanding of complex systems. Community structure is believed to be one of the notable features of complex networks representing real complicated systems. Very often, uncovering community structures in networks can be regarded as an optimization problem, thus, many evolutionary algorithms based approaches have been put forward. Particle swarm optimization (PSO) is an artificial intelligent algorithm originated from social behavior such as birds flocking and fish schooling. PSO has been proved to be an effective optimization technique. However, PSO was originally designed for continuous optimization which confounds its applications to discrete contexts. In this paper, a novel discrete PSO algorithm is suggested for identifying community structures in signed networks. In the suggested method, particles' status has been redesigned in discrete form so as to make PSO proper for discrete scenarios, and particles' updating rules have been reformulated by making use of the topology of the signed network. Extensive experiments compared with three state-of-the-art approaches on both synthetic and real-world signed networks demonstrate that the proposed method is effective and promising. To detect communities in signed networks consisting of both positive and negative links, two new evolutionary algorithms (EAs) and two new memetic algorithms (MAs) are proposed and compared. Furthermore, two measures, namely the improved modularity Q and the improved modularity density D-value, are used as the objective functions. The improved measures not only preserve all properties of the original ones, but also have the ability of dealing with negative links. Moreover, D-value can also control the partition to different resolutions. To fully investigate the performance of these four algorithms and the two objective functions, benchmark social networks and various large-scale randomly generated signed networks are used in the experiments. The experimental results not only show the capability and high efficiency of the four algorithms in successfully detecting communities from signed networks, but also indicate that the two MAs outperform the two EAs in terms of the solution quality and the computational cost. Moreover, by tuning the parameter in D-value, the four algorithms have the multi-resolution ability. Complex networks considering both positive and negative links have gained considerable attention during the past several years. Community detection is one of the main challenges for complex network analysis. Most of the existing algorithms for community detection in a signed network aim at providing a hard-partition of the network where any node should belong to a community or not. However, they cannot detect overlapping communities where a node is allowed to belong to multiple communities. The overlapping communities widely exist in many real-world networks. In this paper, we propose a signed probabilistic mixture (SPM) model for overlapping community detection in signed networks. Compared with the existing models, the advantages of our methodology are (i) providing soft-partition solutions for signed networks; (ii) providing soft memberships of nodes. Experiments on a number of signed networks show that our SPM model: (i) can identify assortative structures or disassortative structures as the same as other state-of-the-art models; (ii) can detect overlapping communities; (iii) outperforms other state-of-the-art models at shedding light on the community detection in synthetic signed networks. Detecting communities in complex networks accurately is a prime challenge, preceding further analyses of network characteristics and dynamics. Until now, community detection took into account only positively valued links, while many actual networks also feature negative links. We extend an existing Potts model to incorporate negative links as well, resulting in a method similar to the clustering of signed graphs, as dealt with in social balance theory, but more general. To illustrate our method, we applied it to a network of international alliances and disputes. Using data from 1993-2001, it turns out that the world can be divided into six power blocs similar to Huntington's civilizations, with some notable exceptions. Social life coalesces into communities through cooperation and conflict. As a case in point, Shwed and Bearman (2010) studied consensus and contention in scientific communities. They used a sophisticated modularity method to detect communities on the basis of scientific citations, which they then interpreted as directed positive network ties. They assumed that a lack of citations implies disagreement. Some scientific citations, however, are contentious and should therefore be represented by negative ties, like conflicting relations in general. After expanding the modularity method to incorporate negative ties, we show that a small proportion of negative ties, commonly present in science, is sufficient to significantly alter the community structure. In addition, our research suggests that without distinguishing negative ties, scientific communities actually represent specialized subfields, not contentious groups. Finally, we cast doubt on the assumption that lack of cites would signal disagreement. To show the general importance of discerning negative ties for understanding conflict and its impact on communities, we also analyze a public debate. In this paper, we propose a method for detecting communities from signed social networks with both positive and negative weights by modeling the problem as a multi-objective problem. In the experiments, both real world and synthetic signed networks whose size ranges from 100 to 1200 nodes are used to validate the performance of the new algorithm. A comparison is also made between the new algorithm and an effective existing algorithm, namely FEC. The experimental results show that our algorithm obtains a good performance on both real world and synthetic data, and outperforms FEC clearly. Community detection in signed complex networks is a challenging research problem aiming at finding groups of entities having positive connections within the same cluster and negative relationships between different clusters. Most of the proposed approaches have been developed for networks having only positive edges. In this paper we propose a multiobjective approach to detect communities in signed networks. The method partitions a network in groups of nodes such that two objectives are contemporarily optimized. The former is that the partitioning should have dense positive intra-connections and sparse negative interconnections, the latter is that it should have as few as possible negative intra-connections and positive inter-connections. We show that the concepts of signed modularity and frustration fulfill these objectives, and that the maximization of signed modularity and the minimization of frustration allow to obtain very good solutions to the problem. An extensive set of experiments on both real-life and synthetic signed networks shows the efficacy of the approach.  â€”We propose a framework for discovery of collaborative community structure in Wiki-based knowledge repositories based on raw-content generation analysis. We leverage topic modelling in order to capture agreement and opposition of contributors and analyze these multi-modal relations to map communities in the contributor base. The key steps of our approach include (i) modeling of pair wise variable-strength contributor interactions that can be both positive and negative, (ii) synthesis of a global network incorporating all pair wise interactions, and (iii) detection and analysis of community structure encoded in such networks. The global community discovery algorithm we propose outperforms existing alternatives in identifying coherent clusters according to objective optimality criteria. Analysis of the discovered community structure reveals coalitions of common interest editors who back each other in promoting some topics and collectively oppose other coalitions or single authors. We couple contributor interactions with content evolution and reveal the global picture of opposing themes within the self-regulated community base for both controversial and featured articles in Wikipedia. Structural balance theory forms the foundation for a generalized blockmodel method useful for delineating the structure of signed social one-mode networks for social actors (for example, people or nations). Heider's unit formation relation was dropped. We re-examine structural balance by formulating Heider's unit formation relations as signed two-mode data. Just as generalized blockmodeling has been extended to analyze two-mode unsigned data, we extend it to analyze signed two-mode network data and provide a formalization of the extension. The blockmodel structure for signed two-mode networks has positive and negative blocks, defined in terms of different partitions of rows and columns. These signed blocks can be located anywhere in the block model. We provide a motivating example and then use the new blockmodel type to delineate the voting patterns of the Supreme Court justices for all of their nonunanimous decisions for the 2006–07 term. Interpretations are presented together with a statement of further... Many complex systems in the real world can be modeled as signed social networks that contain both positive and negative relations. Algorithms for mining social networks have been developed in the past; however, most of them were designed primarily for networks containing only positive relations and, thus, are not suitable for signed networks. In this work, we propose a new algorithm, called FEC, to mine signed social networks where both positive within-group relations and negative between-group relations are dense. FEC considers both the sign and the density of relations as the clustering attributes, making it effective for not only signed networks but also conventional social networks including only positive relations. Also, FEC adopts an agent-based heuristic that makes the algorithm efficient (in linear time with respect to the size of a network) and capable of giving nearly optimal solutions. FEC depends on only one parameter whose value can easily be set and requires no prior knowledge on hidden community structures. The effectiveness and efficacy of FEC have been demonstrated through a set of rigorous experiments involving both benchmark and randomly generated signed networks. Discussion based websites like Epinions.com and Slashdot.com allow users to identify both friends and foes. Such networks are called Signed Social Networks and mining communities of like-minded users from these networks has potential value. We extend existing community detection algorithms that work only on unsigned networks to be applicable to signed networks. In particular, we develop a spectral approach augmented with iterative optimization. We use our algorithms to study both communities and structural balance. Our results indicate that modularity based communities are distinct from structurally balanced communities. Community structure is an important topological property of network. Being able to discover it can provide invaluable help in exploiting and understanding complex networks. Although many algorithms have been developed to complete this task, they all have advantages and limitations. So the issue of how to detect communities in networks quickly and correctly remains an open challenge. Distinct from the existing works, this paper studies the community structure from the view of network evolution and presents a self-organizing network evolving algorithm for mining communities hidden in complex networks. Compared with the existing algorithm, our approach has three distinct features. First, it has a good classification capability and especially works well with the networks without well-defined community structures. Second, it requires no prior knowledge and is insensitive to the build-in parameters. Finally, it is suitable for not only positive networks but also singed networks containing both positive and negative weights. Various types of social relationships, such as friends and foes, can be represented as signed social networks (SNs) that contain both positive and negative links. Although many community detection (CD) algorithms have been proposed, most of them were designed primarily for networks containing only positive links. Thus, it is important to design CD algorithms which can handle large-scale SNs. To this purpose, we first extend the original similarity to the signed similarity based on the social balance theory. Then, based on the signed similarity and the natural contradiction between positive and negative links, two objective functions are designed to model the problem of detecting communities in SNs as a multiobjective problem. Afterward, we propose a multiobjective evolutionary algorithm, called MEAsSN. In MEAs-SN, to overcome the defects of direct and indirect representations for communities, a direct and indirect combined representation is designed. Attributing to this representation, MEAs-SN can switch between different representations during the evolutionary process. As a result, MEAs-SN can benefit from both representations. Moreover, owing to this representation, MEAs-SN can also detect overlapping communities directly. In the experiments, both benchmark problems and large-scale synthetic networks generated by various parameter settings are used to validate the performance of MEAs-SN. The experimental results show the effectiveness and efficacy of MEAs-SN on networks with 1000, 5000, and 10000 nodes and also in various noisy situations. A thorough comparison is also made between MEAs-SN and three existing algorithms, and the results show that MEAs-SN outperforms other algorithms. We study the community structure of networks representing voting on resolutions in the United Nations General Assembly. We construct networks from the voting records of the separate annual sessions between 1946 and 2008 in three different ways: (1) by considering voting similarities as weighted unipartite networks; (2) by considering voting similarities as weighted, signed unipartite networks; and (3) by examining signed bipartite networks in which countries are connected to resolutions. For each formulation, we detect communities by optimizing network modularity using an appropriate null model. We compare and contrast the results that we obtain for these three different network representations. We thereby illustrate the need to consider multiple resolution parameters and explore the effectiveness of each network representation for identifying voting groups amidst the large amount of agreement typical in General Assembly votes. Signed network is an important kind of complex network, which includes both positive relations and negative relations. Communities of a signed network are defined as the groups of vertices, within which positive relations are dense and between which negative relations are also dense. Being able to identify communities of signed networks is helpful for analysis of such networks. Hitherto many algorithms for detecting network communities have been developed. However, most of them are designed exclusively for the networks including only positive relations and are not suitable for signed networks. So the problem of mining communities of signed networks quickly and correctly has not been solved satisfactorily. In this paper, we propose a heuristic algorithm to address this issue. Compared with major existing methods, our approach has three distinct features. First, it is very fast with a roughly linear time with respect to network size. Second, it exhibits a good clustering capability and especially can work well with complex networks without well-defined community structures. Finally, it is insensitive to its built-in parameters and requires no prior knowledge.