Discovering Polarized Communities in Signed Networks

Bonchi, Francesco; Galimberti, Edoardo; Gionis, Aristides; Ordozgoiti, Bruno; Ruffo, Giancarlo

doi:10.1145/3357384.3357977

Cited by 53 publications

(48 citation statements)

References 52 publications

(66 reference statements)

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“…For example, (i) can we extend the current work to finding k-way polarized communities (k > 2)? (ii) how does the signed bipartiteness ratio compare with other polarization measures, such as Polarity proposed in [5]? (iii) how to enforce graph connectivity on both bands in a polarized community?…”

Section: Resultsmentioning

confidence: 99%

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Searching for polarization in signed graphs: a local spectral approach

Han

Ordozgoiti

Gionis

2020

Proceedings of the Web Conference 2020

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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.

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Section: Resultsmentioning

confidence: 99%

“…10 We scan the communities sequentially (in random order), keep track of the nodes that are covered so far and drop any communities that intersect with the covered nodes. [5], which counts the number of edges that agree with the polarized structure and penalizes large communities:…”

Section: Evaluation On Real-world Graphsmentioning

confidence: 99%

Searching for polarization in signed graphs: a local spectral approach

Han

Ordozgoiti

Gionis

2020

Proceedings of the Web Conference 2020

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“…As expected, Eigen achieves higher density than Timbal. This can be explained by the fact that Eigen can be seen as optimizing the following objective [6]:…”

Section: Trading Off Balance and Graph Sizementioning

confidence: 99%

Finding large balanced subgraphs in signed networks

Ordozgoiti

Matakos

Gionis

2020

Proceedings of the Web Conference 2020

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Signed networks are graphs whose edges are labelled with either a positive or a negative sign, and can be used to capture nuances in interactions that are missed by their unsigned counterparts. The concept of balance in signed graph theory determines whether a network can be partitioned into two perfectly opposing subsets, and is therefore useful for modelling phenomena such as the existence of polarized communities in social networks. While determining whether a graph is balanced is easy, finding a large balanced subgraph is hard. The few heuristics available in the literature for this purpose are either ineffective or non-scalable. In this paper we propose an efficient algorithm for finding large balanced subgraphs in signed networks. The algorithm relies on signed spectral theory and a novel bound for perturbations of the graph Laplacian. In a wide variety of experiments on real-world data we show that our algorithm can find balanced subgraphs much larger than those detected by existing methods, and in addition, it is faster. We test its scalability on graphs of up to 34 million edges. CCS CONCEPTS• Theory of computation → Graph algorithms analysis.

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“…The 2correlation-clustering problem [7], also known as the frustration-index problem [2], is also widely studied. Finally, a more recent line of work introduces the problem of discovering antagonistic communities in signed networks [5].…”

Section: Related Workmentioning

confidence: 99%

“…Therefore, it has also been shown the importance of measuring to what extent an unbalanced signed network is close to be balanced [17]. Structural balance is also linked with group polarization, i.e., the division of a group of entities (e.g., nodes of a network) into two subgroups each reaching consensus and having opposite opinions [5]. Network visualization has emerged as a key complement to standard network analysis techniques to fill the gap between computation and interpretation, communicate findings, and deepen insight [16].…”

Section: Introductionmentioning

confidence: 99%

Visualizing Structural Balance in Signed Networks

Galimberti

Madeddu

Bonchi

et al. 2019

Complex Networks and Their Applications VIII

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Network visualization has established as a key complement to network analysis since the large variety of existing network layouts are able to graphically highlight different properties of networks. However, signed networks, i.e., networks whose edges are labeled as friendly (positive) or antagonistic (negative), are target of few of such layouts and none, to our knowledge, is able to show structural balance, i.e., the tendency of cycles towards including an even number of negative edges, which is a well-known theory for studying friction and polarization. In this work we present Structural-balance-viz: a novel visualization method showing whether a connected signed network is balanced or not and, in the latter case, how close the network is to be balanced. Structuralbalance-viz exploits spectral computations of the signed Laplacian matrix to place network's nodes in a Cartesian coordinate system resembling a balance (a scale). Moreover, it uses edge coloring and bundling to distinguish positive and negative interactions. The proposed visualization method has characteristics desirable in a variety of network analysis tasks: Structural-balance-viz is able to provide indications of balance/polarization of the whole network and of each node, to identify two factions of nodes on the basis of their polarization, and to show their cumulative characteristics. Moreover, the layout is reproducible and easy to compare. Structural-balance-viz is validated over synthetic-generated networks and applied to a real-world dataset about political debates confirming that it is able to provide meaningful interpretations.

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Discovering Polarized Communities in Signed Networks

Cited by 53 publications

References 52 publications

Searching for polarization in signed graphs: a local spectral approach

Searching for polarization in signed graphs: a local spectral approach

Finding large balanced subgraphs in signed networks

Visualizing Structural Balance in Signed Networks

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