Visualizing Structural Balance in Signed Networks

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. Structural-balance-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

Applications of Structural Balance in Signed Social Networks

We present measures, models and link prediction algorithms based on the structural balance in signed social networks. Certain social networks contain, in addition to the usual 'friend' links, 'enemy' links. These networks are called signed social networks. A classical and major concept for signed social networks is that of structural balance, i.e., the tendency of triangles to be 'balanced' towards including an even number of negative edges, such as friend-friend-friend and friend-enemy-enemy triangles. In this article, we introduce several new signed network analysis methods that exploit structural balance for measuring partial balance, for finding communities of people based on balance, for drawing signed social networks, and for solving the problem of link prediction. Notably, the introduced methods are based on the signed graph Laplacian and on the concept of signed resistance distances. We evaluate our methods on a collection of four signed social network datasets.Comment: 37 page

Analyzing and Visualizing American Congress Polarization and Balance with Signed Networks

Signed networks and balance theory provide a natural setting for real-world scenarios that show polarization dynamics, positive/negative relationships, and political partisanships. For example, they have been proven effective for studying the increasing polarization of the votes in the two chambers of the American Congress from World War II on. To provide further insights into this particular case study, we propose the application of a framework to analyze and visualize a signed graph's configuration based on the exploitation of the corresponding Laplacian matrix' spectral properties. The overall methodology is comparable with others based on the frustration index, but it has at least two main advantages: first, it requires a much lower computational cost; second, it allows for a quantitative and visual assessment of how arbitrarily small subgraphs (even single nodes) contribute to the overall balance (or unbalance) of the network. The proposed pipeline allows to explore the polarization dynamics shown by the American Congress from 1945 to 2020 at different resolution scales. In fact, we are able to spot and to point out the influence of some (groups of) congressmen in the overall balance, as well as to observe and explore polarization's evolution of both chambers across the years

SNE: Signed Network Embedding

Several network embedding models have been developed for unsigned networks. However, these models based on skip-gram cannot be applied to signed networks because they can only deal with one type of link. In this paper, we present our signed network embedding model called SNE. Our SNE adopts the log-bilinear model, uses node representations of all nodes along a given path, and further incorporates two signed-type vectors to capture the positive or negative relationship of each edge along the path. We conduct two experiments, node classification and link prediction, on both directed and undirected signed networks and compare with four baselines including a matrix factorization method and three state-of-the-art unsigned network embedding models. The experimental results demonstrate the effectiveness of our signed network embedding.Comment: To appear in PAKDD 201

Trading strategies in the Italian interbank market

Using a data set which includes all transactions among banks in the Italian money market, we study their trading strategies and the dependence among them. We use the Fourier method to compute the variance-covariance matrix of trading strategies. Our results indicate that well defined patterns arise. Two main communities of banks, which can be coarsely identified as small and large banks, emerge.Comment: 19 page

Motif-aware temporal GCN for fraud detection in signed cryptocurrency trust networks

Graph convolutional networks (GCNs) is a class of artificial neural networks for processing data that can be represented as graphs. Since financial transactions can naturally be constructed as graphs, GCNs are widely applied in the financial industry, especially for financial fraud detection. In this paper, we focus on fraud detection on cryptocurrency truct networks. In the literature, most works focus on static networks. Whereas in this study, we consider the evolving nature of cryptocurrency networks, and use local structural as well as the balance theory to guide the training process. More specifically, we compute motif matrices to capture the local topological information, then use them in the GCN aggregation process. The generated embedding at each snapshot is a weighted average of embeddings within a time window, where the weights are learnable parameters. Since the trust networks is signed on each edge, balance theory is used to guide the training process. Experimental results on bitcoin-alpha and bitcoin-otc datasets show that the proposed model outperforms those in the literature