Unsigned Networks Research Articles

SNEGAN: Signed Network Embedding by Using Generative Adversarial Nets

Network embedding (NE) aims to learn low-dimensional node representations of networks while preserving essential node structures and properties. Existing NE methods mainly preserve simple link structures in unsigned networks, neglecting conflicting relationships that widely exist in social media and Internet of things. In this paper, we propose a novel generative adversarial nets learning framework (called SNEGAN) for signed network embedding, which tries to preserve link structures signed by positive or negative labels. SNEGAN combines a generator with a signed random walker technique and a graph softmax function to generate fake links that are used to deceive discriminator. Moreover, it combines a discriminator with a tanh function to discriminate truths and signs of links sampled from the generator and real network structures. The generator and discriminator play a two-player minimax game, and they will eventually generate low-dimensional node representations of signed networks. Extensive experiments on both LFR benchmark and real-world signed networks show the superiority of SNEGAN over the state-of-the-art NE methods in tackling both link (sign) prediction and reconstruction tasks.

Trust-Based Missing Link Prediction in Signed Social Networks with Privacy Preservation

With the development of mobile Internet, more and more individuals and institutions tend to express their views on certain things (such as software and music) on social platforms. In some online social network services, users are allowed to label users with similar interests as “trust” to get the information they want and use “distrust” to label users with opposite interests to avoid browsing content they do not want to see. The networks containing such trust relationships and distrust relationships are named signed social networks (SSNs), and some real-world complex systems can be also modeled with signed networks. However, the sparse social relationships seriously hinder the expansion of users’ social circle in social networks. In order to solve this problem, researchers have done a lot of research on link prediction. Although these studies have been proved to be effective in the unsigned social network, the prediction of trust and distrust in SSN has not achieved good results. In addition, the existing link prediction research does not consider the needs of user privacy protection, so most of them do not add privacy protection measures. To solve these problems, we propose a trust-based missing link prediction method (TMLP). First, we use the simhash method to create a hash index for each user. Then, we calculate the Hamming distance between the two users to determine whether they can establish a new social relationship. Finally, we use the fuzzy computing model to determine the type of their new social relationship (e.g., trust or distrust). In the paper, we gradually explain our method through a case study and prove our method’s feasibility.

An Online Dynamic Social Network Evolution Community Discovery Method

Online social network in the study, dynamic implicit community or group structure of discovery and detection is a very key question at the heart of evolution, it is in the medium (Mesoscopic) view to observe the online social network hidden structure characteristic, predict the evolution trend, control of the situation, found that network abnormal mass incidents, etc. It is of great significance. The purpose of this paper is to provide technical advice for community discovery research by studying online dynamic social network evolution community discovery methods. This paper analyzes the characteristics of local clustering coefficient and node similarity calculation in unsigned network, and proposes the extended local clustering coefficient as the structural attribute of the edge in unsigned network. This property can better reflect the characteristics of local network density and network structure. Combining the new edge structure measure with the label propagation algorithm with linear time complexity, a label propagation algorithm combining the extended local clustering coefficient is proposed. The results showed that the accuracy of community discovery was improved by 32.6 percent in dynamic social networks.

Detecting community structure in signed and unsigned social networks by using weighted label propagation.

Detecting community structure is one of the most important problems in analyzing complex networks such as technological, informational, biological, and social networks and has great importance in understanding the operation and organization of these networks. One of the significant properties of social networks is the communication intensity between the users, which has not received much attention so far. Most of the proposed methods for detecting community structure in social networks have only considered communications between users. In this paper, using MinHash and label propagation, an algorithm called weighted label propagation algorithm (WLPA) has been proposed to detect community structure in signed and unsigned social networks. WLPA takes into account the intensity of communications in addition to the communications. In WLPA, first, the similarity of all adjacent nodes is estimated by using MinHash. Then, each edge is assigned a weight equal to the estimated similarity of its end nodes. The weights assigned to the edges somehow indicate the intensity of communication between users. Finally, the community structure of the network is determined through the weighted label propagation. Experiments on the benchmark networks indicate that WLPA is efficient and effective for detecting community structure in both signed and unsigned social networks.

Bipartite synchronization of coupled Lurie networks with signed graph and time-varying delay

This paper addresses the bipartite leader-following and leaderless synchronization in a signed network composed by an array of coupled Lurie systems with time-varying delay, where the signed network contains both the non-delay coupling term and the delay coupling term. By using the pinning control strategy and a gauge transformation to transform the problem of bipartite synchronization for signed network into that of synchronization of unsigned network, choosing an appropriate Lyapunov–Krasovskii functional (LKF), applying Jensen inequality and reciprocally convex inequality to estimate the derivative of the LKF, several sufficient conditions, which guarantee the bipartite leader-following and leaderless synchronization for the coupled Lurie networks with time-varying delay, are newly obtained in terms of linear matrix inequalities (LMIs). When the delay coupling term is not considered, some criteria in terms of low-dimensional LMIs are established by using M-matrix theory. A numerical example is provided to illustrate the effectiveness of the proposed results.

Learning Signed Network Embedding via Graph Attention

Learning the low-dimensional representations of graphs (i.e., network embedding) plays a critical role in network analysis and facilitates many downstream tasks. Recently graph convolutional networks (GCNs) have revolutionized the field of network embedding, and led to state-of-the-art performance in network analysis tasks such as link prediction and node classification. Nevertheless, most of the existing GCN-based network embedding methods are proposed for unsigned networks. However, in the real world, some of the networks are signed, where the links are annotated with different polarities, e.g., positive vs. negative. Since negative links may have different properties from the positive ones and can also significantly affect the quality of network embedding. Thus in this paper, we propose a novel network embedding framework SNEA to learn Signed Network Embedding via graph Attention. In particular, we propose a masked self-attentional layer, which leverages self-attention mechanism to estimate the importance coefficient for pair of nodes connected by different type of links during the embedding aggregation process. Then SNEA utilizes the masked self-attentional layers to aggregate more important information from neighboring nodes to generate the node embeddings based on balance theory. Experimental results demonstrate the effectiveness of the proposed framework through signed link prediction task on several real-world signed network datasets.

Research on collapsed (α, k)-NP-community on signed graph

In social network, the departure of critical users can lead to the disintegration of the entire community, i.e., lead a large number of other users to drop out. This paper aims to find the critical users in the community and prevent the whole community from disintegrating. Most of the other research work is carried out on the unsigned network. In this paper, we study this problem on a signed network and propose a new community model (α, k)-NP-community. Specifically, the nodes in the community model should satisfy the maximum subgraph with no less than ak good friends (positive neighbor) and no more than k enemy (negative neighbor). We propose an effective algorithm to find (α, k)-NP-community. In order to identify the critical users of (α, k)-NP-community, we propose the problem of collapsed (α, k)-NP-community: given a signed graph G, integers α, k, our goal is to find such nodes in graph G, the departure of the best collapser will lead to the smallest (α, k)-NP-community. We prove that the problem is NP-hard. Finally, we present two lemmas to apply the αKCA algorithm, which effectively reduced the number of candidate nodes and accelerated the search process. The results of extensive experiments on four real datasets demonstrate the effectiveness and efficiency of our algorithms.

Social Science–guided Feature Engineering

Many real-world relations can be represented by signed networks with positive links (e.g., friendships and trust) and negative links (e.g., foes and distrust). Link prediction helps advance tasks in social network analysis such as recommendation systems. Most existing work on link analysis focuses on unsigned social networks. The existence of negative links piques research interests in investigating whether properties and principles of signed networks differ from those of unsigned networks and mandates dedicated efforts on link analysis for signed social networks. Recent findings suggest that properties of signed networks substantially differ from those of unsigned networks and negative links can be of significant help in signed link analysis in complementary ways. In this article, we center our discussion on a challenging problem of signed link analysis . Signed link analysis faces the problem of data sparsity, i.e., only a small percentage of signed links are given. This problem can even get worse when negative links are much sparser than positive ones as users are inclined more toward positive disposition rather than negative. We investigate how we can take advantage of other sources of information for signed link analysis. This research is mainly guided by three social science theories, Emotional Information , Diffusion of Innovations , and Individual Personality . Guided by these, we extract three categories of related features and leverage them for signed link analysis. Experiments show the significance of the features gleaned from social theories for signed link prediction and addressing the data sparsity challenge.

Semi-Supervised Gated Spectral Convolution on a Directed Signed Network

A complex network is a powerful tool that enables a complex system in the real world to be represented as a network structure. Due to the heterogeneous edges and nodes implying rich semantic information, network representation has received considerable attention in both research and industrial domain. Over the recent years, the graph convolutional network (GCN) has provided a novel approach for learning network embeddings. However, this primarily supports undirected unsigned networks; that is, it cannot be directly applied to directed signed networks because it is challenging to effectively depict the direction and signs of edges in such models. In this paper, we therefore propose a method for semi-supervised gated spectral convolution in directed signed networks. We first extend the concept of the GCN to directed signed networks, which not only preserves the advantages of the traditional GCN but also properly describes the significance of the directions and signs of the edges. We then innovatively define sign (label) propagation rules in directed signed networks, rendering the networks semi-supervised. Furthermore, we enhance the balance theory to constrain the process of sign propagation to obtain network embedding with better interpretability. To satisfy the needs of large-scale complex networks, we propose a gating mechanism to adaptively forget sign information, which significantly reduces the time-space complexity of the sign propagation process. Finally, we compare the proposed method with state-of-the-art baselines using four real-world data sets for the classical link sign prediction task. Experimental results demonstrate that the proposed method is competitive.

Mitigation of malicious attacks on structural balance of signed networks

The studies of malicious attacks have received great attention due to their catastrophic damages on potential functions of complex networks. An initial attack first causes the failures of the attacked elements (like nodes and edges), and then those failures may trigger a cascade of failures, resulting in the catastrophic damages on the functions (like the largest connected topology and the community structures) of the networks. Previous methods, however, mainly focus on the impacts of malicious attacks on unsigned networks, and signed networks with conflicting relationships have more complex functions than unsigned counterparts. In this paper, we study the impacts of malicious attacks on the structural balance of signed networks which reflects the potentially functional conflicts and tensions in the networks. First, we model malicious attacks as a two-level targeted one: the small-scale node attacks and large-scale cluster attacks, and analyze the failures of the structural balance of signed networks during the attacks. Second, we propose a balance robustness index to evaluate the functional resilience of signed networks to those failures. Finally, to mitigate the balance failures, we present a protection technique with six strategies to protect a small fraction of influential nodes from malicious attacks. Experiments on synthetic data and real signed networks show that their structural balance is fragile to targeted attacks, but their robustness can be improved greatly by protecting a small fraction of influential nodes.

Modularized convex nonnegative matrix factorization for community detection in signed and unsigned networks

NMF-based models in unsigned networks, the links of which are positive links only, have been applied in many aspects, such as community detection, link prediction, etc. However, NMF has been under-explored for community discovery in signed networks due to its constraint of non-negativity. Also, there are few related studies which could find out accurate partitions on both signed and unsigned networks due to their difference of community structure. In this paper, we propose a novel modularized convex nonnegative matrix factorization model which combines signed modularized information with convex NMF model, improving the accuracy of community detection in signed and unsigned networks. As for model selection, we extend the modularity density to signed networks and employ the signed modularity density to determine the number of communities automatically. Finally, the effectiveness of our model is verified on both synthetic and real-world networks.

How to predict recommendation lists that users do not like

It is obviously that many user-object online rating systems usually contain the information of the users’ attitudes: like or dislike the objects, these systems can be represented by signed bipartite networks. The common recommendation systems work on unsigned networks. Even if some consider the negative edges, they are all concerned with the objects that the recommended user likes. However, the objects that the user does not like are more personalized. Based on Network-Based Inference (NBI) and signed bipartite networks, we proposed Signed Network-Based Inference (SNBI) to provide the negative recommendation list, which predicts the objects that users dislike. The SNBI algorithm includes two mechanisms: When allocating resources on signed bipartite networks, first method (SNBI-1) does not allocate resources while second method (SNBI-2) reduces resources if there is a negative edge. By comparing the results on the actual data sets with NBI, we found that SNBI-2 which takes into account the role of the negative edges can better predict the objects that user does not like while maintaining the validity of the positive recommendation list, then gives more personalized recommendation.

On the Logic of Balance in Social Networks

Modal logics for reasoning about social networks is currently an active field of research. There is still a gap, however, between the state of the art in logical formalisations of concepts related to social networks and the much more mature field of social network analysis. In this paper we take a step to bridge that gap. One of the key foundations of social network analysis is balance theory, which is used to analyse signed social networks where agents can have positive (“friends”) or negative (“enemies”) relationships. Certain combinations of positive and negative relationships are considered to be unbalanced, or unstable—in particular the occurrence of cycles with an odd number of negative relationships. Especially relatively short cycles with an odd number of negative relationships are thought to put pressure on the agents to change one or more of the involved relationships from negative to positive or the other way around. Most existing logics for reasoning about social networks are defined for unsigned networks. In this paper we develop a modal logic for reasoning about structural properties of signed social networks, and give a sound and complete Hilbert-style axiomatic system. Furthermore, we completely axiomatise classes of signed social networks that are balanced to a certain degree n, in the sense that there are no cycles of length up to n with an odd number of negative relationships. Finally, we completely axiomatise the class of all fully balanced complete signed social networks, i.e., networks where everyone is connected with everyone else. Axiomatic completeness is non-trivial because neither the balance properties, nor the dichotomy between positive and negative relations, are modally definable. The paper thus provides a logical basis for reasoning about signed social networks in general and balanced networks in particular.

Supervised User Ranking in Signed Social Networks

The task of user ranking in signed networks, aiming to predict potential friends and enemies for each user, has attracted increasing attention in numerous applications. Existing approaches are mainly extended from heuristics of the traditional models in unsigned networks. They suffer from two limitations: (1) mainly focus on global rankings thus cannot provide effective personalized ranking results, and (2) have a relatively unrealistic assumption that each user treats her neighbors’ social strengths indifferently. To address these two issues, we propose a supervised method based on random walk to learn social strengths between each user and her neighbors, in which the random walk more likely visits “potential friends” and less likely visits “potential enemies”. We learn the personalized social strengths by optimizing on a particularly designed loss function oriented on ranking. We further present a fast ranking method based on the local structure among each seed node and a certain set of candidates. It much simplifies the proposed ranking model meanwhile maintains the performance. Experimental results demonstrate the superiority of our approach over the state-of-the-art approaches.

Controllability of Switching Signed Networks

This brief investigates the controllability of switching signed networks, in which the interconnection topologies are directed, weighted, and switched. First, we study the controllability from the union digraph perspective and derive a graph-theoretic sufficient condition. It is shown that a switching signed network can be controllable even if each of its subnetworks is uncontrollable. Second, we consider the controllability of simultaneously structurally balanced signed networks. It is found that the controllability of simultaneously structurally balanced networks is equivalent to the controllability of their corresponding unsigned networks. Finally, several numerical examples are given to illustrate the effectiveness of the theoretical results.

Impact of structural balance on Self-Avoiding Pruning Walk

In a signed network, nodes are connected by two types of logically contradictory links: positive and negative links. These two types of links may play different roles in a dynamic process. In many real-world signed networks, the number of balanced triangles (those that have an odd number of positive links) is higher than that of unbalanced triangles. We refer to the structural balance as the fraction of balanced triangles. In this work, we explore how the structural balance influences a dynamic process. We consider the Self-Avoiding Pruning (SAP) Walk on a signed network which has been recently proposed to model, e.g., a consumer’s purchase behavior on a signed product network, where two products can be complementary or competitive with each other (Wang et al., 2017). First, we propose a model to generate signed networks with a given unsigned network topology, a given desired percentage of positive links and structural balance. Second, we design a sign flipping algorithm that could tune the structural balance of a given signed network without changing the percentage of positive links and the underlying topology. Finally, by using both the signed network models and the signed flipped real-world signed networks, we unravel and explain the effect of structural balance on the SAP walk features.

Community Detection in Signed Social Networks Using Multiobjective Genetic Algorithm

Clustering of like‐minded users is basically the goal of community detection (CD) in social networks and many researchers have proposed different algorithms for the same. In signed social networks (SSNs) where type of link is also considered besides the links itself, CD aims to partition the network in such a way to have less positive inter‐connections and less negative intra‐connections among communities. So, approaches used for CD in unsigned networks do not perform well when directly applied on signed networks. Most of the CD algorithms are based on single objective optimization criteria of optimizing modularity which focuses only on link density without considering the type of links existing in the network. In this work, a multiobjective approach for CD in SSNs is proposed considering both the link density as well as the sign of links. Precisely we are developing a method using modularity, frustration and social balance factor as multiple objectives to be optimized (M‐F‐SBF model). NSGA‐II algorithm is used to maintain elitism and diversity in the solutions. Experiments are performed on both existing benchmarked and real‐world datasets show that our approach has led to better solutions, clearly indicating the effectiveness of our proposed M‐F‐SBF model.

Community Detection in Signed Networks Based on the Signed Stochastic Block Model and Exact ICL

There has been an increasing interest in detecting community in signed networks because signed networks contain more information (both positive and negative edges) than unsigned networks (only positive edges). Many methods have been proposed to find communities in signed networks; however, most of them can be regarded as the discriminative methods that do not concern with how the signed networks are generated so that they are usually difficult to characterize accurately the intrinsic community structure. The existing method SSL which is based on a generative model can achieve high accuracy in community detection in signed networks. However, SSL needs to estimate the models in the possible space one by one, which requires a large amount of calculation. In view of this, we propose a method to find community in signed networks, in which the exact integrated complete data likelihood (ICLex) for the signed stochastic block model proposed in SSL is derived and a greedy search is employed to optimize the value of the derived ICLex for signed networks to find communities. Our method has a rigorous probabilistic interpretation and does not need to estimate the models one by one from the possible space. The knowledge on hyper-parameters of our model is not necessary. In the experiments, the proposed method is tested on the synthetic and real-world networks and compared with several current methods. The experimental results show that our method can find the communities in signed networks more accurately than these current methods and more efficiently than SSL.

Modeling Influence Diffusion over Signed Social Networks

In offline or online worlds, many social systems can be represented as signed social networks including both positive and negative relationships. Although a variety of studies on signed social networks have been conducted motivated by the great application value of unique polarity characteristics, how to model the process of influence propagation over signed social networks is still an important problem that remains pretty much open. Currently, a few studies extended traditional diffusion models (e.g., Independent Cascade model and Linear Threshold model) from unsigned social networks to signed social networks for estimating positive and negative influence of user sets. However, all of above extension models are stochastic and descriptive models. In order to ensure the accuracy of estimated influence, existing models require a significant number of Monte-Carlo simulations which are very time-consuming and not scalable. Aiming at this issue, we propose the Polarity-related Linear Influence Diffusion (PLID) model which can quickly and accurately calculate polarity-related influence of user sets without simulations. To validate effectiveness and efficiency of our proposed model, we make use of our PLID model to solve the positive influence maximization problem in signed social networks under rigorous mathematical proofs. Extensive experiments demonstrate that our PLID model and approximation algorithm significantly outperform state-of-the-art methods in terms of positive influence spread and running time, using Epinions and Slashdot datasets.

Signed Clique Search in Signed Networks: Concepts and Algorithms

Mining cohesive subgraphs from a network is a fundamental problem in network analysis. Most existing cohesive subgraph models are mainly tailored to unsigned networks. In this paper, we study the problem of seeking cohesive subgraphs in a signed network, in which each edge can be positive or negative, denoting friendship or conflict, respectively. We propose a novel model, called maximal $(\alpha, k)$ ( α , k ) -clique, that represents a cohesive subgraph in signed networks. Specifically, a maximal $(\alpha, k)$ ( α , k ) -clique is a clique in which every node has at most $k$ k negative neighbors and at least $\lceil \alpha k \rceil$ ⌈ α k ⌉ positive neighbors ( $\alpha \geq 1$ α ≥ 1 ). We show that the problem of enumerating all maximal $(\alpha, k)$ ( α , k ) -cliques in a signed network is NP-hard. To enumerate all maximal $(\alpha, k)$ ( α , k ) -cliques efficiently, we first develop an elegant signed network reduction technique to significantly prune the signed network. Then, we present an efficient branch and bound enumeration algorithm with several carefully-designed pruning rules to enumerate all maximal $(\alpha, k)$ ( α , k ) -cliques in the reduced signed network. In addition, we also propose an efficient algorithm with three novel upper-bounding techniques to find the maximum $(\alpha, k)$ ( α , k ) -clique in a signed network. The results of extensive experiments on five large real-life datasets demonstrate the efficiency, scalability, and effectiveness of our algorithms.