We investigate degree correlations in two online social networks where users are connected through different types of links. We find that, while subnetworks in which links have a positive connotation, such as endorsement and trust, are characterized by assortative mixing by degree, networks in which links have a negative connotation, such as disapproval and distrust, are characterized by disassortative patterns. We introduce a class of simple theoretical models to analyze the interplay between network topology and the superimposed structure based on the sign of links. Results uncover the conditions that underpin the emergence of the patterns observed in the data, namely the assortativity of positive subnetworks and the disassortativity of negative ones. We discuss the implications of our study for the analysis of signed complex 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 stru…
We introduce a reshuffled approach to empirical analyze signs' organization in real directed signed social networks of Epinions and Slashdots from the global viewpoint. In the reshuffled approach, each negative link has probability $p_{rs}$ to exchange its sign with another positive link chosen randomly. Through calculating the entropies of social status ($S_{in}$ and $S_{out}$) of and mimicking opinion formation of the majority-rule model on each reshuffled signed network, we find that $S_{in}$ and $S_{out}$ reach their own minimum values as well as the magnetization $|m^{*}|$ reaches its max…
Numerous real-world relations can be represented by signed networks with positive links (e.g., trust) and negative links (e.g., distrust). Link analysis plays a crucial role in understanding the link formation and can advance various tasks in social network analysis such as link prediction. The majority of existing works on link analysis have focused on unsigned social networks. The existence of negative links determines that properties and principles of signed networks are substantially distinct from those of unsigned networks, thus we need dedicated efforts on link analysis in signed social …
We empirical study the signs' property in the directed signed social networks of Slashdot and Epinions by using an reshuffled approach. Through calculating the entropy $S_{out}$ and the giant component $G$, we find an interesting 90/10 phenomenon: each individual labels his/her neighbors as friends with $90\%$ or foes with $10\%$ uniformly random from the macroscopic perspective. We also find that the entropy $S_{out}$ is suppressed by the non-randomness of labeling sign. Our present work can prove how do the randomness and the non-randomness coexist in human behavior of labeling signs, qualit…
In this paper, we perform the initial and comprehensive study on the problem of measuring node relevance on signed social networks. We design numerous relevance measurements for signed social networks from both local and global perspectives and investigate the connection between signed relevance measurements, balance theory and signed network properties. Experimental results are conducted to study the effects of signed relevance measurements with four real-world datasets on signed network analysis tasks.
Much recent research on social networks has focused on the modeling and analysis of how opinions evolve as a function of interpersonal relationships. It is also of great interest to model and understand the implications of friendly and antagonistic relationships. In this paper, we propose a new, simple and intuitive model that incorporates the socio-psychological phenomenon of the boomerang effect in opinion dynamics. We establish that, under certain conditions on the structure of the signed network that corresponds to the so-called structural balance property, the opinions in the network pola…
We present an unsupervised model for inducing signed social networks from the content exchanged across network edges. Inference in this model solves three problems simultaneously: (1) identifying the sign of each edge; (2) characterizing the distribution over content for each edge type; (3) estimating weights for triadic features that map to theoretical models such as structural balance. We apply this model to the problem of inducing the social function of address terms, such as 'Madame', 'comrade', and 'dude'. On a dataset of movie scripts, our system obtains a coherent clustering of address …
There is a long-standing belief that in social networks with simultaneous friendly/hostile interactions (signed networks) there is a general tendency to a global balance. Balance represents a state of the network with lack of contentious situations. Here we introduce a method to quantify the degree of balance of any signed (social) network. It accounts for the contribution of all signed cycles in the network and gives, in agreement with empirical evidences, more weight to the shorter than to the longer cycles. We found that, contrary to what is believed, many signed social networks -- in parti…
Arizona State University（亚利桑那州立大学）；IBM T.J. Watson Research Center（IBM托马斯·J·沃森研究中心）；Yahoo Research, Yahoo! Inc（雅虎公司雅虎研究院）
Many real-world relations can be represented by signed networks with positive and negative links, as a result of which signed network analysis has attracted increasing attention from multiple disciplines. With the increasing prevalence of social media networks, signed network analysis has evolved from developing and measuring theories to mining tasks. In this article, we present a review of mining signed networks in the context of social media and discuss some promising research directions and new frontiers. We begin by giving basic concepts and unique properties and principles of signed netwo…
The modeling of networks, specifically generative models, have been shown to provide a plethora of information about the underlying network structures, as well as many other benefits behind their construction. Recently there has been a considerable increase in interest for the better understanding and modeling of networks, but the vast majority of this work has been for unsigned networks. However, many networks can have positive and negative links(or signed networks), especially in online social media, and they inherently have properties not found in unsigned networks due to the added complexi…
We investigate signed networks with community structure with respect to their spectrum and their evolution under a dynamical model of structural balance, a prominent theory of signed social networks. The spectrum of the adjacency matrix generated by a stochastic block model with two equal size communities shows detectability transitions in which the community structure becomes manifest when its signal eigenvalue appears outside the main spectral band. The spectrum also exhibits "sociality" transitions involving the homogeneous structure representing the average tie value. We derive expressions…
University of Sydney（悉尼大学）；Goethe University Frankfurt（法兰克福歌德大学）；IT:U Interdisciplinary Transformation University（IT：U跨学科转型大学）；Central European University（中欧大学）；Complexity Science Hub（复杂性科学中心）
In this paper, we present an experimental analysis of the asynchronous push & pull rumour spreading protocol. This protocol is, to date, the best-performing rumour spreading protocol for simple, scalable, and robust information dissemination in distributed systems. We analyse the effect that multiple parameters have on the protocol's performance, such as using memory to avoid contacting the same neighbor twice in a row, varying the stopping criteria used by nodes to decide when to stop spreading the rumour, employing more sophisticated neighbor selection policies instead of the standard unifor…
Signed directed social networks, in which the relationships between users can be either positive (indicating relations such as trust) or negative (indicating relations such as distrust), are increasingly common. Thus the interplay between positive and negative relationships in such networks has become an important research topic. Most recent investigations focus upon edge sign inference using structural balance theory or social status theory. Neither of these two theories, however, can explain an observed edge sign well when the two nodes connected by this edge do not share a common neighbor (…
The classic influence maximization problem finds a limited number of influential seed users in a social network such that the expected number of influenced users in the network, following an influence cascade model, is maximized. The problem has been studied in different settings, with further generalization of the graph structure, e.g., edge weights and polarities, target user categories, etc. In this paper, we introduce a unique influence diffusion scenario involving a population that split into two distinct groups, with opposing views. We aim at finding the top-$k$ influential seed nodes so…
We propose a signed network formation game, in which pairs of individuals strategically change the signs of the edges in a complete network. These individuals are members of a social network who strategically reduce cognitive dissonances by changing their interpersonal appraisals. We characterize the best-response dynamics for this game and prove that its implementation \pc{can} dynamically drive the network to a sociologically meaningful sign configuration called clustering balance. In this configuration, agents in the social network form one or more clusters that have positive relationships …
We study the evolution of opinions (or beliefs) over a social network modeled as a signed graph. The sign attached to an edge in this graph characterizes whether the corresponding individuals or end nodes are friends (positive links) or enemies (negative links). Pairs of nodes are randomly selected to interact over time, and when two nodes interact, each of them updates its opinion based on the opinion of the other node and the sign of the corresponding link. This model generalizes DeGroot model to account for negative links: when two enemies interact, their opinions go in opposite directions.…
We study the problem of the emergence of cooperation in dynamic signed networks where agent strategies coevolve with relational signs and network topology. Running simulations based on an agent-based model, we compare results obtained in a regular lattice initialization with those obtained on a comparable random network initialization. We show that the increased degree heterogeneity at the outset enlarges the parametric conditions in which cooperation survives in the long run. Furthermore, we show how the presence of sign-dependent emotional strategies catalyze the evolution of cooperation wit…
Relations between users on social media sites often reflect a mixture of positive (friendly) and negative (antagonistic) interactions. In contrast to the bulk of research on social networks that has focused almost exclusively on positive interpretations of links between people, we study how the interplay between positive and negative relationships affects the structure of on-line social networks. We connect our analyses to theories of signed networks from social psychology. We find that the classical theory of structural balance tends to capture certain common patterns of interaction, but that…
Balance theory explains the forces behind the structure of social systems, which are commonly modeled as static undirected signed networks. We expand this modeling approach to incorporate directionality of edges, and consider three levels of analysis: triads, subgroups, and the whole network. For triad-level balance, we operationalize a new measure by utilizing semicycles that satisfy the condition of transitivity. For subgroup-level balance, we propose measures of cohesiveness (intra-group solidarity) and divisiveness (inter-group antagonism) to capture balance within and among subgroups of t…
In this work, we study the behavior of Brazilian politicians and political parties with the help of clustering algorithms for signed social networks. For this purpose, we extract and analyze a collection of signed networks representing voting sessions of the lower house of Brazilian National Congress. We process all available voting data for the period between 2011 and 2016, by considering voting similarities between members of the Congress to define weighted signed links. The solutions obtained by solving Correlation Clustering (CC) problems are the basis for investigating deputies voting net…
Signed network analysis has attracted increasing attention in recent years. This is in part because research on signed network analysis suggests that negative links have added value in the analytical process. A major impediment in their effective use is that most social media sites do not enable users to specify them explicitly. In other words, a gap exists between the importance of negative links and their availability in real data sets. Therefore, it is natural to explore whether one can predict negative links automatically from the commonly available social network data. In this paper, we i…
Structural balance theory assumes triads in networks to gravitate towards stable configurations. The theory has been verified for undirected graphs. Since real-world networks are often directed, we introduce a novel method for considering both transitivity and sign consistency for calculating balance in signed digraphs. We test our approach on graphs that we constructed by using different methods for identifying edge signs: natural language processing to infer signs from underlying text data, and self-reported survey data. Our results show that for various social contexts and edge sign detecti…
We consider a nonlinear dynamical system on a signed graph, which can be interpreted as a mathematical model of social networks in which the links can have both positive and negative connotations. In accordance with a concept from social psychology called structural balance, the negative links play a key role in both the structure and dynamics of the network. Recent research has shown that in a nonlinear dynamical system modeling the time evolution of "friendliness levels" in the network, two opposing factions emerge from almost any initial condition. Here we study active external influence in…
This paper studies the signed networks in the presence of stubborn links, based on the structural balance theory. Each agent in the network has a mixture of positive and negative links represent friendly and antagonistic interactions and his stubbornness about interactions. Structural balance theory affirms that in signed social networks with simultaneous friendly/hostile interactions, there is a general tendency of evolving over time to reduce the tensions. From this perspective, individuals iteratively invert their own sentiments to reduce the felt tensions induced by imbalance. In this pape…
In this work we consider a collective decision-making process in a network of agents described by a nonlinear interconnected dynamical model with sigmoidal nonlinearities and signed interaction graph. The decisions are encoded in the equilibria of the system. The aim is to investigate this multiagent system when the signed graph representing the community is not structurally balanced and in particular as we vary its frustration, i.e., its distance to structural balance. The model exhibits bifurcations, and a ``social effort'' parameter, added to the model to represent the strength of the inter…
A large portion of today's big data can be represented as networks. However, not all networks are the same, and in fact, for many that have additional complexities to their structure, traditional general network analysis methods are no longer applicable. For example, signed networks contain both positive and negative links, and thus dedicated theories and algorithms have been developed. However, previous work mainly focuses on the unipartite setting where signed links connect any pair of nodes. Signed bipartite networks on the one hand, are commonly found, but have primarily been overlooked. T…
Person-to-person evaluations are prevalent in all kinds of discourse and important for establishing reputations, building social bonds, and shaping public opinion. Such evaluations can be analyzed separately using signed social networks and textual sentiment analysis, but this misses the rich interactions between language and social context. To capture such interactions, we develop a model that predicts individual A's opinion of individual B by synthesizing information from the signed social network in which A and B are embedded with sentiment analysis of the evaluative texts relating A to B. …
We address the problem of classifying the links of signed social networks given their full structural topology. Motivated by a binary user behaviour assumption, which is supported by decades of research in psychology, we develop an efficient and surprisingly simple approach to solve this classification problem. Our methods operate both within the active and batch settings. We demonstrate that the algorithms we developed are extremely fast in both theoretical and practical terms. Within the active setting, we provide a new complexity measure and a rigorous analysis of our methods that hold for …
Due to the fact much of today's data can be represented as graphs, there has been a demand for generalizing neural network models for graph data. One recent direction that has shown fruitful results, and therefore growing interest, is the usage of graph convolutional neural networks (GCNs). They have been shown to provide a significant improvement on a wide range of tasks in network analysis, one of which being node representation learning. The task of learning low-dimensional node representations has shown to increase performance on a plethora of other tasks from link prediction and node clas…
Is the enemy of an enemy necessarily a friend? If not, to what extent does this tend to hold? Such questions were formulated in terms of signed (social) networks and necessary and sufficient conditions for a network to be "balanced" were obtained around 1960. Since then the idea that signed networks tend over time to become more balanced has been widely used in several application areas. However, investigation of this hypothesis has been complicated by the lack of a standard measure of partial balance, since complete balance is almost never achieved in practice. We formalize the concept of a m…
Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；University of Chinese Academy of Sciences（中国科学院大学）
Graph or network data is ubiquitous in the real world, including social networks, information networks, traffic networks, biological networks and various technical networks. The non-Euclidean nature of graph data poses the challenge for modeling and analyzing graph data. Recently, Graph Neural Network (GNNs) are proposed as a general and powerful framework to handle tasks on graph data, e.g., node embedding, link prediction and node classification. As a representative implementation of GNNs, Graph Attention Networks (GATs) are successfully applied in a variety of tasks on real datasets. Howeve…
Networks provide useful tools for analyzing diverse complex systems from natural, social, and technological domains. Growing size and variety of data such as more nodes and links and associated weights, directions, and signs can provide accessory information. Link and weight abundance, on the other hand, results in denser networks with noisy, insignificant, or otherwise redundant data. Moreover, typical network analysis and visualization techniques presuppose sparsity and are not appropriate or scalable for dense and weighted networks. As a remedy, network backbone extraction methods aim to re…
We analyse signed networks from the perspective of balance theory which predicts structural balance as a global structure for signed social networks that represent groups of friends and enemies. The scarcity of balanced networks encouraged us to define the notion of partial balance in order to quantify the extent to which a network is balanced. We evaluate several numerical measures of partial balance and recommend using the frustration index, a measure that satisfies key axiomatic properties and allows us to analyse graphs based on their levels of partial balance. The exact algorithms used in…
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 plac…
Relationships between individuals in a social network, genes in biological systems, and spins in magnetic systems often reflect a mixture of positive (friendly) and negative (antagonistic) interactions. However, most studies of complex networks have focused on networks consisting of solely positive interactions. Here, we study threshold cascades on signed networks composed of both positive and negative connections, focusing on when a pair of nodes connected by a negative link can only be activated exclusively to each other. We found that the negative interactions not only suppress global casca…
Influence diffusion and influence maximization in large-scale online social networks (OSNs) have been extensively studied, because of their impacts on enabling effective online viral marketing. Existing studies focus on social networks with only friendship relations, whereas the foe or enemy relations that commonly exist in many OSNs, e.g., Epinions and Slashdot, are completely ignored. In this paper, we make the first attempt to investigate the influence diffusion and influence maximization in OSNs with both friend and foe relations, which are modeled using positive and negative edges on sign…
Most studies of disease spreading consider the underlying social network as obtained without the contagion, though epidemic influences people's willingness to contact others: A "friendly" contact may be turned to "unfriendly" to avoid infection. We study the susceptible-infected disease-spreading model on signed networks, in which each edge is associated with a positive or negative sign representing the friendly or unfriendly relation between its end nodes. In a signed network, according to Heider's theory, edge signs evolve such that finally a state of structural balance is achieved, correspo…
What defines a group of friends? Rethinking community structure in signed, directed networks
Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matemáticas, Universidad Carlos III de Madrid（马德里卡洛斯三世大学复杂系统跨学科小组数学系）；Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Universidad de Zaragoza（萨拉戈萨大学生物计算与复杂系统物理研究所）；Center for Complex Networks and Systems Research, Luddy School of Informatics, Computing, and Engineering, Indiana University Bloomington（印第安纳大学布鲁明顿分校卢迪信息、计算与工程学院复杂网络与系统研究中心）
Assessing frustration in real-world signed networks: a statistical theory of balance
IMT School for Advanced Studies（意大利高等研究院）；INdAM-GNAMPA Istituto Nazionale di Alta Matematica ‘Francesco Severi’（阿尔塔数学国家研究所·GNAMPA）；Lorentz Institute for Theoretical Physics, University of Leiden（莱顿大学洛伦兹理论物理研究所）；Scuola Normale Superiore（比萨高等师范学院）
We study online social networks in which relationships can be either positive (indicating relations such as friendship) or negative (indicating relations such as opposition or antagonism). Such a mix of positive and negative links arise in a variety of online settings; we study datasets from Epinions, Slashdot and Wikipedia. We find that the signs of links in the underlying social networks can be predicted with high accuracy, using models that generalize across this diverse range of sites. These models provide insight into some of the fundamental principles that drive the formation of signed l…
