Node representation learning for signed directed networks has received considerable attention in many real-world applications such as link sign prediction, node classification and node recommendation. The challenge lies in how to adequately encode the complex topological information of the networks. Recent studies mainly focus on preserving the first-order network topology which indicates the closeness relationships of nodes. However, these methods generally fail to capture the high-order topology which indicates the local structures of nodes and serves as an essential characteristic of the network topology. In addition, for the first-order topology, the additional value of non-existent links is largely ignored. In this paper, we propose to learn more representative node embeddings by simultaneously capturing the first-order and high-order topology in signed directed networks. In particular, we reformulate the representation learning problem on signed directed networks from a variational auto-encoding perspective and further develop a decoupled variational embedding (DVE) method. DVE leverages a specially designed auto-encoder structure to capture both the first-order and high-order topology of signed directed networks, and thus learns more representative node embedding. Extensive experiments are conducted on three widely used real-world datasets. Comprehensive results on both link sign prediction and node recommendation task demonstrate the effectiveness of DVE. Qualitative results and analysis are also given to provide a better understanding of DVE.
Seoul National University（首尔国立大学）；Korea Institute of Energy Technology（韩国能源技术研究院）
Graph contrastive learning has become a powerful technique for several graph mining tasks. It learns discriminative representation from different perspectives of augmented graphs. Ubiquitous in our daily life, singed-directed graphs are the most complex and tricky to analyze among various graph types. That is why singed-directed graph contrastive learning has not been studied much yet, while there are many contrastive studies for unsigned and undirected. Thus, this paper proposes a novel signed-directed graph contrastive learning, SDGCL. It makes two different structurally perturbed graph view…
University of North Carolina at Charlotte（北卡罗来纳大学夏洛特分校）；University of Arkansas（阿肯色大学）
It has been shown that the adjacency eigenspace of a network contains key information of its underlying structure. However, there has been no study on spectral analysis of the adjacency matrices of directed signed graphs. In this paper, we derive theoretical approximations of spectral projections from such directed signed networks using matrix perturbation theory. We use the derived theoretical results to study the influences of negative intra cluster and inter cluster directed edges on node spectral projections. We then develop a spectral clustering based graph partition algorithm, SC-DSG, an…
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…
CAS Key Laboratory of Network Data Science and Technology, Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所网络数据科学与技术重点实验室）；University of Chinese Academy of Sciences（中国科学院大学）
Network embedding is aimed at mapping nodes in a network into low-dimensional vector representations. Graph Neural Networks (GNNs) have received widespread attention and lead to state-of-the-art performance in learning node representations. However, most GNNs only work in unsigned networks, where only positive links exist. It is not trivial to transfer these models to signed directed networks, which are widely observed in the real world yet less studied. In this paper, we first review two fundamental sociological theories (i.e., status theory and balance theory) and conduct empirical studies o…
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…
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 (…
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…
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 undirect…
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…
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…
Dense regions in networks are an indicator of interesting and unusual information. However, most existing methods only consider simple, undirected, unweighted networks. Complex networks in the real-world often have rich information though: edges are asymmetrical and nodes/edges have categorical and numerical attributes. Finding dense subgraphs in such networks in accordance with this rich information is an important problem with many applications. Furthermore, most existing algorithms ignore the higher-order relationships (i.e., motifs) among the nodes. Motifs are shown to be helpful for dense…
On the Effects of Decentralized Moderation on Network Robustness and Information Diffusion in Mastodon
Fondazione Bruno Kessler（布鲁诺·凯斯勒基金会）；Department of Informatics, Modeling, Electronics and System Engineering University of Calabria（卡塔尼亚大学信息、建模、电子与系统工程系）；Department of Computing, Northeastern University London（伦敦东北大学计算机系）；Institute for Cross-Disciplinary Physics and Complex Systems (IFISC), CSIC-UIB（跨学科物理与复杂系统研究所 (IFISC)，西班牙国家研究委员会-巴利阿里群岛大学）；“Enrico Fermi” Research Center (CREF)（“恩里科·费米”研究中心 (CREF)）
A complexity-theoretic approach to studying biological networks is proposed. A simple graph representation is used where molecules (DNA, RNA, proteins and chemicals) are vertices and relations between them are directed and signed (promotional (+) or inhibitory (-)) edges. Based on this model, the problem of network evolution (NE) is defined formally as an optimization problem and subsequently proven to be fundamentally hard (NP-hard) by means of reduction from the Knapsack problem (KP). Second, for empirical validation, various biological networks of experimentally-validated interactions are c…
Multiscale dynamical embeddings of complex networks
Institute for Data, Systems and Society, Massachusetts Institute of Technology（麻省理工学院数据、系统与社会研究所）；Department of Engineering Science, University of Oxford（牛津大学工程学系）；ICTEAM, Université catholique de Louvain（天主教鲁汶大学ICTEAM学院）；CORE, Université catholique de Louvain（天主教鲁汶大学CORE中心）；Mathematical Institute, University of Oxford（牛津大学数学研究所）；Department of Mathematics, Imperial College London（帝国理工学院伦敦数学系）
Previous network models have imagined that connections change to promote structural balance, or to reflect hierarchies. We propose a model where agents adjust their connections to appear credible to an external observer. In particular, we envision a signed, directed network where positive edges represent endorsements or trust and negative edges represent accusations or doubt, and consider both the strategies an external observer might use to identify credible nodes and the strategies nodes might use to then appear credible by changing their outgoing edges. First, we establish that an external …
