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This paper focuses on the problem of bipartite secure containment control for a specific class of discrete-time multi-agent systems with multiple dynamic leaders. The followers are divided into two subgroups that cooperate within each subgroup and compete with the other subgroup. Similarly, the leaders exhibit cooperative-competitive behavior towards these subgroups. The main objective is to ensure that cooperating followers gradually enter the dynamic convex hull formed by leaders while competing followers enter the opposite convex hull. To protect sensitive information, only the difference between the real state and the encrypted state of the position and velocity is quantized and transmitted, rather than the actual state itself. As a result, the permissible range of the gain parameters and other relevant parameters is determined. Furthermore, a precise definition of the minimum channel capacity is provided to understand the factors that influence the requirement for minimum channel capacity. Finally, an illustrative example is presented to demonstrate the effectiveness of the developed secure control method. [ABSTRACT FROM AUTHOR]

Network dismantling is an important question that has attracted much attention from many different research areas, including the disruption of criminal organizations, the maintenance of stability in sensor networks, and so on. However, almost all current algorithms focus on unsigned networks, and few studies explore the problem of signed network dismantling due to its complexity and lack of data. Importantly, there is a lack of an effective quality function to assess the performance of signed network dismantling, which seriously restricts its deeper applications. To address these questions, in this paper, we design a new objective function and further propose an effective algorithm named as DSEDR, which aims to search for the best dismantling strategy based on evolutionary deep reinforcement learning. Especially, since the evolutionary computation is able to solve global optimization and the deep reinforcement learning can speed up the network computation, we integrate it for the signed network dismantling efficiently. To verify the performance of DSEDR, we apply it to a series of representative artificial and real network data and compare the efficiency with some popular baseline methods. Based on the experimental results, DSEDR has superior performance to all other methods in both efficiency and interpretability. [ABSTRACT FROM AUTHOR]

This paper is concerned with the bipartite secure control issue for a class of discrete-time nonlinear multi-agent systems under a dynamic encryption–decryption approach. First, the coupling relationships between agents are portrayed through a signed graph topology containing the edges of positive and negative connection weights. Next, the information transmissions between agents and their neighbors are executed via a shared communication network. The dynamic encryption–decryption approach is implemented to transform original signals into ciphertexts. Under the assumption that the signed graph is structurally balanced, a signed-network-based bipartite secure controller is designed to achieve the desired state control for the nonlinear multi-agent system and sufficient conditions are obtained for the existence of the desired signed-network-based state controller. Furthermore, a precise definition of the minimum channel capacity is proposed to understand the factors affecting the minimum channel capacity. Finally, the effectiveness of the proposed approach is illustrated by two simulation examples. [ABSTRACT FROM AUTHOR]

Due to the discrepancy between an individual's expressed opinion and private opinion in many social situations, this paper aims to study the convergence and bipartite consensus of expressed and private opinion (EPO) model on signed directed network $ \mathcal {G}(W) $ G (W) without satisfying common strong connectivity. First, by constructing an enlarged network $ \mathcal {G}(P) $ G (P) of $ \mathcal {G}(W) $ G (W) and studying the properties of CSCCs in $ \mathcal {G}(P) $ G (P) , we establish some general convergence criteria for the EPO model. Second, we explore the relationship between the final private opinion, final expressed opinion and initial opinion of an individual and prove that the self-confidence of an individual can influence the gap between his final expressed opinion and group pressure. Third, by structural balance theory, we establish the bipartite consensus criterion of the EPO model. Finally, numerical simulations are presented to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

This paper mainly studies the convergence of time-varying discrete-time Altafini model. Firstly, we convert the bipartite consensus of the Altafini model with n nodes into consensus of the DeGroot model with $ 2n $ 2 n nodes by adopting lifting approach. Secondly, based on structural balance theory and node relabelling theory, the consensus of enlarged DeGroot model can be further equivalently converted into the consensus of one simple DeGroot model with n nodes. Thirdly, by using the equivalent transformation and the ergodic coefficient theory, we change the sufficient condition from 'repeatedly jointly strongly connected' graphs to 'repeatedly jointly scrambling' graphs, and verify that the new condition also can lead to the bipartite consensus of the Altafini model. This novel criterion allows for determining the bipartite consensus of the Altafini model without the condition of 'repeatedly jointly strongly connected' graphs. Next, we provide a concise proof for the case of opinions converging to 0 with the condition of 'repeatedly jointly strongly connected' by the ergodic coefficient theory. Finally, we develop a reasonable coevolution model to illustrate the effectiveness and strong applicability of our main theoretical results. [ABSTRACT FROM AUTHOR]

The existing signed graph neural networks mainly focus on the design process of neighbor aggregation function, but ignore the correlation between nodes, which leads to the decline of the representation ability of neural networks. In order to solve the above problems, a SDEGNN (Signed Distance Encoding based on Graph Neural Network) model based on enhanced signed distance encoding is proposed in this paper. Firstly, the problem of limited representation ability in signed graph neural networks is discussed. Secondly, in order to capture the correlation between nodes, signed distance encoding is proposed as the node feature representation to enhance the representation ability of the model. Thirdly, the signed distance encoding is injected into the information aggregation process of the signed graph convolutional network, and the objective function is proposed to optimize the SDEGNN model. The SDEGNN model is verified performance by three real signed network datasets Bitcoin-OTC, Bitcoin-Alpha, and Wiki-RfA. The experimental results show that the SDEGNN model can effectively improve the accuracy of link sign prediction tasks. [ABSTRACT FROM AUTHOR]

A signed network Σ = (G , σ) with the underlying graph G = (V , E) , used as a mathematical model for analyzing social networks, has each edge in E with a weight 1 or − 1 assigned by the signature function σ. In this paper, we deal with two types of Detour Distance Laplacian (DDL) matrices for signed networks. We characterize balance in signed social networks using these matrices and we compute the DDL spectrum of certain unbalanced signed networks, as balanced signed networks behave like unsigned ones. [ABSTRACT FROM AUTHOR]

In online education platforms, accurately predicting student performance is essential for timely dropout prevention and interventions for at-risk students. This task is made difficult by the prevalent use of Multiple-Choice Questions (MCQs) in learnersourcing platforms, where noise in student-generated content and the limitations of existing unsigned graph-based models, specifically their inability to distinguish the semantic meaning between correct and incorrect responses, hinder accurate performance predictions. To address these issues, we introduce the L arge L anguage M odel enhanced S igned B ipartite graph C ontrastive L earning (LLM-SBCL) model—a novel Multimodal Model utilizing Signed Graph Neural Networks (SGNNs) and a Large Language Model (LLM). Our model uses a signed bipartite graph to represent students' answers, with positive and negative edges denoting correct and incorrect responses, respectively. To mitigate noise impact, we apply contrastive learning to the signed graphs, combined with knowledge point embeddings from the LLM to further enhance our model's predictive performance. Upon evaluating our model on five real-world datasets, it demonstrates superior accuracy and stability, exhibiting an average F1 improvement of 3.7% over the best baseline models. • Student-question interactions modeled via a signed bipartite graph. • Problem cast as link sign prediction in signed bipartite graph. • Contrastive learning employed to handle student content noise. • Using large language model to extract knowledge from questions. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the evolutionary dynamic model for signed edges as observed in online signed social networks. We introduce the incremental mechanism of signed edges behind a simple random walk and explain how this relates to Brownian motion and the diffusive process. We prove how a one-dimensional thermal diffusion equation can be obtained to describe such edge-generating mechanism, and moreover obtain a macroscopic probability distribution of positive and negative edges. The result reveals that the signed edge growth dynamics process can be regarded as a thermodynamic diffusion process. Both empirically and theoretically, we validate that signed network links follow the classic statistic mechanism, i.e., local Brownian motion gives rise to the global emergence pattern of the Gaussian process. The investigation might discover a new and universal characteristic for signed networks, and shed light on some potential applications, such as information spreading, evolutionary games, trust transmission, and dynamic structural balance. [ABSTRACT FROM AUTHOR]

The intention of this paper is to explore the distributed control issues for directed signed networks in the face of external disturbances under strongly connected topologies. A new class of nonsingular transformations is provided by introducing an output variable, with which the consensus can be equivalently transformed into the output stability regardless of whether the associated signed digraphs are structurally balanced or not. By taking advantage of the standard robust H ∞ control theory, the bipartite consensus and state stability results can be built for signed networks under structurally balanced and unbalanced conditions, respectively, in which the desired disturbance rejection performances can also be satisfied. Furthermore, the mathematical expression can be given for the terminal states of signed networks under the influence of external disturbances. In addition, two simulations are presented to verify the correctness of our developed results. [ABSTRACT FROM AUTHOR]

This technical note deals with a coupled epidemic-opinion dynamical model over a multiplex network, where the interplay between polarized opinions over social interaction network regarding protective measures and disease spreading captured by susceptible-exposed-infected-vigilant (SEIV) epidemic model over transmission network is investigated. For this coupled model, sufficient condition of the disease free state is obtained for the network epidemic model, while the perceived disease severity drops to zero at this state through opinion sharing. The simulation results corroborate the findings. [ABSTRACT FROM AUTHOR]

Structural balance is a classic property of signed graphs satisfying Heider'sseminal axioms. Mathematical sociologists have studied balance theory since itsinception in the 1040s. Recent research has focused on the development ofdynamic models explaining the emergence of structural balance. In this paper,we introduce a novel class of parsimonious dynamic models for structuralbalance based on an interpersonal influence process. Our proposed models aregradient flows of an energy function, called the dissonance function, whichcaptures the cognitive dissonance arising from violations of Heider's axioms.Thus, we build a new connection with the literature on energy landscapeminimization. This gradient flow characterization allows us to study thetransient and asymptotic behaviors of our model. We provide mathematical andnumerical results describing the critical points of the dissonance function.

A node is a structurally balanced (respectively, unbalanced) node if and only if the absolute value of its corresponding entry in the right eigenvector associated with the zero eigenvalue of the Laplacian matrix is equal to (respectively, is less than) one. The corresponding entry in the right eigenvector is called the algebraic trait for the structurally balanced property of a node. This paper aims to explore the algebraic trait for the structurally balanced property of a node under a signed digraph with a spanning tree by using a geometric-based method. Such a geometric point of view reveals the relationships of the links in a network for structurally balanced and structurally unbalanced nodes. The structurally balanced property of a node is determined by its parent nodes, and the connections between itself and its parent nodes. First of all, a hierarchical structure of its parent nodes is proposed, based on which the Laplacian matrix of the underlying topology can be written as a lower triangular matrix. Then, according to the lower triangular Laplacian matrix, the mathematical expression of the right eigenvector associated with the zero eigenvalue is derived. Based on this, as well as the definition of the structurally balanced node, the algebraic trait for the structurally balanced property of a node is obtained. Finally, a numerical example is provided to verify theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the authors consider both the nodes' opinions dynamics and signed network edges' evolution. Simulated Annealing Algorithm is applied for searching the minimal global energy function, and bounded confidence model is used for nodes' opinions updating. The authors find that the local and global level of balance of signed network is consistent with collective opinions 2-polarization. This property is explainable in terms of the structure balance of the sign distributions on the nodes and edges. The level of balance and the final opinions polarization pattern are achieved depends on the initial density of signed network, and the percentage of initial positive edges. Numerical simulations of the proposed model display a rich and intuitive behavior of the opinions polarization processes. In particular, the authors show that opinions persistent fluctuations is consistent with minimal global the energy function. This work verify that signed social networks are indeed limited balanced, could be used to explain ubiquitous binary polarization phenomenon of real world. [ABSTRACT FROM AUTHOR]

ESG ratings are data-driven indices, focused on three key pillars (Environmental, Social, and Governance), which are used by investors in order to evaluate companies and countries, in terms of Sustainability. A reasonable question which arises is how these ratings are associated to each other. The research purpose of this work is to provide the first analysis of correlation networks, constructed from ESG ratings of selected economies. The networks are constructed based on Pearson correlation and analyzed in terms of some well-known tools from Network Science, namely: degree centrality of the nodes, degree centralization of the network, network density and network balance. We found that the Prevalence of Overweight and Life Expectancy are the most central ESG ratings, while unexpectedly, two of the most commonly used economic indicators, namely the GDP growth and Unemployment, are at the bottom of the list. China’s ESG network has remarkably high positive and high negative centralization, which has strong implications on network’s vulnerability and targeted controllability. Interestingly, if the sign of correlations is omitted, the above result cannot be captured. This is a clear example of why signed network analysis is needed. The most striking result of our analysis is that the ESG networks are extremely balanced, i.e. they are split into two anti-correlated groups of ESG ratings (nodes). It is impressive that USA’s network achieves 97.9% balance, i.e. almost perfect structural split into two anti-correlated groups of nodes. This split of network structure may have strong implications on hedging risk, if we see ESG ratings as underlying assets for portfolio selection. Investing into anti-correlated assets, called as "hedge assets", can be useful to offset potential losses. Our future direction is to apply and extend the proposed signed network analysis to ESG ratings of corporate organizations, aiming to design optimal portfolios with desired balance between risk and return.

Predicting drug-drug adverse reactions (DDADRs) is an important task because many patients inevitably take multiple medicines to pursue sound therapeutic results. However, predicting DDADRs is an extremely challenging task. Graph representation is a popular learning method which can simultaneously learn the attribute information of nodes and graph structural information. In this paper, we propose DMVDGI, a novel self-supervised multi-view graph learning framework for predicting DDADRs. Specifically, we first describe drug features with multi-view data, which makes the drug feature representation more comprehensive due to containing multiple biomedical information. Then, we depict the drug-drug interactions (DDIs) with the signed network, which can clearly express the positive and negative relationships between drugs. The DDI signed network makes the drug feature representations imply rich semantic information. Finally, we train our model using contrastive learning, utilizing the mutual information between local-global representations to optimize model parameters. Besides, we conduct extensive experiments to verify the effectiveness of our model. The results show that our model is superior to baseline methods, and the best performance of AUROC outperforms the baseline model by 8%. More encouragingly, our DMVDGI model is superior to some supervised baseline methods on several benchmarks. To the best of our knowledge, the DMVDGI model is the first self-supervised multi-view graph model for predicting DDADRs. [ABSTRACT FROM AUTHOR]

Network node embedding is mapping nodes in a network to a low-dimensional vector representation, so that vector space-based learning methods can be directly applied to handle downstream tasks such as link prediction. Most of the existing network node embedding models were for unsigned networks and could not be directly used to deal with signed networks (usually need to be converted into unsigned networks for processing, thus discarding a lot of valuable information embedded in the positive and negative signs on the edges). A node embedding model (SNEDA) based on graphical neural networks was proposed that could directly deal with symbolic networks. Based on structural balance theory and status theory, the paths between nodes were divided into 20 different motif structures according to the direction and the positive and negative information on the edges. A network propagation model was designed with two levels of attention mechanism, which could capture the contribution and influence of different neighboring nodes to the vector representation of node i by node-level attention mechanism when aggregating the direct neighboring information of node i, and captured the vector representation of different motif to node i by path-level attention when aggregating the second-order and higher-order neighboring information of node i. A two-level attention mechanism was introduced to integrate different contributions and influences at the node level and path level, which could it not only improve the time efficiency of the algorithm but also make the final vector representation of node i more beneficial to improve the prediction accuracy of the downstream link prediction task. Through experiments conducted on four real social network datasets, the SNEDA model improved the AUC and F1 metrics by about 3.1% and 1.1%, respectively, compared with the benchmark model, and the results showed that the network representation obtained by the model could improve the accuracy of link prediction. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of dynamic event-triggered bipartite consensus control for nonlinear multi-agent systems based on signed networks. A new dynamic event-triggered control mechanism is proposed, whereby an adjustment variable is introduced to dynamically schedule the triggering frequency, enabling the minimization of the triggering times while ensuring system performance. Based on the designed event-triggered control algorithm, sufficient conditions are derived to guarantee that bipartite consensus can be reached by the considered nonlinear multi-agent system. Furthermore, it is proved that Zeno behavior will not occur. Numerical examples are provided in this paper to verify the effectiveness of the proposed control algorithm. The simulation results reveal that, compared with the static event-triggered mechanism and the traditional dynamic event-triggered mechanism, the proposed event-triggered algorithm can further reduce the triggering times and enhance the flexibility of the event-triggered mechanism. [ABSTRACT FROM AUTHOR]

Signed network embedding is an approach to learning low-dimensional representations of nodes in signed networks with both positive and negative links, which facilitates downstream tasks such as link prediction with general data mining frameworks. Due to the distinct properties and significant added value of negative links, existing signed network embedding methods usually design dedicated methods based on social theories such as balance theory and status theory. However, existing signed network embedding methods ignore the characteristics of multiple facets of each node and mix them up in one single representation, which limits the ability to capture the fine-grained attentions between node pairs. In this paper, we propose MUSE , a MU lti-faceted attention-based S igned network E mbedding framework to tackle this problem. Specifically, a joint intra- and inter-facet attention mechanism is introduced to aggregate fine-grained information from neighbor nodes. Moreover, balance theory is also utilized to guide information aggregation from multi-order balanced and unbalanced neighbors. Experimental results on four real-world signed network datasets demonstrate the effectiveness of our proposed framework. [ABSTRACT FROM AUTHOR]

Signed graph neural networks learn low-dimensional representations for nodes in signed networks with positive and negative links, which helps with many downstream tasks like link prediction. However, most existing signed graph neural networks ignore individual characteristics of nodes and thus limit the ability to learn the underlying structure of real signed graphs. To address this limitation, a deep graph neural network framework SiNP to learn Signed network embedding with Node Polarity is proposed. To be more explicit, a node-signed property metric mechanism is developed to encode the individual characteristics of the nodes. In addition, a graph convolution layer is added so that both positive and negative information from neighboring nodes can be combined. The final embedding of nodes is produced by concatenating the outcomes of these two portions. Finally, extensive experiments have been conducted on four significant real-world signed network datasets to demonstrate the efficiency and superiority of the proposed method in comparison to the state-of-the-art. [ABSTRACT FROM AUTHOR]

This paper investigates the controllability of general linear discrete-time multi-agent systems with directed and weighted signed networks by using graphic and algebraic methods. The non-delay and delay cases are considered respectively. For the case of no time delay, the upper bound condition of the controllable subspace is given by using the equitable partition method, and the influence of coefficient matrix selection of individual dynamics is illustrated. For the case of single delay and multiple delays, the equitable partition method is extended to deal with time-delay systems, and some conclusions are obtained. In particular, some simplified algebraic criteria for controllability of systems with time delay are obtained by using augmented system method and traditional algebraic controllability criteria. [ABSTRACT FROM AUTHOR]

ESG ratings are data-driven indices, focused on three key pillars (Environmental, Social, and Governance), which are used by investors in order to evaluate companies and countries, in terms of Sustainability. A reasonable question which arises is how these ratings are associated to each other. The research purpose of this work is to provide the first analysis of correlation networks, constructed from ESG ratings of selected economies. The networks are constructed based on Pearson correlation and analyzed in terms of some well-known tools from Network Science, namely: degree centrality of the nodes, degree centralization of the network, network density and network balance. We found that the Prevalence of Overweight and Life Expectancy are the most central ESG ratings, while unexpectedly, two of the most commonly used economic indicators, namely the GDP growth and Unemployment, are at the bottom of the list. China's ESG network has remarkably high positive and high negative centralization, which has strong implications on network's vulnerability and targeted controllability. Interestingly, if the sign of correlations is omitted, the above result cannot be captured. This is a clear example of why signed network analysis is needed. The most striking result of our analysis is that the ESG networks are extremely balanced, i.e. they are split into two anti-correlated groups of ESG ratings (nodes). It is impressive that USA's network achieves 97.9% balance, i.e. almost perfect structural split into two anti-correlated groups of nodes. This split of network structure may have strong implications on hedging risk, if we see ESG ratings as underlying assets for portfolio selection. Investing into anti-correlated assets, called as "hedge assets", can be useful to offset potential losses. Our future direction is to apply and extend the proposed signed network analysis to ESG ratings of corporate organizations, aiming to design optimal portfolios with desired balance between risk and return. [ABSTRACT FROM AUTHOR]

In signed networks, GNNs are used to get node embedding by aggregating node neighbor information. Most of the existing methods aggregate neighbor information from the node level, and the different paths between nodes and neighbors will also affect node embedding. The target node and its neighbors have different link positive,negative signs and link directions, which together constitute different paths.These different paths have different contributions to the target node.Based on the structural balance theory and status theory, this paper divides the different paths between nodes and their neighbors into 20 kinds of motifs, which are using to capture the different effects of paths on target nodes. Comprehensive consideration at the node level and path level, SNEDA (Signed Network Embedding via dual attention Mechanism) is proposed based on the graph attention Network. The model has two attention mechanisms: node-level attention captures different influences between nodes at the node level; path-level attention captures the different influences between motifs at the path level. The final vector representation of nodes is obtained by aggregating neighbor information selectively based on important motifs, and the vector representation is applied to link prediction. Experiments on four real social network data sets show that the network representation obtained by the model can improve the accuracy of link prediction. Experimental results demonstrate the effectiveness of the proposed framework through a signed link prediction task on four real-world signed network datasets.

Signed network embedding concentrates on learning fixed-length representations for nodes in signed networks with positive and negative links, which contributes to many downstream tasks in social media, such as link prediction. However, most signed network embedding approaches neglect hierarchical graph pooling in the networks, limiting the capacity to learn genuine signed graph topology. To overcome this limitation, this paper presents a unique deep learning-based Signed network embedding model with Hierarchical Graph Pooling (SHGP). To be more explicit, a hierarchical pooling mechanism has been developed to encode the high-level features of the networks. Moreover, a graph convolution layer is introduced to aggregate both positive and negative information from neighbor nodes, and the concatenation of two parts generates the final embedding of the nodes. Extensive experiments on three large real-world signed network datasets demonstrate the effectiveness and excellence of the proposed method. [ABSTRACT FROM AUTHOR]

Economic integration is underway in East Asia and the Asia-Pacific region, including the Association of Southeast Asian Nations (ASEAN) community-building process, with the Comprehensive and Progressive Agreement for Trans-Pacific Partnership (CPTPP) coming into effect in 2018 and the Regional Comprehensive Economic Partnership (RCEP) in 2022. While these Regional Trade Agreements (RTAs) have deepened multilateral relations, there is an insufficient mechanism to quantify multilateral diplomacy within the region. Therefore, this study analyzed the region from three perspectives: countries that have contributed to diplomacy for intra-regional cooperation (diplomatic ranking), the cohesiveness of countries in diplomatic stances (diplomatic clusters), and the synchronization period of cooperative events (diplomatic synchronization); and we quantified them by the ranking of diplomatic centrality, blockmodeling of the signed network, and analytic signal, respectively. For analysis, we used bilateral event data to create a political distance network consisting of the original East Asia Summit (EAS) member countries (ASEAN+6) and the United States for the period 1985–2020 and to define diplomatic centrality. Diplomatic ranking indicated three major trends: 1985–1992, 1993–2011, and 2012–2020. Until 1992, Japan, the ASEAN member states (AMS), and Australia ranked at the top, and from 1993 to 2011, Japan and China almost dominated the top. Since 2012, AMS have joined Japan and China in the top ranks. Diplomatic clusters showed the stances of Australia and New Zealand were closest. Throughout the 36 years, the stances of Japan and Republic of Korea were also closer, followed by China, AMS, and the United States. Diplomatic synchronization quantified the progress of regionalism in East Asia. Furthermore, diplomatic rankings in synchronous periods revealed the difference between the diplomatic positions of Japan and China in East Asia and illustrated that AMS were at the center of multilateral diplomacy in the region in 2018–2019.

Aiming at the disadvantages of negative link feature fusion and effective information mining in signed social networks, resulting in low prediction performance, a new feature fusion negative link prediction method is proposed. Based on the classic structural balance theory and social status theory, this method constructed four features related to negative signs, including node feature, structural feature, similarity feature, and scoring feature, and used logistic regression algorithms to realize negative links prediction. Its effectiveness was verified on Epinions and Slashdot two typical signed network data sets. Experimental results show that compared with the benchmark method, the accuracy of this method is increased by about 4.5% and 10.4% on the two data sets, respectively, and the F1 score is increased by about 27.3% and 31.5%, which achieve the goal of improving the effect of negative link prediction.

We propose modeling signed networks by considering two layers in a social network for generation of positive and negative links where both the layers comprise of identical set of nodes. The growth process is modeled based on preferential attachment, formation of links probabilistically asserting structural balance of local groups, and internal growth which happens without addition of new nodes. We prove that the degree distribution of a generated network follows a power-law whose exponent depends on the largest eigenvalue of a matrix which governs the dynamics of growth of degrees of nodes with respect to positive and negative links. A computable formula for average degree and lower-bounds for the number of balanced and unbalanced triads of modelled networks are also obtained. A method for structural reconstruction of real signed networks is formulated through estimation the values of the model parameters to generate the network that can inherit different structural properties of the corresponding real network. Experimental results show that our model which we term as 2L-SNM can replicate properties of several real world signed networks much more robustly than competitive state-of-the-art techniques. [ABSTRACT FROM AUTHOR]

Abstract The position of a node in a social network, or node centrality, can be quantified in several ways. Traditionally, it can be defined by considering the local connectivity of a node (degree) and some non-local characteristics (distance). Here, we present an approach that can quantify the interaction structure of signed digraphs and we define a node centrality measure for these networks. The basic principle behind our approach is to determine the sign and strength of direct and indirect effects of one node on another along pathways. Such an approach allows us to elucidate how a node is structurally connected to other nodes in the social network, and partition its interaction structure into positive and negative components. Centrality here is quantified in two ways providing complementary information: total effect is the overall effect a node has on all nodes in the same social network; while net effect describes, whether predominately positive or negative, the manner in which a node can exert on the social network. We use Sampson’s like-dislike relation network to demonstrate our approach and compare our result to those derived from existing centrality indices. We further demonstrate our approach by using Hungarian school classroom social networks.

MiRNAs are a class of small non-coding RNA molecules that play an important role in many biological processes, and determining miRNA-disease associations can benefit drug development and clinical diagnosis. Although great efforts have been made to develop miRNA-disease association prediction methods, few attention has been paid to in-depth classification of miRNA-disease associations, e.g. up/down-regulation of miRNAs in diseases. In this paper, we regard known miRNA-disease associations as a signed bipartite network, which has miRNA nodes, disease nodes and two types of edges representing up/down-regulation of miRNAs in diseases, and propose a s igned g raph n eural n etwork method (SGNNMD) for predicting deregulation types of m iRNA- d isease associations. SGNNMD extracts subgraphs around miRNA-disease pairs from the signed bipartite network and learns structural features of subgraphs via a labeling algorithm and a neural network, and then combines them with biological features (i.e. miRNA–miRNA functional similarity and disease–disease semantic similarity) to build the prediction model. In the computational experiments, SGNNMD achieves highly competitive performance when compared with several baselines, including the signed graph link prediction methods, multi-relation prediction methods and one existing deregulation type prediction method. Moreover, SGNNMD has good inductive capability and can generalize to miRNAs/diseases unseen during the training. [ABSTRACT FROM AUTHOR]

Signed networks admitting antagonistic interactions among agents may polarize, cluster, or fluctuate in the presence of time-varying communication topologies. Whether and how signed networks can be stabilized regardless of their sign patterns is one of the fundamental problems in the network system control areas. To address this problem, this paper targets at presenting a self-appraisal mechanism in the protocol of each agent, for which a notion of diagonal dominance degree is proposed to represent the dominant role of agent’s self-appraisal over external impacts from all other agents. Selection conditions on diagonal dominance degrees are explored such that signed networks in the presence of directed time-varying topologies can be ensured to achieve the uniform asymptotic stability despite any sign patterns. Further, the established stability results can be applied to achieve bipartite consensus tracking of time-varying signed networks and realize state-feedback stabilization of time-varying systems. Simulations are implemented to verify our uniform asymptotic stability results for directed time-varying signed networks. [ABSTRACT FROM AUTHOR]

Community detection and link prediction are two basic tasks of complex network system analysis, which are widely used in the detection of telecom fraud organizations and recommendation systems in the real world. In ordinary unsigned networks, these two analyses have been developed for a long time. However, due to the existence of negative edges, the study of community detection and link prediction in signed networks is still limited now. Most existing methods have high computational complexity and ignore the generation of the networks based on heuristics. In this paper, we propose a regularized convex nonnegative matrix factorization model (RC-NMF) from the perspective of the generative model to detection communities in the signed network. This algorithm introduces graph regularization to constrain nodes with negative edges into different communities and nodes with positive edges into the same communities as much as possible. Experiments on synthetic signed networks and several real-world signed networks validate the effectiveness and accuracy of the proposed approach both in community detection and link prediction. [ABSTRACT FROM AUTHOR]

Pharmaceutical drug combinations can effectively treat various medical conditions. However, some combinations can cause serious adverse drug reactions (ADR). Therefore, predicting ADRs is an essential and challenging task. Some existing studies rely on single-modal information, such as drug-drug interaction or drug-drug similarity, to predict ADRs. However, those approaches ignore relationships among multi-source information. Other studies predict ADRs using integrated multi-modal drug information; however, such studies generally describe these relations as heterogeneous unsigned networks rather than signed ones. In fact, multi-modal relations of drugs can be classified as positive or negative. If these two types of relations are depicted simultaneously, semantic correlation of drugs in the real world can be predicted effectively. Therefore, in this study, we propose an innovative heterogeneous signed network model called SC-DDIS, to learn drug representations. SC-DDIS integrates multi-modal features, such as drug-drug interactions, drug-protein interactions, drug-chemical interactions, and other heterogeneous information, into drug embedding. Drug embedding means using feature vectors to express drugs. Then, the SC-DDIS model is also used for ADR prediction tasks. First, we fuse heterogeneous drug relations, positive/negative, to obtain a drug-drug interaction signed network (DDISN). Then, inspired by social network, we extend structural balance theory and apply it to DDISN. Using extended structural balance theory, we constrain sign propagation in DDISN. We learn final embedding of drugs by training a graph spectral convolutional neural network. Finally, we train a decoding matrix to decode the drug embedding to predict ADRs. Experimental results demonstrate effectiveness of the proposed model compared to several conventional multi-relational prediction approaches and the state-of-the-art deep learning-based Decagon model. [ABSTRACT FROM AUTHOR]

In signed networks, the cooperation and antagonism cause great difficulties for their behavior analysis, especially, when they are subject to time-varying topologies. This is different from unsigned networks involving only cooperations, of which behavior analysis can be feasibly achieved based on the nonnegative matrix theory. With these facts, this article first bridges a relation between signed and unsigned networks and then takes advantage of the relation for the behavior analysis of signed networks under directed switching topologies. In particular, a solution is provided for the connection of signed and unsigned networks via solving a class of linear dynamic systems, which is obtained by separating antagonisms from cooperations. The solution makes it possible to employ the convergence results for unsigned networks to address the convergence issues for signed networks. If the joint spanning tree condition is met, then switching signed networks can achieve the quasi-interval bipartite consensus. Moreover, the established results can be applied to signed networks with both continuous-time and discrete-time dynamics. [ABSTRACT FROM AUTHOR]

This paper is devoted to the convergence problem for second-order signed networks that are associated with two signed graphs in the presence of heterogeneous topologies. An eigenvalue analysis approach is presented to develop convergence results for second-order signed networks, which employs a sign-consistency property for signed graph pairs. When the sign-consistency of two heterogeneous signed graphs and the connectivity of their union are given, bipartite consensus (respectively, state stability) can be derived for second-order signed networks if and only if the union signed graph is structurally balanced (respectively, unbalanced). Two examples are provided to illustrate the effectiveness of the obtained results.