Signs Of Edges Research Articles

Multidimensional attributes expose Heider balance dynamics to measurements

Most of studied social interactions arise from dyadic relations. An exception is Heider Balance Theory that postulates the existence of triad dynamics, which however has been elusive to observe. Here, we discover a sufficient condition for the Heider dynamics observability: assigning the edge signs according to multiple opinions of connected agents. Using longitudinal records of university student mutual contacts and opinions, we create a coevolving network on which we introduce models of student interactions. These models account for: multiple topics of individual student opinions, influence of such opinions on dyadic relations, and influence of triadic relations on opinions. We show that the triadic influence is empirically measurable for static and dynamic observables when signs of edges are defined by multidimensional differences between opinions on all topics. Yet, when these signs are defined by a difference between opinions on each topic separately, the triadic interactions’ influence is indistinguishable from noise.

Signed graphs from proper coloring of graphs

Let χ(G) denote the chromatic number of a graph G. Under the proper coloring of a graph G with χ(G) colors, we define a signed graph from it. The obtained signed graph is defined as parity colored signed graph and denoted as Sc. The signs of edges of G are defined from the colors of the vertices as +( − ) if the colors on the adjacent vertices are of the same (opposite) parity. In this paper, we initiate a study on Sc. We further investigate the chromatic rna number of some classes of graphs concerning proper coloring.

Constructing refined null models for statistical analysis of signed networks* *Project supported by the National Natural Science Foundation of China (Grant Nos. 61773091 and 61603073), the LiaoNing Revitalization Talents Program (Grant No. XLYC1807106), and the Natural Science Foundation of Liaoning Province, China (Grant No. 2020-MZLH-22).

The establishment of effective null models can provide reference networks to accurately describe statistical properties of real-life signed networks. At present, two classical null models of signed networks (i.e., sign and full-edge randomized models) shuffle both positive and negative topologies at the same time, so it is difficult to distinguish the effect on network topology of positive edges, negative edges, and the correlation between them. In this study, we construct three refined edge-randomized null models by only randomizing link relationships without changing positive and negative degree distributions. The results of nontrivial statistical indicators of signed networks, such as average degree connectivity and clustering coefficient, show that the position of positive edges has a stronger effect on positive-edge topology, while the signs of negative edges have a greater influence on negative-edge topology. For some specific statistics (e.g., embeddedness), the results indicate that the proposed null models can more accurately describe real-life networks compared with the two existing ones, which can be selected to facilitate a better understanding of complex structures, functions, and dynamical behaviors on signed networks.

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.

Random walk-based ranking in signed social networks: model and algorithms

How can we rank nodes in signed social networks? Relationships between nodes in a signed network are represented as positive (trust) or negative (distrust) edges. Many social networks have adopted signed networks to express trust between users. Consequently, ranking friends or enemies in signed networks has received much attention from the data mining community. The ranking problem, however, is challenging because it is difficult to interpret negative edges. Traditional random walk-based methods such as PageRank and random walk with restart cannot provide effective rankings in signed networks since they assume only positive edges. Although several methods have been proposed by modifying traditional ranking models, they also fail to account for proper rankings due to the lack of ability to consider complex edge relations. In this paper, we propose Signed Random Walk with Restart (SRWR), a novel model for personalized ranking in signed networks. We introduce a signed random surfer so that she considers negative edges by changing her sign for walking. Our model provides proper rankings considering signed edges based on the signed random walk. We develop two methods for computing SRWR scores: SRWR-Iter and SRWR-Pre which are iterative and preprocessing methods, respectively. SRWR-Iter naturally follows the definition of SRWR, and iteratively updates SRWR scores until convergence. SRWR-Pre enables fast ranking computation which is important for the performance of applications of SRWR. Through extensive experiments, we demonstrate that SRWR achieves the best accuracy for link prediction, predicts trolls $$4\times $$ more accurately, and shows a satisfactory performance for inferring missing signs of edges compared to other competitors. In terms of efficiency, SRWR-Pre preprocesses a signed network $$4.5 \times $$ faster and requires $$11 \times $$ less memory space than other preprocessing methods; furthermore, SRWR-Pre computes SRWR scores up to $$14 \times $$ faster than other methods in the query phase.

Evolving the attribute flow for dynamical clustering in signed networks

In real networks, clustering is of great value to the analysis, design, and optimization of numerous complex systems in natural science and engineering, e.g. power supply systems ,modern transportation networks, and real-world networks. However, the majority of them simply pay attention to the density of edges rather than the signs of edges as the attributes to cluster, which usually suffer a high-level computational complexity. In this paper, a new rule is proposed to update the attributes flow, which can guarantee network clustering reach a state of optimal convergence. The positive and negative update rule we introduced, represent the cooperative and hostile relationship, and the attribute configuration will convergence and one can identify the reasonable cluster configuration automatically. An algorithm with high efficiency is proposed: a nearly linear relationship is found between the time complexity and the size in sparse networks. Finally, we conduct the verification of the algorithmic performance by a representative simulations on Correlates of War data.

Optimizing transformations of structural balance in signed networks with potential relationships

Abstract A signed network includes positive edges, negative edges and “0” edges, the last of which denote potential relationships. However, “0” edges are commonly ignored in transformations of unbalanced networks. In this paper, we take “0” edges into account and solve the optimization problem in a more comprehensive way. We transform the unbalanced network by not only changing signs of edges but also changing edges into potential. The experimental results show that our method can solve this problem efficiently, and that our solutions are cost-saving.

Structural balance in fully signed networks

Node attributes play an important role in shaping network structures, but are generally ignored in transformations of structural balance. A fully signed network consisting of signs of edges and nodes expresses both properties of relationship and node attributes. In this article, we generalize the definition of structural balance in fully signed networks. We transform the unbalanced fully signed network by not only changing signs of edges but also changing the signs of nodes. We propose a memetic algorithm to transform unbalanced networks at the lowest cost. Experiments show that our algorithm can solve this problem efficiently, and different node attribute assignments may lead to different optimized structures. © 2016 Wiley Periodicals, Inc. Complexity 21: 497–511, 2016

Ranking Nodes in Signed Social Networks

Social networks are inevitable part of modern life. A class of social networks is those with both positive (friendship or trust) and negative (enmity or distrust) links. Ranking nodes in signed networks remains a hot topic in computer science. In this manuscript, we review different ranking algorithms to rank the nodes in signed networks, and apply them to the sign prediction problem. Ranking scores are used to obtain reputation and optimism, which are used as features in the sign prediction problem. Reputation of a node shows patterns of voting towards the node and its optimism demonstrates how optimistic a node thinks about others. To assess the performance of different ranking algorithms, we apply them on three signed networks including Epinions, Slashdot and Wikipedia. In this paper, we introduce three novel ranking algorithms for signed networks and compare their ability in predicting signs of edges with already existing ones. We use logistic regression as the predictor and the reputation and optimism values for the trustee and trustor as features (that are obtained based on different ranking algorithms). We find that ranking algorithms resulting in correlated ranking scores, leads to almost the same prediction accuracy. Furthermore, our analysis identifies a number of ranking algorithms that result in higher prediction accuracy compared to others.

Clause trees: a tool for understanding and implementing resolution in automated reasoning

A new methodology/data structure, the clause tree, is developed for automated reasoning based on resolution in first order logic. A clause tree T on a set S of clauses is a 4-tuple 〈 N, E, L, M〉, where N a set of nodes, divided into clause nodes and atom nodes, E is a set of edges, each of which joins a clause node to an atom node, L is a labeling of N ∪ E which assigns to each clause node a clause of S, to each atom node an instance of an atom of some clause of S, and to each edge either + or −. The edge joining a clause node to an atom node is labeled by the sign of the corresponding literal in the clause. A resolution is represented by unifying two atom nodes of different clause trees which represent complementary literals. The merge of two identical literals is represented by placing the path joining the two corresponding atom nodes into the set M of chosen merge paths. The tail of the merge path becomes a closed leaf, while the head remains an open leaf which can be resolved on. The clause cl(T) that T represents is the set of literals corresponding to the labels of the open leaves modified by the signs of the incident edges. The fundamental purpose of a clause tree T is to show that cl(T) can be derived from S using resolution. Loveland's model elimination ME, the selected literal procedure SL, and Shostak's graph construction procedure GC are explained in a unified manner using clause trees. The condition required for choosing a merge path whose head is not a leaf is given. This allows a clause tree to be built in one way (the build ordering) but justified as a proof in another (the proof ordering). The ordered clause set restriction and the foothold score restriction are explained using the operation on clause trees of merge path reversal. A new procedure called ALPOC, which combines ideas from ME, GC and Spencer's ordered clause set restriction (OC), to form a new procedure tighter than any of the top down procedures above, is developed and shown to be sound and complete. Another operation on clause trees called surgery is defined, and used to define a minimal clause tree. Any non-minimal clause tree can be reduced to a minimal clause tree using surgery, thereby showing that non-minimal clause trees are redundant. A sound procedure MinALPOC that produces only minimal clause trees is given. Mergeless clause trees are shown to be equivalent to each of input resolution, unit resolution and relative Horn sets, thereby giving short proofs of some known results. Many other new proof procedures using clause trees are discussed briefly, leaving many open questions.

An algorithm for identifying Morishima and anti-Morishima matrices and balanced digraphs

We present an algorithm for identifying Morishima and anti-Morishima matrices. Since Morishima matrices have signed diagraphs that are balanced, our algorithm also identifies such diagraphs. We actually work with a signed graph and our algorithm is a depth first traversal with certain markers added to keep track of parsing of nodes and signs of edges. The algorithm is of course, linear in the amount of input.