相关论文: Finding large balanced subgraphs in signed network…
An edge-weighted graph $G=(V,E)$ is called stable if the value of a maximum-weight matching equals the value of a maximum-weight fractional matching. Stable graphs play an important role in some interesting game theory problems, such as…
We propose a novel method for topological analysis of unweighted graphs which is based on \textit{persistent homology}. The proposed method maps the input graph to a complete weighted graph where the weighting function maps each edge to a…
This work addresses the edge-based synchronization problem in first-order multi-agent systems containing both cooperative and antagonistic interactions with one or multiple leader groups. The presence of multiple leaders and antagonistic…
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…
A signed graph $(G,\sigma)$ is a graph $G$ together with an assignment $\sigma$ of either a positive sign or a negative sign to each edge. A signed graph is unbalanced if it contains a cycle with odd number of negative edges. The spectral…
Identifying critical nodes and links in graphs is a crucial task. These nodes/links typically represent critical elements/communication links that play a key role in a system's performance. However, a majority of the methods available in…
A $k$-edge-coloured graph is colour-balanced if each colour appears equally often. Resolving a conjecture of Pardey and Rautenbach, we show that any colour-balanced $k$-edge-coloured complete graph $K_{2kt}$ contains a perfect matching that…
Structural balance is an important characteristic of graphs/networks where edges can be positive or negative, with direct impact on the study of real-world complex systems. When a network is not structurally balanced, it is important to…
Subgraph densities play a crucial role in network analysis, especially for the identification and interpretation of meaningful substructures in complex graphs. Localized subgraph densities, in particular, can provide valuable insights into…
Motivated by discrete Laplacian differential operators with various accuracy orders in numerical analysis, we introduce new matrices attached to a simple graph that can be considered graph Laplacians with higher accuracy. In particular, we…
We consider the problem of sampling from data defined on the nodes of a weighted graph, where the edge weights capture the data correlation structure. As shown recently, using spectral graph theory one can define a cut-off frequency for the…
We study the problem of detecting whether an inhomogeneous random graph contains a planted community. Specifically, we observe a single realization of a graph. Under the null hypothesis, this graph is a sample from an inhomogeneous random…
Pattern counting in graphs is a fundamental primitive for many network analysis tasks, and a number of methods have been developed for scaling subgraph counting to large graphs. Many real-world networks carry a natural notion of strength of…
In network science, identifying optimal partitions of a signed network into internally cohesive and mutually divisive clusters based on generalized balance theory is computationally challenging. We reformulate and generalize two binary…
The theory of sampling and recovery of bandlimited graph signals has been extensively studied. However, in many cases, the observation of a signal is quite coarse. For example, users only provide simple comments such as "like" or "dislike"…
Imbalanced node classification widely exists in real-world networks where graph neural networks (GNNs) are usually highly inclined to majority classes and suffer from severe performance degradation on classifying minority class nodes.…
Signed graphs encode positive (attractive) and negative (repulsive) relations between nodes. We extend spectral clustering to signed graphs via the one-parameter family of Signed Power Mean Laplacians, defined as the matrix power mean of…
Finding hidden layers in complex networks is an important and a non-trivial problem in modern science. We explore the framework of quantum graphs to determine whether concealed parts of a multi-layer system exist and if so then what is…
Nonlinear networked systems are of interest in several areas of research, such as multi-agent systems and social networks. In this paper, we examine the controllability of several classes of nonlinear networked dynamics on which the…
Graphs provide a powerful representation formalism that offers great promise to benefit tasks like handwritten signature verification. While most state-of-the-art approaches to signature verification rely on fixed-size representations,…