Related papers: Structural Balance of Complex Weighted Graphs and …
Polynomial algorithms are given for the following two problems: given a graph with $n$ vertices and $m$ edges, where $m \ge 3 n^{3/2}$, find a complete balanced bipartite subgraph with parts about $\ln n/(\ln (n^2/m))$, given a graph with…
It is well known that a graph $G$ has a symmetric spectrum if and only if it is bipartite, a signed graph $\Gamma=(G,\sigma)$ has a symmetric spectrum if $G$ is bipartite. However, there exists a spectrally symmetric signed graph…
In bipartite matching problems, agents on two sides of a graph want to be paired according to their preferences. The stability of a matching depends on these preferences, which in uncertain environments also reflect agents' beliefs about…
A bipartite covering of a (multi)graph $G$ is a collection of bipartite graphs, so that each edge of $G$ belongs to at least one of them. The capacity of the covering is the sum of the numbers of vertices of these bipartite graphs. In this…
This paper studies the consensus problem for multiagent systems with transmission constraints. A novel model of multiagent systems is proposed where the information transmissions between agents are disturbed by irregular distortions or…
We propose a random bipartite graph with weights assigned to both parts of the vertex sets. Edges are formed independently with probabilities that depend on these weights. This bipartite graph naturally gives rise to a random intersection…
This paper focuses on the convergence of infor- mation in distributed systems of agents communicating over a network. The information on which the convergence is sought is not represented by real numbers, rather by sets of real numbers,…
Complex unit gain graphs may exhibit various kinds of symmetry. In this work, we explore structural symmetry, spectral symmetry and sign-symmetry in such graphs, and their respective relations to one-another. Our main result is a…
We study two agent based models of opinion formation - one stochastic in nature and one deterministic. Both models are defined in terms of an underlying graph; we study how the structure of the graph affects the long time behavior of the…
In this paper, we introduce a corresponding between bipartite graphs with a perfect matching and digraphs, which implicates an equivalent relation between the extendibility of bipartite graphs and the strongly connectivity of digraphs. Such…
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…
In this paper, we study the consensus problem of multiple agents on a kind of famous graph, Peterson graph. It is an undirected graph with 10 vertices and 15 edges. Each agent randomly walks on this graph and communicates with each other if…
Weight-equitable partitions of graphs, which are a natural extension of the well-known equitable partitions, have been shown to be a powerful tool to weaken the regularity assumption in several well-known eigenvalue bounds. In this work we…
Perfect matchings and maximum weight matchings are two fundamental combinatorial structures. We consider the ratio between the maximum weight of a perfect matching and the maximum weight of a general matching. Motivated by the computer…
The paper investigates consensus problem for continuous-time multi-agent systems with time-varying communication graphs subject to process noises. Borrowing the ideas from input-to-state stability (ISS) and integral input-to-state stability…
A cyber security problem in a networked system formulated as a resilient graph problem based on a game-theoretic approach is considered. The connectivity of the underlying graph of the network system is reduced by an attacker who removes…
This paper investigates the role persistent arcs play for a social network to reach a global belief agreement under discrete-time or continuous-time evolution. Each (directed) arc in the underlying communication graph is assumed to be…
Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…
We consider a multi-agent consensus problem in the presence of adversarial agents. The adversaries are able to listen to the inter-agent communications and try to estimate the state of the agents. The agents have a limited bit-rate for…
Statistical network models are useful for understanding the underlying formation mechanism and characteristics of complex networks. However, statistical models for \textit{signed networks} have been largely unexplored. In signed networks,…