相关论文: Equal relation between the extra connectivity and …
Motivated by problems modeling the spread of infections in networks, in this paper we explore which bipartite graphs are most resilient to widespread infections under various parameter settings. Namely, we study bipartite networks with a…
We study the problem of guaranteeing the connectivity of a given graph by protecting or strengthening edges. Herein, a protected edge is assumed to be robust and will not fail, which features a non-uniform failure model. We introduce the…
A graph is said to be {\it total-colored} if all the edges and the vertices of the graph is colored. A path in a total-colored graph is a {\it total proper path} if $(i)$ any two adjacent edges on the path differ in color, $(ii)$ any two…
A key challenge in network science is the detection of communities, which are sets of nodes in a network that are densely connected internally but sparsely connected to the rest of the network. A fundamental result in community detection is…
The Survivable Network Design problem (SNDP) is a well-studied problem, motivated by the design of networks that are robust to faults under the assumption that any subset of edges up to a specific number can fail. We consider non-uniform…
Graph neural networks (GNNs) are becoming increasingly popular for EEG-based depression detection. However, previous GNN-based methods fail to sufficiently consider the characteristics of depression, thus limiting their performance.…
Recently, there has been a growing concern about the overload status of the power grid networks, and the increasing possibility of cascading failures. Many researchers have studied these networks to provide design guidelines for more robust…
We consider a method to jointly estimate sparse precision matrices and their underlying graph structures using dependent high-dimensional datasets. We present a penalized maximum likelihood estimator which encourages both sparsity and…
A conflict graph represents logical relations between binary variables, and effective use of the graph can significantly accelerate branch-and-cut solvers for mixed-integer programming (MIP). In this paper we develop efficient parallel…
We introduce the notion of a network's conduciveness, a probabilistically interpretable measure of how the network's structure allows it to be conducive to roaming agents, in certain conditions, from one portion of the network to another.…
Network reliability is a well-studied problem that requires to measure the probability that a target node is reachable from a source node in a probabilistic (or uncertain) graph, i.e., a graph where every edge is assigned a probability of…
A central question of evolutionary dynamics on graphs is whether or not a mutation introduced in a population of residents survives and eventually even spreads to the whole population, or gets extinct. The outcome naturally depends on the…
For any finite abelian group $G$ and any subset $S\seq G$, we determine the connectivity of the addition Cayley graph induced by $S$ on $G$. Moreover, we show that if this graph is not complete, then it possesses a minimum vertex cut of a…
Let $G$ be a connected graph and $g$ be a non-negative integer. The $g$-extra connectivity of $G$ is the minimum cardinality of a set of vertices in $G$, if it exists, whose removal disconnects $G$ and leaves every component with more than…
The Zero divisor Graph of a commutative ring $R$, denoted by $\Gamma[R]$, is a graph whose vertices are non-zero zero divisors of $R$ and two vertices are adjacent if their product is zero. Chemical graph theory is a branch of mathematical…
Fiber graphs of Gr\"obner bases from contingency tables are important in statistical hypothesis testing, where one studies random walks on these graphs using the Metropolis-Hastings algorithm. The connectivity of the graphs has implications…
Despite the tremendous success of graph-based learning systems in handling structural data, it has been widely investigated that they are fragile to adversarial attacks on homophilic graph data, where adversaries maliciously modify the…
A good computer network is hard to disrupt. It is desired that the computer communication network remains connected even when some of the links or nodes fail. Since the communication links are expensive, one wants to achieve these goals…
The power graph $\mathcal{P}(G)$ of a given finite group $G$ is the simple undirected graph whose vertices are the elements of $G$, in which two distinct vertices are adjacent if and only if one of them can be obtained as an integral power…
This work considers the robustness of uncertain consensus networks. The first set of results studies the stability properties of consensus networks with negative edge weights. We show that if either the negative weight edges form a cut in…