相关论文: Spread of Influence in Graphs

Graph are a ubiquitous data representation, as they represent a flexible and compact representation. For instance, the 3D structure of RNA can be efficiently represented as $\textit{2.5D graphs}$, graphs whose nodes are nucleotides and…

The Ramsey number $r(H)$ of a graph $H$ is the minimum integer $n$ such that any two-coloring of the edges of the complete graph $K_n$ contains a monochromatic copy of $H$. While this definition only asks for a single monochromatic copy of…

Graphical domination was first introduced in [1] in the context of combinatorial threshold-linear networks (CTLNs). There it was shown that when a domination relationship exists between a pair of vertices in a graph, certain fixed points in…

We consider the problem of diffusing information in networks that contain malicious nodes. We assume that each normal node in the network has no knowledge of the network topology other than an upper bound on the number of malicious nodes in…

When dealing with large graphs, such as those that arise in the context of online social networks, a subset of nodes may be labeled. These labels can indicate demographic values, interest, beliefs or other characteristics of the nodes…

Random graph (RG) models play a central role in the complex networks analysis. They help to understand, control, and predict phenomena occurring, for instance, in social networks, biological networks, the Internet, etc. Despite a large…

There has been significant interest in the networking community on the impact of cascade effects on the diffusion of networking technology upgrades in the Internet. Thinking of the global Internet as a graph, where each node represents an…

A simple model is proposed to simulate the evolution of interpersonal relationships in a class. The small social network is simply assumed as an undirected and weighted graph, in which students are represented by vertices, and the extent of…

Emergence of dominating cliques in Erd\"os-R\'enyi random graph model ${\bbbg(n,p)}$ is investigated in this paper. It is shown this phenomenon possesses a phase transition. Namely, we have argued that, given a constant probability $p$, an…

We study the rainbow version of the graph commonness property: a graph $H$ is $r$-rainbow common if the number of rainbow copies of $H$ (where all edges have distinct colors) in an $r$-coloring of edges of $K_n$ is maximized asymptotically…

We study spreading processes in temporal graphs, i. e., graphs whose connections change over time. These processes naturally model real-world phenomena such as infectious diseases or information flows. More precisely, we investigate how…

In many real network systems, nodes usually cooperate with each other and form groups, in order to enhance their robustness to risks. This motivates us to study a new type of percolation, group percolation, in interdependent networks under…

Node features of graph neural networks (GNNs) tend to become more similar with the increase of the network depth. This effect is known as over-smoothing, which we axiomatically define as the exponential convergence of suitable similarity…

This study introduces a comprehensive framework that situates information cascades within the domain of higher-order interactions, utilizing a double-threshold hypergraph model. We propose that individuals (nodes) gain awareness of…

For an edge-colored graph $G$, we call an edge-cut $M$ of $G$ monochromatic if the edges of $M$ are colored with a same color. The graph $G$ is called monochromatically disconnected if any two distinct vertices of $G$ are separated by a…

We introduce a model for a growing random graph based on simultaneous reproduction of the vertices. The model can be thought of as a generalisation of the reproducing graphs of Southwell and Cannings and Bonato et al to allow for a random…

The definition of edge-regularity in graphs is a relaxation of the definition of strong regularity, so strongly regular graphs are edge-regular and, not surprisingly, the family of edge-regular graphs is much larger and more diverse than…

Graphs consisting of vocal nodes ("the vocal minority") and silent nodes ("the silent majority"), namely VS-Graph, are ubiquitous in the real world. The vocal nodes tend to have abundant features and labels. In contrast, silent nodes only…

Information dissemination is a fundamental problem in parallel and distributed computing. In its simplest variant, the broadcasting problem, a message has to be spread among all nodes of a graph. A prominent communication protocol for this…

Given an $n$-vertex graph $G$ with minimum degree at least $d n$ for some fixed $d > 0$, the distribution $G \cup \mathbb{G}(n,p)$ over the supergraphs of $G$ is referred to as a (random) {\sl perturbation} of $G$. We consider the…