相关论文: Spread of Influence in Graphs

It is often observed that agents tend to imitate the behavior of their neighbors in a social network. This imitating behavior might lead to the strategic decision of adopting a public behavior that differs from what the agent believes is…

We consider a random graph in which vertices can have one of two possible colours. Each vertex switches its colour at a rate that is proportional to the number of vertices of the other colour to which it is connected by an edge. Each edge…

Zero forcing in a graph refers to the evolution of vertex states under repeated application of a color change rule. Typically the states are chosen to be blue and white, and a forcing set is an initial set of blue vertices such that all of…

Graph-learning algorithms can fail when graph structure is adversarially perturbed, intrinsically noisy or constructed from imperfect observations. Here we show that some nodes bear much greater responsibility than others for allowing…

A bootstrap percolation process on a graph G is an "infection" process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round every uninfected node which has at least r infected neighbours…

In this paper, we study the following problem. Consider a setting where a proposal is offered to the vertices of a given network $G$, and the vertices must conduct a vote and decide whether to accept the proposal or reject it. Each vertex…

The Linear Threshold Model is a widely used model that describes how information diffuses through a social network. According to this model, an individual adopts an idea or product after the proportion of their neighbors who have adopted it…

Graph structure learning aims to learn connectivity in a graph from data. It is particularly important for many computer vision related tasks since no explicit graph structure is available for images for most cases. A natural way to…

In this paper, we initiate the study of the vertex coloring problem of a graph in the semi streaming model. In this model, the input graph is defined by a stream of edges, arriving in adversarial order and any algorithm must process the…

Consider a graph whose vertices are colored in one of two colors, say black or white. A white vertex is called integrated if it has at least as many black neighbors as white neighbors, and similarly for a black vertex. The coloring as a…

The network coloring game has been proposed in the literature of social sciences as a model for conflict-resolution circumstances. The players of the game are the vertices of a graph with $n$ vertices and maximum degree $\Delta$. The game…

Graph burning is a discrete-time process that models the spread of influence in a network. Vertices are either burning or unburned, and in each round, a burning vertex causes all of its neighbours to become burning before a new fire source…

For any positive edge density $p$, a random graph in the Erd\H{o}s-Renyi $G_{n,p}$ model is connected with non-zero probability, since all edges are mutually independent. We consider random graph models in which edges that do not share…

As is well known, a graph is a mathematical object modeling the existence of a certain relation between pairs of elements of a given set. Therefore, it is not surprising that many of the first results concerning graphs made reference to…

We study the evolution of opinions (or beliefs) over a social network modeled as a signed graph. The sign attached to an edge in this graph characterizes whether the corresponding individuals or end nodes are friends (positive links) or…

The spread of an infection, a contagion, meme, emotion, message and various other spreadable objects have been discussed in several works. Burning and firefighting have been discussed in particular on static graphs. Graph burning simulates…

The divide and color model on a graph $G$ arises by first deleting each edge of $G$ with probability $1-p$ independently of each other, then coloring the resulting connected components (\emph{i.e.}, every vertex in the component) black or…

We study a \emph{Plurality-Consensus} process in which each of $n$ anonymous agents of a communication network initially supports an opinion (a color chosen from a finite set $[k]$). Then, in every (synchronous) round, each agent can revise…

Frei et al. [6] showed that the problem to decide whether a graph is stable with respect to some graph parameter under adding or removing either edges or vertices is $\Theta_2^{\text{P}}$-complete. They studied the common graph parameters…

An edge coloring of a graph $G$ is \emph{woody} if no cycle is monochromatic. The \emph{arboricity} of a graph $G$, denoted by $\arb (G)$, is the least number of colors needed for a woody coloring of $G$. A coloring of $G$ is \emph{strongly…