相关论文: Counting Vertices in a Voter-type Model
In this paper we consider a simple virus infection spread model on a finite population of $n$ agents connected by some neighborhood structure. Given a graph $G$ on $n$ vertices, we begin with some fixed number of initial infected vertices.…
The voter model is a classical interacting particle system modelling how consensus is formed across a network. We analyse the time to consensus for the voter model when the underlying graph is a subcritical scale-free random graph.…
Consider an undirected graph G, representing a social network, where each node is blue or red, corresponding to positive or negative opinion on a topic. In the voter model, in discrete time rounds, each node picks a neighbour uniformly at…
When modelling epidemics or spread of information on online social networks, it is crucial to include not just the density of the connections through which infections can be transmitted, but also the variability of susceptibility. Different…
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…
We study simple interacting particle systems on heterogeneous networks, including the voter model and the invasion process. These are both two-state models in which in an update event an individual changes state to agree with a neighbor.…
Graph embedding techniques have led to significant progress in recent years. However, present techniques are not effective enough to capture the patterns of networks. This paper propose neighbor2vec, a neighbor-based sampling strategy used…
The Voter model is a well-studied stochastic process that models the invasion of a novel trait $A$ (e.g., a new opinion, social meme, genetic mutation, magnetic spin) in a network of individuals (agents, people, genes, particles) carrying…
We consider a Spatial Markov Chain model for the spread of viruses. The model is based on the principle to represent a graph connecting nodes, which represent humans. The vertices between the nodes represent relations between humans. In…
We introduce a new random graph model motivated by biological questions relating to speciation. This random graph is defined as the stationary distribution of a Markov chain on the space of graphs on $\{1, \ldots, n\}$. The dynamics of this…
Accurately analyzing graph properties of social networks is a challenging task because of access limitations to the graph data. To address this challenge, several algorithms to obtain unbiased estimates of properties from few samples via 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…
Complex networks are a recent type of frameworks used to study complex systems with many interacting elements, such as Self-Organized Criticality (SOC). The network node's tendency to link to other nodes of similar type is characterized by…
We study the growth of two competing infection types on graphs generated by the configuration model with a given degree sequence. Starting from two vertices chosen uniformly at random, the infection types spread via the edges in the graph…
Graph neural networks (GNNs) have been widely used in many real applications, and recent studies have revealed their vulnerabilities against topology attacks. To address this issue, existing efforts have mainly been dedicated to improving…
Consider two networks on overlapping, non-identical vertex sets. Given vertices of interest in the first network, we seek to identify the corresponding vertices, if any exist, in the second network. While in moderately sized networks graph…
Given a transition matrix $P$ indexed by a finite set $V$ of vertices, the voter model is a discrete-time Markov chain in $\{0,1\}^V$ where at each time-step a randomly chosen vertex $x$ imitates the opinion of vertex $y$ with probability…
The goal of this note is to assess whether simple machine learning algorithms can be used to determine whether and how a given network has been attacked. The procedure is based on the $k$-Nearest Neighbor and the Random Forest…
We propose and analyze a quasirandom analogue of the classical push model for disseminating information in networks ("randomized rumor spreading"). In the classical model, in each round each informed vertex chooses a neighbor at random and…
Small-world graphs, which combine randomized and structured elements, are seen as prevalent in nature. Jon Kleinberg showed that in some graphs of this type it is possible to route, or navigate, between vertices in few steps even with very…