相关论文: Counting Vertices in a Voter-type Model

The voter model with anti-voter bonds is a variant of the classical voter model in which the edges of the underlying graph are assigned signs. At each update, a voter chooses a neighbour according to a transition kernel; interactions across…

The voter model is a classical interacting particle system, modelling how global consensus is formed by local imitation. We analyse the time to consensus for a particular family of voter models when the underlying structure is a scale-free…

We study the voter dynamics model on heterogeneous graphs. We exploit the non-conservation of the magnetization to characterize how consensus is reached on networks with different connectivity patterns. For a network of N sites with an…

A graph is called a chain graph if it is bipartite and the neighborhoods of the vertices in each color class form a chain with respect to inclusion. A threshold graph can be obtained from a chain graph by making adjacent all pairs of…

Many applications in network analysis require algorithms to sample uniformly at random from the set of all graphs with a prescribed degree sequence. We present a Markov chain based approach which converges to the uniform distribution of all…

We study the classical Election problem in anonymous net- works, where solutions can rely on the use of random bits, which may be either shared or unshared among nodes. We provide a complete char- acterization of the conditions under which…

The Prisoner's Dilemma Process on a graph $G$ is an iterative process where each vertex, with a fixed strategy (cooperate or defect), plays the game with each of its neighbours. At the end of a round each vertex may change its strategy to…

Given a network, the statistical ensemble of its graph-Voronoi diagrams with randomly chosen cell centers exhibits properties convertible into information on the network's large scale structures. We define a node-pair level measure called…

We study the asymptotic behavior of the number of paths of length $N$ on several classes of infinite graphs with a single special vertex. This vertex can work as an entropic trap for the path, i.e. under certain conditions the dominant part…

As a fundamental structure in real-world networks, in addition to graph topology, communities can also be reflected by abundant node attributes. In attributed community detection, probabilistic generative models (PGMs) have become the…

Random walks defined on undirected graphs assign the absolute scores to all nodes based on the quality of path they provide for random walkers. In city space syntax, the notion of segregation acquires a statistical interpretation with…

We propose the following model of a random graph on n vertices. Let F be a distribution in R_+^{n(n-1)/2} with a coordinate for every pair i$ with 1 \le i,j \le n. Then G_{F,p} is the distribution on graphs with n vertices obtained by…

We consider a setting where individuals interact in a network, each choosing actions which optimize utility as a function of neighbors' actions. A central authority aiming to maximize social welfare at equilibrium can intervene by paying…

We study which property testing and sublinear time algorithms can be transformed into graph streaming algorithms for random order streams. Our main result is that for bounded degree graphs, any property that is constant-query testable in…

Hypergraphs, graph generalizations where edges are conglomerates of $r$ nodes called hyperedges of rank $r\geq 2$, are excellent models to study systems with interactions that are beyond the pairwise level. For hypergraphs, the node degree…

In this article, we propose a new type of square matrix associated with an undirected graph by trading off the naturally imbedded symmetry in them. The proposed matrix is defined using the neighbourhood sets of the vertices. It is called as…

Standard Convolutional Neural Networks (CNNs) can be easily fooled by images with small quasi-imperceptible artificial perturbations. As alternatives to CNNs, the recently proposed Capsule Networks (CapsNets) are shown to be more robust to…

We investigate the behaviour of $r$-neighbourhood bootstrap percolation on the binomial $k$-uniform random hypergraph $H_k(n,p)$ for given integers $k\geq 2$ and $r\geq 2$. In $r$-neighbourhood bootstrap percolation, infection spreads…

We study competing first passage percolation on graphs generated by the configuration model with infinite-mean degrees. Initially, two uniformly chosen vertices are infected with type 1 and type 2 infection, respectively, and the infection…

Data-driven neighborhood definitions and graph constructions are often used in machine learning and signal processing applications. k-nearest neighbor~(kNN) and $\epsilon$-neighborhood methods are among the most common methods used for…