相关论文: The averaging process on infinite graphs

In this paper, we present two main results. First, by only one conjecture (Conjecture 2.9) for recognizing a vertex symmetric graph, which is the hardest task for our problem, we construct an algorithm for finding an isomorphism between two…

We consider a model of binary opinion dynamics where one opinion is inherently 'superior' than the other and social agents exhibit a 'bias' towards the superior alternative. Specifically, it is assumed that an agent updates its choice to…

We consider a type of pull voting suitable for discrete numeric opinions which can be compared on a linear scale, for example, 1 ('disagree strongly'), 2 ('disagree'), $\ldots,$ 5 ('agree strongly'). On observing the opinion of a random…

When opinion spread is studied, peer pressure is often modeled by interactions of more than two individuals (higher-order interactions). In our work, we introduce a two-layer random hypergraph model, in which hyperedges represent households…

Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have…

We analyze a class of distributed quantized consensus algorithms for arbitrary static networks. In the initial setting, each node in the network has an integer value. Nodes exchange their current estimate of the mean value in the network,…

We say that a vertex $v$ in a connected graph $G$ is decisive if the numbers of walks from $v$ of each length determine the graph $G$ rooted at $v$ up to isomorphism among all connected rooted graphs with the same number of vertices. On the…

People's opinions evolve over time as they interact with their friends, family, colleagues, and others. In the study of opinion dynamics on networks, one often encodes interactions between people in the form of dyadic relationships, but…

There is arbitrariness in optimum solutions of graph-theoretic problems that can give rise to unfairness. Incorporating fairness in such problems, however, can be done in multiple ways. For instance, fairness can be defined on an individual…

Let $G = (V,E)$ be a connected directed graph on $n$ vertices. Assign values from the set $\{1,2,\dots,n\}$ to the vertices of $G$ and update the values according to the following rule: uniformly at random choose a vertex and update its…

A cornerstone of geometric reconstruction, rotation averaging seeks the set of absolute rotations that optimally explains a set of measured relative orientations between them. In spite of being an integral part of bundle adjustment and…

By constructing jointly a random graph and an associated exploration process, we define the dynamics of a "parking process" on a class of uniform random graphs as a measure-valued Markov process, representing the empirical degree…

We prove new lower bounds on the likely size of a maximum independent set in a random graph with a given average degree. Our method is a weighted version of the second moment method, where we give each independent set a weight based on the…

This paper is concerned with certain invariant random processes (called factors of IID) on infinite trees. Given such a process, one can assign entropies to different finite subgraphs of the tree. There are linear inequalities between these…

We generalize the poissonian evolving random graph model of Bauer and Bernard to deal with arbitrary degree distributions. The motivation comes from biological networks, which are well-known to exhibit non poissonian degree distribution. A…

Suppose in a graph $G$ vertices can be either red or blue. Let $k$ be odd. At each time step, each vertex $v$ in $G$ polls $k$ random neighbours and takes the majority colour. If it doesn't have $k$ neighbours, it simply polls all of them,…

In this paper we consider a well-known generalization of the Barab\'asi and Albert preferential attachment model - the Buckley-Osthus model. Buckley and Osthus proved that in this model the degree sequence has a power law distribution. As a…

A simple random walk on a graph is a sequence of movements from one vertex to another where at each step an edge is chosen uniformly at random from the set of edges incident on the current vertex, and then transitioned to next vertex.…

In this paper we further investigate the well-studied problem of finding a perfect matching in a regular bipartite graph. The first non-trivial algorithm, with running time $O(mn)$, dates back to K\"{o}nig's work in 1916 (here $m=nd$ is the…

Graph partitioning, or the dividing of a graph into two or more parts based on certain conditions, arises naturally throughout discrete mathematics, and problems of this kind have been studied extensively. In the 1990s, Ando conjectured…