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

We present a method to estimate block membership of nodes in a random graph generated by a stochastic blockmodel. We use an embedding procedure motivated by the random dot product graph model, a particular example of the latent position…

The task of \emph{community detection} in a graph formalizes the intuitive task of grouping together subsets of vertices such that vertices within clusters are connected tighter than those in disparate clusters. This paper approaches…

An open neighbourhood locating-dominating set is a set $S$ of vertices of a graph $G$ such that each vertex of $G$ has a neighbour in $S$, and for any two vertices $u,v$ of $G$, there is at least one vertex in $S$ that is a neighbour of…

For a family of linear preferential attachment graphs, we provide rates of convergence for the total variation distance between the degree of a randomly chosen vertex and an appropriate power law distribution as the number of vertices tends…

Adaptive networks model social, physical, technical, or biological systems as attributed graphs evolving at the level of both their topology and data. They are naturally described by graph transformation, but the majority of authors take an…

Every link in R^3 can be represented by a one-vertex ribbon graph. We prove a Markov type theorem on this subset of link diagrams.

The voter process is a classic stochastic process that models the invasion of a mutant trait $A$ (e.g., a new opinion, belief, legend, genetic mutation, magnetic spin) in a population of agents (e.g., people, genes, particles) who share a…

In the modern age of social media and networks, graph representations of real-world phenomena have become an incredibly useful source to mine insights. Often, we are interested in understanding how entities in a graph are interconnected.…

We present a new neighbor sampling method on temporal graphs. In a temporal graph, predicting different nodes' time-varying properties can require the receptive neighborhood of various temporal scales. In this work, we propose the TNS…

Graph data, such as chemical networks and social networks, may be deemed confidential/private because the data owner often spends lots of resources collecting the data or the data contains sensitive information, e.g., social relationships.…

We apply the power-of-two-choices paradigm to a random walk on a graph: rather than moving to a uniform random neighbour at each step, a controller is allowed to choose from two independent uniform random neighbours. We prove that this…

Node regression consists in predicting the value of a graph label at a node, given observations at the other nodes. To gain some insight into the performance of various estimators for this task, we perform a theoretical study in a context…

The goal of network representation learning is to learn low-dimensional node embeddings that capture the graph structure and are useful for solving downstream tasks. However, despite the proliferation of such methods, there is currently no…

Graph neural networks (GNNs) have achieved tremendous success in the task of graph classification and its diverse downstream real-world applications. Despite the huge success in learning graph representations, current GNN models have…

Given a graph $G = (V,E)$ with vertex weights $w(v)$ and a desired number of parts $k$, the goal in graph partitioning problems is to partition the vertex set V into parts $V_1,\ldots,V_k$. Metrics for compactness, contiguity, and balance…

We consider the problem of jointly estimating a collection of graphical models for discrete data, corresponding to several categories that share some common structure. An example for such a setting is voting records of legislators on…

Pull voting is a random process in which vertices of a connected graph have initial opinions chosen from a set of $k$ distinct opinions, and at each step a random vertex alters its opinion to that of a randomly chosen neighbour. If the…

Common experience suggests that many networks might possess community structure - division of vertices into groups, with a higher density of edges within groups than between them. Here we describe a new computer algorithm that detects…

We introduce a general two colour interacting urn model on a finite directed graph, where each urn at a node, reinforces all the urns in its out-neighbours according to a fixed, non-negative and balanced reinforcement matrix. We show that…

Discrete-time discrete-state finite Markov chains are versatile mathematical models for a wide range of real-life stochastic processes. One of most common tasks in studies of Markov chains is computation of the stationary distribution.…