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

We propose a new model, the Neighbor Mixture Model (NMM), for modeling node labels in a graph. This model aims to capture correlations between the labels of nodes in a local neighborhood. We carefully design the model so it could be an…

In the voter model, vertices of a graph (interpreted as voters) adopt one out of two opinions (0 and 1), and update their opinions at random times by copying the opinion of a neighbor chosen uniformly at random. This process is dual to a…

We observe the outcome of the discrete time noisy voter model at a single vertex of a graph. We show that certain pairs of graphs can be distinguished by the frequency of repetitions in the sequence of observations. We prove that this…

Distributed voting is a fundamental topic in distributed computing. In pull voting, in each step every vertex chooses a neighbour uniformly at random, and adopts its opinion. The voting is completed when all vertices hold the same opinion.…

Subgraph counts - in particular the number of occurrences of small shapes such as triangles - characterize properties of random networks, and as a result have seen wide use as network summary statistics. However, subgraphs are typically…

The newly introduced neighborhood matrix extends the power of adjacency and distance matrices to describe the topology of graphs. The adjacency matrix enumerates which pairs of vertices share an edge and it may be summarized by the degree…

In a random graph, counts for the number of vertices with given degrees will typically be dependent. We show via a multivariate normal and a Poisson process approximation that, for graphs which have independent edges, with a possibly…

This paper introduces the Attracting Random Walks model, which describes the dynamics of a system of particles on a graph with $n$ vertices. At each step, a single particle moves to an adjacent vertex (or stays at the current one) with…

In the voter model, each node of a graph has an opinion, and in every round each node chooses independently a random neighbour and adopts its opinion. We are interested in the consensus time, which is the first point in time where all nodes…

In this paper, we study the graph-based semi-supervised learning for classifying nodes in attributed networks, where the nodes and edges possess content information. Recent approaches like graph convolution networks and attention mechanisms…

We propose a new yet natural algorithm for learning the graph structure of general discrete graphical models (a.k.a. Markov random fields) from samples. Our algorithm finds the neighborhood of a node by sequentially adding nodes that…

Broadcasting algorithms are important building blocks of distributed systems. In this work we investigate the typical performance of the classical and well-studied push model. Assume that initially one node in a given network holds some…

The statistical mechanics of spin models, such as the Ising or Potts models, on generic random graphs can be formulated economically by considering the N --> 1 limit of Hermitian matrix models. In this paper we consider the N --> 1 limit in…

Graph neural networks (GNNs) emerge as a powerful family of representation learning models on graphs. To derive node representations, they utilize a global model that recursively aggregates information from the neighboring nodes. However,…

Bootstrap percolation is a process that is used to model the spread of an infection on a given graph. In the model considered here each vertex is equipped with an individual threshold. As soon as the number of infected neighbors exceeds…

Graph convolutional neural networks, which learn aggregations over neighbor nodes, have achieved great performance in node classification tasks. However, recent studies reported that such graph convolutional node classifier can be deceived…

In the evolving voter model, when an individual interacts with a neighbor having an opinion different from theirs, they will with probability $1-\alpha$ imitate the neighbor but with probability $ \alpha$ will sever the connection and…

We consider the problem of finding a specific target individual hiding in a social network. We propose a method for network vertex search that looks for the target vertex by sequentially examining the neighbors of a set of "known" vertices…

We consider a general preferential attachment model, where the probability that a newly arriving vertex connects to an older vertex is proportional to a sublinear function of the indegree of the older vertex at that time. It is well known…

We introduce and study the reverse voter model, a dynamics for spin variables similar to the well-known voter dynamics. The difference is in the way neighbors influence each other: once a node is selected and one among its neighbors chosen,…