相关论文: Community detection thresholds and the weak Ramanu…

Unsupervised node clustering (or community detection) is a classical graph learning task. In this paper, we study algorithms, which exploit the geometry of the graph to identify densely connected substructures, which form clusters or…

The spectrum of a network or graph $G=(V,E)$ with adjacency matrix $A$, consists of the eigenvalues of the normalized Laplacian $L= I - D^{-1/2} A D^{-1/2}$. This set of eigenvalues encapsulates many aspects of the structure of the graph,…

Community detection techniques are useful for social media platforms to discover tightly connected groups of users who share common interests. However, this functionality often comes at the expense of potentially exposing individuals to…

Stochastic Block Models (SBMs) are a fundamental tool for community detection in network analysis. But little theoretical work exists on the statistical performance of Bayesian SBMs, especially when the community count is unknown. This…

We propose a robust, scalable, integrated methodology for community detection and community comparison in graphs. In our procedure, we first embed a graph into an appropriate Euclidean space to obtain a low-dimensional representation, and…

Many systems are naturally represented by a multilayer network in which edges exist in multiple layers that encode different, but potentially related, types of interactions, and it is important to understand limitations on the detectability…

Community detection in a complex network is an important problem of much interest in recent years. In general, a community detection algorithm chooses an objective function and captures the communities of the network by optimizing the…

Given an underlying graph, we consider the following \emph{dynamics}: Initially, each node locally chooses a value in $\{-1,1\}$, uniformly at random and independently of other nodes. Then, in each consecutive round, every node updates its…

The maximization of generalized modularity performs well on networks in which the members of all communities are statistically indistinguishable from each other. However, there is no theory bounding the maximization performance in more…

We consider the problem of estimating community memberships of nodes in a network, where every node is associated with a vector determining its degree of membership in each community. Existing provably consistent algorithms often require…

There has been a recent interest in understanding the power of local algorithms for optimization and inference problems on sparse graphs. Gamarnik and Sudan (2014) showed that local algorithms are weaker than global algorithms for finding…

Community detection is a fundamental problem in social network analysis consisting in unsupervised dividing social actors (nodes in a social graph) with certain social connections (edges in a social graph) into densely knitted and highly…

Consider a pair of sparse correlated stochastic block models $\mathcal S(n,\tfrac{\lambda}{n},\epsilon;s)$ subsampled from a common parent stochastic block model with two symmetric communities, average degree $\lambda=O(1)$, divergence…

Let $N$ components be partitioned into two communities, denoted ${\cal P}_+$ and ${\cal P}_-$, possibly of different sizes. Assume that they are connected via a directed and weighted Erd\"os-R\'enyi (DWER) random graph with unknown…

We consider three distinct and well studied problems concerning network structure: community detection by modularity maximization, community detection by statistical inference, and normalized-cut graph partitioning. Each of these problems…

Community detection in networks is a key exploratory tool with applications in a diverse set of areas, ranging from finding communities in social and biological networks to identifying link farms in the World Wide Web. The problem of…

For a fixed d-regular graph H, a random n-lift is obtained by replacing each vertex v of H by a "fibre" containing n vertices, then placing a uniformly random matching between fibres corresponding to adjacent vertices of H. We show that…

We consider graphs where edges and their signs are added independently at random from among all pairs of nodes. We establish strong concentration inequalities for adjacency and Laplacian matrices obtained from this family of random graph…

We present a new algorithm for community detection. The algorithm uses random walks to embed the graph in a space of measures, after which a modification of $k$-means in that space is applied. The algorithm is therefore fast and easily…

Inspired by the increasing interest in self-organizing social opportunistic networks, we investigate the problem of distributed detection of unknown communities in dynamic random graphs. As a formal framework, we consider the dynamic…