Related papers: Uniqueness of communities in regular stochastic bl…
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…
\cite{bickel2009nonparametric} developed a general framework to establish consistency of community detection in stochastic block model (SBM). In most applications of this framework, the community label is discrete. For example, in…
We develop an information-theoretic view of the stochastic block model, a popular statistical model for the large-scale structure of complex networks. A graph $G$ from such a model is generated by first assigning vertex labels at random…
Finding communities in networks is a problem that remains difficult, in spite of the amount of attention it has recently received. The Stochastic Block-Model (SBM) is a generative model for graphs with "communities" for which, because of…
We investigate how to select the number of communities for weighted networks without a full likelihood modeling. First, we propose a novel weighted degree-corrected stochastic block model (DCSBM), where the mean adjacency matrix is modeled…
Let $k,d $ be positive integers. We determine a sequence of constants that are asymptotic to the probability that the cluster at the origin in a $d$-dimensional Poisson Boolean model with balls of fixed radius is of order $k$, as the…
Clustering and community detection with multiple graphs have typically focused on aligned graphs, where there is a mapping between nodes across the graphs (e.g., multi-view, multi-layer, temporal graphs). However, there are numerous…
We study community detection in the contextual stochastic block model arXiv:1807.09596 [cs.SI], arXiv:1607.02675 [stat.ME]. In arXiv:1807.09596 [cs.SI], the second author studied this problem in the setting of sparse graphs with…
We consider spectral clustering algorithms for community detection under a general bipartite stochastic block model (SBM). A modern spectral clustering algorithm consists of three steps: (1) regularization of an appropriate adjacency or…
We count the asymptotic number of triangles in uniform random graphs where the degree distribution follows a power law with degree exponent $\tau\in(2,3)$. We also analyze the local clustering coefficient $c(k)$, the probability that two…
Community detection in multi-layer networks has emerged as a crucial area of modern network analysis. However, conventional approaches often assume that nodes belong exclusively to a single community, which fails to capture the complex…
Breaking of equivalence between the microcanonical ensemble and the canonical ensemble, describing a large system subject to hard and soft constraints, respectively, was recently shown to occur in large random graphs. Hard constraints must…
We consider the problem of detecting whether a power-law inhomogeneous random graph contains a geometric community, and we frame this as an hypothesis testing problem. More precisely, we assume that we are given a sample from an unknown…
The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of…
We study the frequentist properties of Bayesian statistical inference for the stochastic block model, with an unknown number of classes of varying sizes. We equip the space of vertex labellings with a prior on the number of classes and,…
In network inference applications, it is often desirable to detect community structure, namely to cluster vertices into groups, or blocks, according to some measure of similarity. Beyond mere adjacency matrices, many real networks also…
Although the inference of global community structure in networks has recently become a topic of great interest in the physics community, all such algorithms require that the graph be completely known. Here, we define both a measure of local…
Motivated by multi-subject experiments in neuroimaging studies, we develop a modeling framework for joint community detection in a group of related networks, which can be considered as a sample from a population of networks. The proposed…
The modularity of a graph is a parameter that measures its community structure; the higher its value (between $0$ and $1$), the more clustered the graph is. In this paper we show that the modularity of a random $3$-regular graph is at least…
This paper presents a novel approach to estimating community membership probabilities for network vertices generated by the Degree Corrected Mixed Membership Stochastic Block Model while preserving individual edge privacy. Operating within…