相关论文: Computational Complexity, Phase Transitions, and M…

Community detection is one of the most important problems in network analysis. Among many algorithms proposed for this task, methods based on statistical inference are of particular interest: they are mathematically sound and were shown to…

This paper studies a statistical network model generated by a large number of randomly sized overlapping communities, where any pair of nodes sharing a community is linked with probability $q$ via the community. In the special case with…

Consider the following asynchronous, opportunistic communication model over a graph $G$: in each round, one edge is activated uniformly and independently at random and (only) its two endpoints can exchange messages and perform local…

We give upper and lower bounds on the information-theoretic threshold for community detection in the stochastic block model. Specifically, let $k$ be the number of groups, $d$ be the average degree, the probability of edges between vertices…

As communities represent similar opinions, similar functions, similar purposes, etc., community detection is an important and extremely useful tool in both scientific inquiry and data analytics. However, the classic methods of community…

The study of networks has received increased attention recently not only from the social sciences and statistics but also from physicists, computer scientists and mathematicians. One of the principal problem in networks is community…

This article presents an efficient hierarchical clustering algorithm that solves the problem of core community detection. It is a variant of the standard community detection problem in which we are particularly interested in the connected…

We present efficient counting and sampling algorithms for random $k$-SAT when the clause density satisfies $\alpha \le \frac{2^k}{\mathrm{poly}(k)}.$ In particular, the exponential term $2^k$ matches the satisfiability threshold…

The richness of definitions and features of the community-detection problem has led to an impressive body of literature. In fact, many community-detection methods and surveys have been introduced in recent years. The goal here is to present…

Community detection involves grouping the nodes in the network and is one of the most-studied tasks in network science. Conventional methods usually require the specification of the number of communities $K$ in the network. This number is…

As one of the main subjects of investigation in data science, network science has been demonstrated a wide range of applications to real-world networks analysis and modeling. For example, the pervasive presence of structural or topological…

A key challenge in network science is the detection of communities, which are sets of nodes in a network that are densely connected internally but sparsely connected to the rest of the network. A fundamental result in community detection is…

We introduce a novel approach for studying random k-coverage, using Morse theory for the k-nearest neighbor (k-NN) distance function. We prove a sharp phase transition for the number of critical points of the k-NN distance function, from…

Many networks can be usefully decomposed into a dense core plus an outlying, loosely-connected periphery. Here we propose an algorithm for performing such a decomposition on empirical network data using methods of statistical inference. Our…

Graphs may be used to represent many different problem domains -- a concrete example is that of detecting communities in social networks, which are represented as graphs. With big data and more sophisticated applications becoming widespread…

We study the problem of detecting a structured, low-rank signal matrix corrupted with additive Gaussian noise. This includes clustering in a Gaussian mixture model, sparse PCA, and submatrix localization. Each of these problems is…

Community detection methods play a central role in understanding complex networks by revealing highly connected subsets of entities. However, most community detection algorithms generate partitions of the nodes, thus (i) forcing every node…

We present a comprehensive and versatile theoretical framework to study site and bond percolation on clustered and correlated random graphs. Our contribution can be summarized in three main points. (i) We introduce a set of iterative…

We introduce a prime number generator in the form of a stochastic algorithm. The character of such algorithm gives rise to a continuous phase transition which distinguishes a phase where the algorithm is able to reduce the whole system of…

We formalize the problem of detecting a community in a network into testing whether in a given (random) graph there is a subgraph that is unusually dense. We observe an undirected and unweighted graph on N nodes. Under the null hypothesis,…