Related papers: Computational Complexity, Phase Transitions, and M…
This paper studies the problem of detecting the presence of a small dense community planted in a large Erd\H{o}s-R\'enyi random graph $\mathcal{G}(N,q)$, where the edge probability within the community exceeds $q$ by a constant factor.…
Consider a network consisting of two subnetworks (communities) connected by some external edges. Given the network topology, the community detection problem can be cast as a graph partitioning problem that aims to identify the external…
Community detection in graphs is the problem of finding groups of vertices which are more densely connected than they are to the rest of the graph. This problem has a long history, but it is undergoing a resurgence of interest due to the…
We derive rigorous bounds for well-defined community structure in complex networks for a stochastic block model (SBM) benchmark. In particular, we analyze the effect of inter-community "noise" (inter-community edges) on any "community…
We survey the application of a relatively new branch of statistical physics--"community detection"-- to data mining. In particular, we focus on the diagnosis of materials and automated image segmentation. Community detection describes the…
Hypergraphs are widely adopted tools to examine systems with higher-order interactions. Despite recent advancements in methods for community detection in these systems, we still lack a theoretical analysis of their detectability limits.…
Here we study the NP-complete $K$-SAT problem. Although the worst-case complexity of NP-complete problems is conjectured to be exponential, there exist parametrized random ensembles of problems where solutions can typically be found in…
In this paper, we study the sensitivity of the spectral clustering based community detection algorithm subject to a Erdos-Renyi type random noise model. We prove phase transitions in community detectability as a function of the external…
Recently, a phase transition has been discovered in the network community detection problem below which no algorithm can tell which nodes belong to which communities with success any better than a random guess. This result has, however, so…
Community detection, also known as graph partitioning, is a well-known NP-hard combinatorial optimization problem with applications in diverse fields such as complex network theory, transportation, and smart power grids. The problem's…
We study networks that display community structure -- groups of nodes within which connections are unusually dense. Using methods from random matrix theory, we calculate the spectra of such networks in the limit of large size, and hence…
Determining community structure is a central topic in the study of complex networks, be it technological, social, biological or chemical, in static or interacting systems. In this paper, we extend the concept of community detection from…
We consider a random sparse graph with bounded average degree, in which a subset of vertices has higher connectivity than the background. In particular, the average degree inside this subset of vertices is larger than outside (but still…
Recently, it was shown that there is a phase transition in the community detection problem. This transition was first computed using the cavity method, and has been proved rigorously in the case of $q=2$ groups. However, analytic…
We study the problem of community detection (CD) on Euclidean random geometric graphs where each vertex has two latent variables: a binary community label and a $\mathbb{R}^d$ valued location label which forms the support of a Poisson point…
The structural phase transitions and computational complexity of random 3-SAT instances are traditionally described using thermodynamic analogies from statistical physics, such as Replica Symmetry Breaking and energy landscapes. While…
Community detection is a key data analysis problem across different fields. During the past decades, numerous algorithms have been proposed to address this issue. However, most work on community detection does not address the issue of…
Community detection is expensive, and the cost generally depends at least linearly on the number of vertices in the graph. We propose working with a reduced graph that has many fewer nodes but nonetheless captures key community structure.…
The community detection problem for graphs asks one to partition the n vertices V of a graph G into k communities, or clusters, such that there are many intracluster edges and few intercluster edges. Of course this is equivalent to finding…
We consider a model for random hypergraphs with identifiability, an analogue of connectedness. This model has a phase transition in the proportion of identifiable vertices when the underlying random graph becomes critical. The phase…