When Does Bottom-up Beat Top-down in Hierarchical Community Detection?

The investigation of community structure in networks is a task of great importance in many disciplines, namely physics, sociology, biology and computer science where systems are often represented as graphs. One of the challenges is to find local communities from a local viewpoint in a graph without global information in order to reproduce the subjective hierarchical vision for each vertex. In this paper we present the improvement of an information dynamics algorithm in which ...

Community detection for large networks is a challenging task due to the high computational cost as well as the heterogeneous community structure. Stochastic block model (SBM) is a popular model to analyze community structure where nodes belonging to the same communities are connected with equal probability. Modularity optimization methods provide a fast and effective way for community detection under SBM with assortative community structure, where nodes within communities are...

A fundamental problem in the analysis of network data is the detection of network communities, groups of densely interconnected nodes, which may be overlapping or disjoint. Here we describe a method for finding overlapping communities based on a principled statistical approach using generative network models. We show how the method can be implemented using a fast, closed-form expectation-maximization algorithm that allows us to analyze networks of millions of nodes in reasona...

We consider the problem of learning latent community structure from multiple correlated networks. We study edge-correlated stochastic block models with two balanced communities, focusing on the regime where the average degree is logarithmic in the number of vertices. Our main result derives the precise information-theoretic threshold for exact community recovery using multiple correlated graphs. This threshold captures the interplay between the community recovery and graph ma...

Discovering and characterizing the large-scale topological features in empirical networks are crucial steps in understanding how complex systems function. However, most existing methods used to obtain the modular structure of networks suffer from serious problems, such as being oblivious to the statistical evidence supporting the discovered patterns, which results in the inability to separate actual structure from noise. In addition to this, one also observes a resolution lim...

The stochastic block model and its variants have been a popular tool in analyzing large network data with community structures. In this paper we develop an efficient network cross-validation (NCV) approach to determine the number of communities, as well as to choose between the regular stochastic block model and the degree corrected block model. The proposed NCV method is based on a block-wise node-pair splitting technique, combined with an integrated step of community recove...

We study the problem of community recovery from coarse measurements of a graph. In contrast to the problem of community recovery of a fully observed graph, one often encounters situations when measurements of a graph are made at low-resolution, each measurement integrating across multiple graph nodes. Such low-resolution measurements effectively induce a coarse graph with its own communities. Our objective is to develop conditions on the graph structure, the quantity, and pro...

Community structure is one of the most relevant features encountered in numerous real-world applications of networked systems. Despite the tremendous effort of scientists working on this subject over the past few decades to characterize, model, and analyze communities, more investigations are needed to better understand the impact of community structure and its dynamics on networked systems. Here, we first focus on generative models of communities in complex networks and thei...

We analyze the information-theoretic limits for the recovery of node labels in several network models. This includes the Stochastic Block Model, the Exponential Random Graph Model, the Latent Space Model, the Directed Preferential Attachment Model, and the Directed Small-world Model. For the Stochastic Block Model, the non-recoverability condition depends on the probabilities of having edges inside a community, and between different communities. For the Latent Space Model, th...

Although much of the focus of statistical works on networks has been on static networks, multiple networks are currently becoming more common among network data sets. Usually, a number of network data sets, which share some form of connection between each other are known as multiple or multi-layer networks. We consider the problem of identifying the common community structures for multiple networks. We consider extensions of the spectral clustering methods for the multiple sp...