Related papers: Stochastic fluctuations and the detectability limi…
Modularity maximization has been one of the most widely used approaches in the last decade for discovering community structure in networks of practical interest in biology, computing, social science, statistical mechanics, and more.…
Community detection is a crucial task in network analysis that can be significantly improved by incorporating subject-level information, i.e. covariates. However, current methods often struggle with selecting tuning parameters and analyzing…
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…
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 rigorously prove a central limit theorem for neural network models with a single hidden layer. The central limit theorem is proven in the asymptotic regime of simultaneously (A) large numbers of hidden units and (B) large numbers of…
As two main focuses of the study of complex networks, the community structure and the dynamics on networks have both attracted much attention in various scientific fields. However, it is still an open question how the community structure is…
Spectral clustering is a widely used method for community detection in networks. We focus on a semi-supervised community detection scenario in the Partially Labeled Stochastic Block Model (PL-SBM) with two balanced communities, where a…
Many networks including social networks, computer networks, and biological networks are found to divide naturally into communities of densely connected individuals. Finding community structure is one of fundamental problems in network…
Community detecting is one of the main approaches to understanding networks \cite{For2010}. However it has been a longstanding challenge to give a definition for community structures of networks. Here we found that community structures are…
Modularity maximization using greedy algorithms continues to be a popular approach toward community detection in graphs, even after various better forming algorithms have been proposed. Apart from its clear mechanism and ease of…
In this paper, we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups. Specifically,…
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…
The stochastic block model (SBM) is a popular framework for studying community detection in networks. This model is limited by the assumption that all nodes in the same community are statistically equivalent and have equal expected degrees.…
A degree-corrected distribution-free model is proposed for weighted social networks with latent structural information. The model extends the previous distribution-free models by considering variation in node degree to fit real-world…
Identifying significant community structures in networks with incomplete data is a challenging task, as the reliability of solutions diminishes with increasing levels of missing information. However, in many empirical contexts, some…
In this work, we study the problem of community detection in the stochastic block model with adversarial node corruptions. Our main result is an efficient algorithm that can tolerate an $\epsilon$-fraction of corruptions and achieves error…
Multi-layer networks are networks on a set of entities (nodes) with multiple types of relations (edges) among them where each type of relation/interaction is represented as a network layer. As with single layer networks, community detection…
Population rate or activity equations are the foundation of a common approach to modeling for neural networks. These equations provide mean field dynamics for the firing rate or activity of neurons within a network given some connectivity.…
Uncovering the community structure exhibited by real networks is a crucial step towards an understanding of complex systems that goes beyond the local organization of their constituents. Many algorithms have been proposed so far, but none…
We investigate the statistics of fluctuations in a classical stochastic network of nodes joined by connectors. The nodes carry generalized charge that may be randomly transferred from one node to another. Our goal is to find the time…