Related papers: Eigenvector dynamics under perturbation of modular…
While symmetry has been exploited to analyze synchronization patterns in complex networks, the identification of symmetries in large-size network remains as a challenge. We present in the present work a new method, namely the method of…
Community structure is a key feature omnipresent in real-world network data. Plethora of methods have been proposed to reveal subsets of densely interconnected nodes using criteria such as the modularity index. These approaches have been…
Motivated by its relevance to various types of dynamical behavior of network systems, the maximum eigenvalue $\lambda_Q$ of the adjacency matrix $A$ of a network has been considered, and mean-field-type approximations to $\lambda_Q$ have…
We consider three distinct and well studied problems concerning network structure: community detection by modularity maximization, community detection by statistical inference, and normalized-cut graph partitioning. Each of these problems…
Detecting communities in a network, based only on the adjacency matrix, is a problem of interest to several scientific disciplines. Recently, Zhang and Moore have introduced an algorithm in [P. Zhang and C. Moore, Proceedings of the…
Quantifying the eigenvalue spectra of large random matrices allows one to understand the factors that contribute to the stability of dynamical systems with many interacting components. This work explores the effect that the interaction…
Many real-world networks, including nervous systems, exhibit meso-scale structure. This means that their elements can be grouped into meaningful sub-networks. In general, these sub-networks are unknown ahead of time and must be "discovered"…
In network science, a group of nodes connected with each other at higher probability than with those outside the group is referred to as a community. From the perspective that individual communities are associated with functional modules…
There has been a surge of interest in community detection in homogeneous single-relational networks which contain only one type of nodes and edges. However, many real-world systems are naturally described as heterogeneous multi-relational…
Modularity maximization is one of the state-of-the-art methods for community detection that has gained popularity in the last decade. Yet it suffers from the resolution limit problem by preferring under certain conditions large communities…
A basic question in network community detection is how modular a given network is. This is usually addressed by evaluating the quality of partitions detected in the network. The Girvan-Newman (GN) modularity function is the standard way to…
This paper investigates community detection by modularity maximisation on bipartite networks. In particular we are interested in how the operation of projection, using one node set of the bipartite network to infer connections between nodes…
In the current work, we study the eigenvalue distribution results of a class of non-normal matrix-sequences which may be viewed as a low rank perturbation, depending on a parameter $\beta>1$, of the basic Toeplitz matrix-sequence…
We present and discuss a mathematical procedure for identification of small "communities" or segments within large bipartite networks. The procedure is based on spectral analysis of the matrix encoding network structure. The principal tool…
Recent theoretical and experimental work in neuroscience has focused on the representational and dynamical character of neural manifolds --subspaces in neural activity space wherein many neurons coactivate. Importantly, neural populations…
Recent years have seen a surge of interest in the analysis of complex networks, facilitated by the availability of relational data and the increasingly powerful computational resources that can be employed for their analysis. Naturally, the…
The functions of complex networks are usually determined by a small set of vital nodes. Finding the best set of vital nodes (eigenshield nodes) is critical to the network's robustness against rumor spreading and cascading failures, which…
We have analyzed the detectability limits of network communities in the framework of the popular Girvan and Newman benchmark. By carefully taking into account the inevitable stochastic fluctuations that affect the construction of each and…
Despite the prevalence of community detection algorithms, relatively less work has been done on understanding whether a network is indeed modular and how resilient the community structure is under perturbations. To address this issue, we…
We present a compact matrix formulation of the modularity, a commonly used quality measure for the community division in a network. Using this formulation we calculate the density of modularities, a statistical measure of the probability of…