Related papers: Testing Network Structure Using Relations Between …
We consider the problem of detecting a community of densely connected vertices in a high-dimensional bipartite graph of size $n_1 \times n_2$. Under the null hypothesis, the observed graph is drawn from a bipartite Erd\H{o}s-Renyi…
A given neural network in the brain is involved in many different tasks. This implies that, when considering a specific task, the network's connectivity contains a component which is related to the task and another component which can be…
We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of…
We study spatial embeddings of random graphs in which nodes are randomly distributed in geographical space. We let the edge probability between any two nodes to be dependent on the spatial distance between them and demonstrate that this…
We propose a novel method to test the existence of community structure of undirected real-valued edge-weighted graph. The method is based on Wigner semicircular law on the asymptotic behavior of the random distribution for eigenvalues of a…
This article explores the relationship between communities and short cycles in complex networks, based on the fact that nodes more densely connected amongst one another are more likely to be linked through short cycles. By identifying…
Electronic databases, from phone to emails logs, currently provide detailed records of human communication patterns, offering novel avenues to map and explore the structure of social and communication networks. Here we examine the…
Hierarchical networks actually have many applications in the real world. Firstly, we propose a new class of hierarchical networks with scale-free and fractal structure, which are the networks with triangles compared to traditional…
The labeled stochastic block model is a random graph model representing networks with community structure and interactions of multiple types. In its simplest form, it consists of two communities of approximately equal size, and the edges…
We consider a crucial aspect of self-organization of a sensor network consisting of a large set of simple sensor nodes with no location hardware and only very limited communication range. After having been distributed randomly in a given…
Urban road networks are typical complex systems, which are crucial to our society and economy. In this study, topological characteristics of a number of urban road networks based on purely physical roads rather than routes of vehicles or…
The large amount of work on community detection and its applications leaves unaddressed one important question: the statistical validation of the results. In this paper we present a methodology able to clearly detect if the community…
Research on the vulnerability of electric networks with a complex network approach has produced significant results in the last decade, especially for transmission networks. These studies have shown that there are causal relations between…
We propose a generalized stochastic block model to explore the mesoscopic structures in signed networks by grouping vertices that exhibit similar positive and negative connection profiles into the same cluster. In this model, the group…
k-connectivity of random graphs is a fundamental property indicating reliability of multi-hop wireless sensor networks (WSN). WSNs comprising of sensor nodes with limited power resources are modeled by random graphs with unreliable nodes,…
The inference of an underlying network topology from local observations of a complex system composed of interacting units is usually attempted by using statistical similarity measures, such as Cross-Correlation (CC) and Mutual Information…
Knowing the structure of an offline social network facilitates a variety of analyses, including studying the rate at which infectious diseases may spread and identifying a subset of actors to immunize in order to reduce, as much as…
One property of networks that has received comparatively little attention is hierarchy, i.e., the property of having vertices that cluster together in groups, which then join to form groups of groups, and so forth, up through all levels of…
Random spatial networks-that is, graphs whose connectivity is governed by geometric proximity-have emerged as fundamental models for systems constrained by an underlying spatial structure. A prototypical example is the random geometric…
We provide a framework for determining the centralities of agents in a broad family of random networks. Current understanding of network centrality is largely restricted to deterministic settings, but practitioners frequently use random…