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We study the structure of loops in networks using the notion of modulus of loop families. We introduce a new measure of network clustering by quantifying the richness of families of (simple) loops. Modulus tries to minimize the expected…
Uncertainty propagation in non-linear dynamical systems has become a key problem in various fields including control theory and machine learning. In this work we focus on discrete-time non-linear stochastic dynamical systems. We present a…
The issue of partitioning a network into communities has attracted a great deal of attention recently. Most authors seem to equate this issue with the one of finding the maximum value of the modularity, as defined by Newman. Since the…
In this note, we develop semi-analytical techniques to obtain the full correlational structure of a stochastic network of nonlinear neurons described by rate variables. Under the assumption that pairs of membrane potentials are jointly…
In this paper, we investigate community detection in networks in the presence of node covariates. In many instances, covariates and networks individually only give a partial view of the cluster structure. One needs to jointly infer the full…
Networks with node covariates offer two advantages to community detection methods, namely, (i) exploit covariates to improve the quality of communities, and more importantly, (ii) explain the discovered communities by identifying the…
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…
The increasing prevalence of network data in a vast variety of fields and the need to extract useful information out of them have spurred fast developments in related models and algorithms. Among the various learning tasks with network…
Graph theoretical analysis of the community structure of networks attempts to identify the communities (or modules) to which each node affiliates. However, this is in most cases an ill-posed problem, as the affiliation of a node to a single…
Community detection is a fundamental problem in the analysis of complex networks. It is the analogue of clustering in network data mining. Within community detection methods, hierarchical algorithms are popular. However, their iterative…
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…
Community structure in networks is observed in many different domains, and unsupervised community detection has received a lot of attention in the literature. Increasingly the focus of network analysis is shifting towards using network…
The process of stochastic Turing instability on a network is discussed for a specific case study, the stochastic Brusselator model. The system is shown to spontaneously differentiate into activator-rich and activator-poor nodes, outside the…
We present a fast spectral algorithm for community detection in complex networks. Our method searches for the partition with the maximum value of the modularity via the interplay of several refinement steps that include both agglomeration…
Network segmentation is a popular security practice for limiting lateral movement, yet practitioners lack a metric to measure how segmented a network actually is. We define segmentedness as the fraction of potential node-pair communications…
Collective dynamics result from interactions among noisy dynamical components. Examples include heartbeats, circadian rhythms, and various pattern formations. Because of noise in each component, collective dynamics inevitably involve…
We study how to detect groups in a complex network each of which consists of component nodes sharing a similar connection pattern. Based on the mixture models and the exploratory analysis set up by Newman and Leicht (Newman and Leicht 2007…
Most methods proposed to uncover communities in complex networks rely on their structural properties. Here we introduce the stability of a network partition, a measure of its quality defined in terms of the statistical properties of a…
We propose a novel method to find the community structure in complex networks based on an extremal optimization of the value of modularity. The method outperforms the optimal modularity found by the existing algorithms in the literature. We…
Many networks of interest in the sciences, including a variety of social and biological networks, are found to divide naturally into communities or modules. The problem of detecting and characterizing this community structure has attracted…