Clustering in complex directed networks.

By Giorgio Fagiolo. Physical review. E, Statistical, nonlinear, and soft matter physics, 2006

763 citations recorded by the source corpus.

Many empirical networks display an inherent tendency to cluster, i.e., to form circles of connected nodes. This feature is typically measured by the clustering coefficient (CC). The CC, originally introduced for binary, undirected graphs, has been recently generalized to weighted, undirected networks. Here we extend the CC to the case of (binary and weighted) directed networks and we compute its expected value for random graphs. We distinguish between CCs that count all directed triangles in the graph (independently of the direction of their edges) and CCs that only consider particular types of directed triangles (e.g., cycles). The main concepts are illustrated by employing empirical data on world-trade flows.

Subfields: Molecular Biology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ded16476171d3ac42d8ff071213450356c96cdde

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In Molecular Biology

In Statistical and Nonlinear Physics

Citations in the corpus

Structural Properties of the Caenorhabditis elegans Neuronal Network (2009, methodology): “Although there are several definitions of clustering for dir ected graphs in the literature [72], we use the clustering of the out-connected neighbors since it capture s signal flow emanating from a given neuron.”
The evolution of the world trade web: a weighted-network analysis (2010, methodology): “where wij are the weights associated to links and di is the degree of node i (see Onnela et al. 2005; Saramaki et al. 2007; Fagiolo 2007).”
Water for food: The global virtual water trade network (2011, methodology): “The explicit equations for the directed clustering coefficients, as given by Fagiolo [2007], in the notation used in this paper are”
Complex network measures of brain connectivity: Uses and interpretations (2010, methodology): “Directed clustering coef ﬁ cient (Fagiolo, 2007), where the network is fully subdivided into a set of nonoverlapping modules M , and e uv is the proportion of all links that connect nodes in module u with nodes in module v .”
Mathematical Formulation of Multilayer Networks (2013, background): “Several different definitions for local clustering coefficients have been developed for weighted and undirected networks [49,52–54] and for directed networks [55].”
ROBUST TIMING AND MOTOR PATTERNS BY TAMING CHAOS IN RECURRENT NEURAL NETWORKS (2012, methodology): “Here we analyzed the presence cyclic clusters, which are associated with recurrency and self-sustained activity, by using a directed, weighted version of the clustering coefficients (Fagiolo, 2007).”
Identifying Influential Nodes in Large-Scale Directed Networks: The Role of Clustering (2013, background): “Some literatures showed that the clustering has negative correlation with degree in undirected networks [38] or with total degree in directed networks [39].”
COVID-19 lockdown induces disease-mitigating structural changes in mobility networks (2020, neutral): “34).”
Multilayer networks (2013, background): “Consequently, attempting to define a multilayer clustering coefficient runs into even more significant complications than trying to define weighted [288] or directed [119] clustering coefficients.”