Generalizations of the clustering coefficient to weighted complex networks.

By J. Saramaki, Mikko Kivelä, Jukka-Pekka Onnela, Kimmo K. Kaski, János Kertész. Physical review. E, Statistical, nonlinear, and soft matter physics, 2006

696 citations recorded by the source corpus.

The recent high level of interest in weighted complex networks gives rise to a need to develop new measures and to generalize existing ones to take the weights of links into account. Here we focus on various generalizations of the clustering coefficient, which is one of the central characteristics in the complex network theory. We present a comparative study of the several suggestions introduced in the literature, and point out their advantages and limitations. The concepts are illustrated by simple examples as well as by empirical data of the world trade and weighted coauthorship networks.

Subfields: Molecular Biology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/eed00d930ec2154720aa06be0caf9571ce5650a4

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Citations in the corpus

Topological properties of stock market networks: The case of Brazil (2010, positive): “The weighted clustering coefficient [26] can be measured as:”
International trade and financial integration: a weighted network analysis (2010, background): “Hence, in the context yAmong the weighted clustering coefficients reviewed in Saramaki et al. (2007), the one used here is the only one that takes into account the weights of all three edges in any triangle (while disregarding weights not participating in any triangle), and that is invariant to…”
State of the aRt personality research: A tutorial on network analysis of personality data in R (2015, neutral): “All of these generalizations coincide with the unweighted clustering coefficient when edge weights become binary (Saramäki et al., 2007).”
Stability and variability of personality networks. A tutorial on recent developments in network psychometrics (2017, background): “This property has been recently extended to consider edge weights (Saramäki et al., 2007) and signs (Costantini & Perugini, 2014).”
Analysing ecological networks of species interactions (2018, background): “The clustering coefficient can also be defined globally, for the entire graph (Soffer & Vazquez, 2005; Saramäki et al., 2007) and is calculated as CC2 = 3Nt Nc , where N t is the number of triangles in graph G (a is connected to b and c, b to a and c, and c to a and b) and N c is the number of three”
COVID-19 lockdown induces disease-mitigating structural changes in mobility networks (2020, neutral): “[40] J.”
Stock network stability in times of crisis (2014, methodology): “Additionally, we calculate the weighted clustering coefficient [30] and the assortativity coefficient [31].”
Network analysis: a brief overview and tutorial (2018, background): “Clustering: the extent to which a node is part of a cluster of nodes can be estimated (Saramäki et al., 2007).”
Complex network measures of brain connectivity: Uses and interpretations (2010, background): “See Saramaki et al. (2007) for other variants.”
Mathematical Formulation of Multilayer Networks (2013, background): “(5) to explore generalizations of the several existing weighted clustering coefficients for ordinary networks [52].”
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.”
The evolution of the world trade web: a weighted-network analysis (2010, methodology): “Third, one can straightforwardly compute a weighted clustering coeﬃcient by suitably weighting each triangle using the weights w ij associated to its three edges (see Appendix A, and Fagiolo, 2007; Saramaki et al., 2007).”
Patterns of coevolving amino acids unveil structural and dynamical domains (2017, background): “…propensity is conveniently captured by ∆ C = C − C rand , that is, the difference of the clustering coefﬁcients of the k -nearest neighbors graph, C , and of a randomized, reshufﬂed version, C rand (63), measuring the probability that two neighbors of a vertex are also connected between themselves.”
The statistical physics of real-world networks (2018, background): “[57] J.”