Related papers: Taxonomy of Cohesion Coefficients for Weighted and…
In this paper, we provide novel definitions of clustering coefficient for weighted and directed multilayer networks. We extend in the multilayer theoretical context the clustering coefficients proposed in the literature for weighted…
In this paper, we consider the problem of assessing local clustering in complex networks. Various definitions for this measure have been proposed for the cases of networks having weighted edges, but less attention has been paid to both…
Based on an expert systems approach, the issue of community detection can be conceptualized as a clustering model for networks. Building upon this further, community structure can be measured through a clustering coefficient, which is…
A fundamental property of complex networks is the tendency for edges to cluster. The extent of the clustering is typically quantified by the clustering coefficient, which is the probability that a length-2 path is closed, i.e., induces a…
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…
While the majority of approaches to the characterization of complex networks has relied on measurements considering only the immediate neighborhood of each network node, valuable information about the network topological properties can be…
The clustering coefficient is a valuable tool for understanding the structure of complex networks. It is widely used to analyze social networks, biological networks, and other complex systems. While there is generally a single common…
The local structure of unweighted networks can be characterized by the number of times a subgraph appears in the network. The clustering coefficient, reflecting the local configuration of triangles, can be seen as a special case of this…
Usual formulations of the clustering coefficient can be shown to be insufficient in the task of describing the local topology of very simple networks. Motivated by this, we review some alternatives in order to present an extension, the…
Weights and directionality of the edges carry a large part of the information we can extract from a complex network. However, many network measures were formulated initially for undirected binary networks. The necessity to incorporate…
Recent advances in the study of networked systems have highlighted that our interconnected world is composed of networks that are coupled to each other through different "layers" that each represent one of many possible subsystems or types…
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,…
Clustering coefficient is one of the most useful indices in complex networks. However, graph theoretic properties of this metric have not been discussed much in the literature, especially in graphs resulting from some binary operations. In…
The classic clustering coefficient and the lately proposed closure coefficient quantify the formation of triangles from two different perspectives, with the focal node at the centre or at the end in an open triad respectively. As many…
We develop a full theoretical approach to clustering in complex networks. A key concept is introduced, the edge multiplicity, that measures the number of triangles passing through an edge. This quantity extends the clustering coefficient in…
Clustering coefficient is an important topological feature of complex networks. It is, however, an open question to give out its analytic expression on weighted networks yet. Here we applied an extended mean-field approach to investigate…
Hypergraphs are generalizations of simple graphs that allow for the representation of complex group interactions beyond pairwise relationships. Clustering coefficients quantify local link density in networks and have been widely studied for…
We present a new approach to the calculation of measures in weighted networks, based on the translation of a weighted network into an ensemble of edges. This leads to a straightforward generalization of any measure defined on unweighted…
The formation of triangles in complex networks is an important network property that has received tremendous attention. The formation of triangles is often studied through the clustering coefficient. The closure coefficient or transitivity…
In recent work we presented a new approach to the analysis of weighted networks, by providing a straightforward generalization of any network measure defined on unweighted networks. This approach is based on the translation of a weighted…