Related papers: Higher-order clustering in networks
Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be…
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…
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…
We obtain the clustering coefficient, the degree-dependent local clustering, and the mean clustering of networks with arbitrary correlations between the degrees of the nearest-neighbor vertices. The resulting formulas allow one to determine…
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…
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…
Clustering is typically measured by the ratio of triangles to all triples, open or closed. Generating clustered networks, and how clustering affects dynamics on networks, is reasonably well understood for certain classes of networks…
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,…
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…
It has been shown that many complex networks shared distinctive features, which differ in many ways from the random and the regular networks. Although these features capture important characteristics of complex networks, their applicability…
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…
We introduce a clustering coefficient for nondirected and directed hypergraphs, which we call the quad clustering coefficient. We determine the average quad clustering coefficient and its distribution in real-world hypergraphs and compare…
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…
Many real-world networks display a natural bipartite structure. It is necessary and important to study the bipartite networks by using the bipartite structure of the data. Here we propose a modification of the clustering coefficient given…
A prominent parameter in the context of network analysis, originally proposed by Watts and Strogatz (Collective dynamics of `small-world' networks, Nature 393 (1998) 440-442), is the clustering coefficient of a graph $G$. It is defined as…
Looking to overcome the limitations of traditional networks, the network science community has lately given much attention to the so-called higher-order networks, where group interactions are modeled alongside pairwise ones. While degree…
One of the main characteristics of real-world networks is their large clustering. Clustering is one aspect of a more general but much less studied structural organization of networks, i.e. edge multiplicity, defined as the number of…
The percolation properties of clustered networks are analyzed in detail. In the case of weak clustering, we present an analytical approach that allows to find the critical threshold and the size of the giant component. Numerical simulations…
A commonly used characteristic of statistical dependence of adjacency relations in real networks, the clustering coefficient, evaluates chances that two neighbours of a given vertex are adjacent. An extension is obtained by considering…