Related papers: Disparity of clustering coefficients in the Holme-…

In this letter, we consider the effect of clustering coefficient on the synchronizability of coupled oscillators located on scale-free networks. The analytic result for the value of clustering coefficient aiming at a highly clustered…

In this paper, we present a detailed analysis of the global clustering coefficient in scale-free graphs. Many observed real-world networks of diverse nature have a power-law degree distribution. Moreover, the observed degree distribution…

In this paper, we analyze the behavior of the global clustering coefficient in scale free graphs. We are especially interested in the case of degree distribution with an infinite variance, since such degree distribution is usually observed…

We derive the finite size dependence of the clustering coefficient of scale-free random graphs generated by the configuration model with degree distribution exponent $2<\gamma<3$. Degree heterogeneity increases the presence of triangles in…

Probabilistic networks display a wide range of high average clustering coefficients independent of the number of nodes in the network. In particular, the local clustering coefficient decreases with the degree of the subtending node in a…

We investigate the presence of triangles in a class of correlated random graphs in which hidden variables determine the pairwise connections between vertices. The class rules out self-loops and multiple edges and allows for negative degree…

We consider a random graph process in which, at each time step, a new vertex is added with m out-neighbours, chosen with probabilities proportional to their degree plus a strictly positive constant. We show that the expectation of the…

The global clustering coefficient is an effective measure for analyzing and comparing the structures of complex networks. The random annulus graph is a modified version of the well-known Erd\H{o}s-R\'{e}nyi random graph. It has been…

Link prediction is a fundamental problem in graph theory with diverse applications, including recommender systems, community detection, and identifying spurious connections. While feature-based methods achieve high accuracy, their reliance…

The clustering coefficient quantifies how well connected are the neighbors of a vertex in a graph. In real networks it decreases with the vertex degree, which has been taken as a signature of the network hierarchical structure. Here we show…

We establish asymptotic vertex degree distribution and examine its relation to the clustering coefficient in two popular random intersection graph models of Godehardt and Jaworski [Electron. Notes Discrete Math. 10 (2001) 129-132]. For…

In this paper we consider the clustering coefficient and clustering function in a random graph model proposed by Krioukov et al.~in 2010. In this model, nodes are chosen randomly inside a disk in the hyperbolic plane and two nodes are…

In the context of growing networks, we introduce a simple dynamical model that unifies the generic features of real networks: scale-free distribution of degree and the small world effect. While the average shortest path length increases…

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…

Clustering is a fundamental property of complex networks and it is the mathematical expression of a ubiquitous phenomenon that arises in various types of self-organized networks such as biological networks, computer networks or social…

We study the scenario of graph-based clustering algorithms such as spectral clustering. Given a set of data points, one first has to construct a graph on the data points and then apply a graph clustering algorithm to find a suitable…

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…

A wide variety of complex networks (social, biological, information etc.) exhibit local clustering with substantial variation in the clustering coefficient (the probability of neighbors being connected). Existing models of large graphs…

Measuring graph clustering quality remains an open problem. To address it, we introduce quality measures based on comparisons of intra- and inter-cluster densities, an accompanying statistical test of the significance of their differences…

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…