Related papers: Relative Clustering Coefficient
We develop a network in which the natural numbers are the vertices. We use the decomposition of natural numbers by prime numbers to establish the connections. We perform data collapse and show that the degree distribution of these networks…
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…
In Network Science node neighbourhoods, also called ego-centered networks have attracted large attention. In particular the clustering coefficient has been extensively used to measure their local cohesiveness. In this paper, we show how,…
We propose a cyclic coefficient $R$ which represents the cyclic characteristics of complex networks. If the network forms a perfect tree-like structure then $R$ becomes zero. The larger value of $R$ represents that the network is more…
Correlation clustering provides a method for separating the vertices of a signed graph into the optimum number of clusters without specifying that number in advance. The main goal in this type of clustering is to minimize the number of…
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…
We consider sparse random intersection graphs with the property that the clustering coefficient does not vanish as the number of nodes tends to infinity. We find explicit asymptotic expressions for the correlation coefficient of degrees of…
Relations between average clustering coefficient and global clustering coefficient, local efficiency, radiality, closeness, betweenness and stress centralities were obtained for simple graphs.
An important source of high clustering coefficient in real-world networks is transitivity. However, existing approaches for modeling transitivity suffer from at least one of the following problems: i) they produce graphs from a specific…
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…
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…
We consider a generalized version of the correlation clustering problem, defined as follows. Given a complete graph $G$ whose edges are labeled with $+$ or $-$, we wish to partition the graph into clusters while trying to avoid errors: $+$…
Statistical significance of network clustering has been an unresolved problem since it was observed that community detection algorithms produce false positives even in random graphs. After a phase transition between undetectable and…
Clustering and closure coefficients are among the most widely applied indicators in the description of the topological structure of a network. Many distinct definitions have been proposed over time, particularly in the case of weighted…
A computational theory for clustering and a semi-supervised clustering algorithm is presented. Clustering is defined to be the obtainment of groupings of data such that each group contains no anomalies with respect to a chosen grouping…
Link prediction in complex network based on solely topological information is a challenging problem. In this paper, we propose a novel similarity index, which is efficient and parameter free, based on clustering ability. Here clustering…
Mode clustering is a nonparametric method for clustering that defines clusters using the basins of attraction of a density estimator's modes. We provide several enhancements to mode clustering: (i) a soft variant of cluster assignment, (ii)…
In network data analysis, summary statistics of a network can provide us with meaningful insight into the structure of the network. The average clustering coefficient is one of the most popular and widely used network statistics. In this…
We develop a cluster expansion for the probability of full connectivity of high density random networks in confined geometries. In contrast to percolation phenomena at lower densities, boundary effects, which have previously been largely…
Network models with latent geometry have been used successfully in many applications in network science and other disciplines, yet it is usually impossible to tell if a given real network is geometric, meaning if it is a typical element in…