Related papers: Strongly clustered random graphs via triadic closu…
Triadic closure, the formation of a connection between two nodes in a network sharing a common neighbor, is considered a fundamental mechanism determining the clustered nature of many real-world topologies. In this work we define a static…
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…
Complex network theory crucially depends on the assumptions made about the degree distribution, while fitting degree distributions to network data is challenging, in particular for scale-free networks with power-law degrees. We present a…
The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…
We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…
We present a generator of random networks where both the degree-dependent clustering coefficient and the degree distribution are tunable. Following the same philosophy as in the configuration model, the degree distribution and the…
Graphs are commonly used to represent and visualize causal relations. For a small number of variables, this approach provides a succinct and clear view of the scenario at hand. As the number of variables under study increases, the graphical…
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…
Random graphs with power-law degrees can model scale-free networks as sparse topologies with strong degree heterogeneity. Mathematical analysis of such random graphs proved successful in explaining scale-free network properties such as…
Degree correlation is an important topological property common to many real-world networks. In this paper, the statistical measures for characterizing the degree correlation in networks are investigated analytically. We give an exact proof…
The configuration model generates random graphs with any given degree distribution, and thus serves as a null model for scale-free networks with power-law degrees and unbounded degree fluctuations. For this setting, we study the local…
The coexistence of sparsity and clustering (non-vanishing average fraction of triangles per node) is one of the few structural features that, irrespective of finer details, are ubiquitously observed across large real-world networks. This…
We study a recently introduced class of scale-free networks showing a high clustering coefficient and non-trivial connectivity correlations. We find that the connectivity probability distribution strongly depends on the fine details of the…
The purpose of this paper is to analyze the degree index and clustering index in random graphs. The degree index in our setup is a certain measure of degree irregularity whose basic properties are well studied in the literature, and the…
Mixing patterns in large self-organizing networks, such as the Internet, the World Wide Web, social and biological networks are often characterized by degree-degree {dependencies} between neighbouring nodes. One of the problems with the…
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…
Graph clustering (or community detection) has long drawn enormous attention from the research on web mining and information networks. Recent literature on this topic has reached a consensus that node contents and link structures should be…
Random networks are widely used to model complex networks and research their properties. In order to get a good approximation of complex networks encountered in various disciplines of science, the ability to tune various statistical…
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…
Clustering trajectory data attracted considerable attention in the last few years. Most of prior work assumed that moving objects can move freely in an euclidean space and did not consider the eventual presence of an underlying road network…