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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…
In this paper, we propose a novel statistic of networks, the normalized clustering coefficient, which is a modified version of the clustering coefficient that is robust to network size, network density and degree heterogeneity under…
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…
Small-world networks by Watts and Strogatz are a class of networks that are highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. These characteristics result in networks with unique…
Recent results from statistical physics show that large classes of complex networks, both man-made and of natural origin, are characterized by high clustering properties yet strikingly short path lengths between pairs of nodes. This class…
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…
In this paper we introduce a new model of data packet transport, based on a stochastic approach with the aim of characterizing the load distribution on complex networks. Moreover we analyze the load standard deviation as an index of…
We study the behavior of the clustering coefficient in tagged networks. The rich variety of tags associated with the nodes in the studied systems provide additional information about the entities represented by the nodes which can be…
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…
In this paper, a new multi-hop weighted clustering procedure is proposed for homogeneous Mobile Ad hoc networks. The algorithm generates double star embedded non-overlapping cluster structures, where each cluster is managed by a leader node…
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 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…
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…
The performance of the Hopfield neural network model is numerically studied on various complex networks, such as the Watts-Strogatz network, the Barab{\'a}si-Albert network, and the neuronal network of the C. elegans. Through the use of a…
We describe and develop three recent novelties in network research which are particularly useful for studying social systems. The first one concerns the discovery of some basic dynamical laws that enable the emergence of the fundamental…
A computer model is described which is used to assess the dynamical complexity of a class of networks of spiking neurons with small-world properties. Networks are constructed by forming an initially segregated set of highly intra-connected…
Apart from the role the clustering coefficient plays in the definition of the small-world phenomena, it also has great relevance for practical problems involving networked dynamical systems. To study the impact of the clustering coefficient…
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…
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…
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…