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Heterogeneity is a key aspect of complex networks, often emerging by looking at the distribution of node properties, from the milestone observations on the degree to the recent developments in mixing pattern estimation. Mixing patterns, in…

We analyze the process of informational exchange through complex networks by measuring network efficiencies. Aiming to study non-clustered systems, we propose a modification of this measure on the local level. We apply this method to an…

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…

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…

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…

We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module and the inter-module connections are defined by the joint degree-degree distribution of nodes for each pair of modules.…

Most research concerning the influence of network structure on phenomena taking place on the network focus on relationships between global statistics of the network structure and characteristic properties of those phenomena, even though…

We investigate the clustering ability in bipartite networks where cycles of size three are absent and therefore the standard definition of clustering coefficient cannot be used. Instead, we use another coefficient given by the fraction of…

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,…

Empirical complex systems must differentially respond to external perturbations and, at the same time, internally distribute information to coordinate their components. While networked backbones help with the latter, they limit the…

The clustering coefficient quantifies the abundance of connected triangles in a network and is a major descriptive statistics of networks. For example, it finds an application in the assessment of small-worldness of brain networks, which is…

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…

The representation of complex systems as networks is inappropriate for the study of certain problems. We show several examples of social, biological, ecological and technological systems where the use of complex networks gives very limited…

Small-worlds represent efficient communication networks that obey two distinguishing characteristics: a high clustering coefficient together with a small characteristic path length. This paper focuses on an interesting paradox, that…

This paper develops a mathematical framework to study signal networks, in which nodes can be active or inactive, and their activation or deactivation is driven by external signals and the states of the nodes to which they are connected via…

The structure of many complex networks includes edge directionality and weights on top of their topology. Network analysis that can seamlessly consider combination of these properties are desirable. In this paper, we study two important…

Researchers have long observed that the ``small-world" property, which combines the concepts of high transitivity or clustering with a low average path length, is ubiquitous for networks obtained from a variety of disciplines, including…

We propose a model of network growth that generalizes the deactivation model previously suggested for complex networks. Several topological features of this generalized model, such as the degree distribution and clustering coefficient, have…

Based on an expert systems approach, the issue of community detection can be conceptualized as a clustering model for networks. Building upon this further, community structure can be measured through a clustering coefficient, which is…

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…