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 …

We develop a statistical theory to characterize correlations in weighted networks. We define
the appropriate metrics quantifying correlations and show that strictly uncorrelated weighted …

The connections in many networks are not merely binary entities, either present or not, but
have associated weights that record their strengths relative to one another. Recent studies of …

We review the main tools which allow for the statistical characterization of weighted
networks. We then present two case studies, the airline connection network and the scientific …

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 …

Networked structures arise in a wide array of different contexts such as technological and
transportation infrastructures, social phenomena, and biological systems. These highly …

Can complex engineered and biological networks be coarse-grained into smaller and more
understandable versions in which each node represents an entire pattern in the original …

Given any complex directed network, a set of acyclic subgraphs can be extracted that will
provide valuable information about its hierarchical structure. This Letter presents how the …

Several definitions of clustering coefficient for weighted networks have been proposed in
literature, but less attention has been paid to both weighted and directed networks. We …

Complex systems may also 1 emerge from a large number of interdependent and interacting
elements. Networks have proven to be effective models of natural or man-made complex …