The entropy of network ensembles characterizes the amount of information encoded in the
network structure and can be used to quantify network complexity and the relevance of given …

For scale-free networks with degrees following a power law with an exponent τ∈(2, 3), the
structures of motifs (small subgraphs) are not yet well understood. We introduce a method …

Random geometric graphs (RGGs) can be formalized as hidden-variables models where the
hidden variables are the coordinates of the nodes. Here we develop a general approach to …

Random graphs with power-law degrees can model scale-free networks as sparse
topologies with strong degree heterogeneity. Mathematical analysis of such random graphs …

This paper studies a statistical network model generated by a large number of randomly
sized overlapping communities, where any pair of nodes sharing a community is linked with …

Subgraphs reveal information about the geometry and functionalities of complex networks.
For scale-free networks with unbounded degree fluctuations, we obtain the asymptotics of …

We study the average nearest-neighbour degree a (k) of vertices with degree k. In many real-
world networks with power-law degree distribution, a (k) falls off with k, a property ascribed …

In this paper we study typical distances in the configuration model, when the degrees have
asymptotically infinite variance. We assume that the empirical degree distribution follows a …

Sampling uniform simple graphs with power-law degree distributions with degree exponent
is a non-trivial problem. Firstly, we propose a method to sample uniform simple graphs that …

When studying topological or dynamical properties of random scale-free networks, it is tacitly
assumed that degree–degree correlations are not present. However, simple constraints …