We study the percolation behavior of two interdependent scale-free (SF) networks under
random failure of 1-p fraction of nodes. Our results are based on numerical solutions of …

The existence of explosive phase transitions in random (Erdös Rényi-type) networks has
been recently documented by Achlioptas, D'Souza, and Spencer [Science 323, 1453 (2009) …

We discuss some properties of the research collaboration graph for mathematicians, look at
its evolution over time, and survey some random models that might produce graphs of this …

Complex networks in both nature and technology have been shown to display characteristic,
small subgraphs (so-called motifs) which appear to be related to their underlying …

The network characteristics based on the phonological similarities in the lexicons of several
languages were examined. These languages differed widely in their history and linguistic …

During the past two decades, percolation has long served as a basic paradigm for network
resilience, community formation and so on in complex systems. While the percolation …

We develop a statistical theory of networks. A network is a set of vertices and links given by
its adjacency matrix c, and the relevant statistical ensembles are defined in terms of a …

Genome-scale molecular networks, including protein interaction and gene regulatory
networks, have taken centre stage in the investigation of the burgeoning disciplines of …

Networks are mathematical objects widely used in multiple disciplines to model the structure
of complex systems. From the network of neurons in the human brain to the social networks …

We have obtained exact results for the Ising model on a hierarchical lattice incorporating
three key features characterizing many real-world networks—a scale-free degree …