Complex networks describe a wide range of systems in nature and society. Frequently cited
examples include the cell, a network of chemicals linked by chemical reactions, and the …

Praise for the Third Edition “Researchers of any kind of extremal combinatorics or theoretical
computer science will welcome the new edition of this book.”-MAA Reviews Maintaining a …

Although the theory of random graphs is one of the youngest branches of graph theory, in
importance it is second to none. It began with some sporadic papers of Erdős in the 1940s …

Complex networks are key to describing the connected nature of the society that we live in.
This book, the second of two volumes, describes the local structure of random graph models …

Given a sequence of nonnegative real numbers λ0, λ1… which sum to 1, we consider
random graphs having approximately λi n vertices of degree i. Essentially, we show that if Σ i …

The “classical” random graph models, in particular G (n, p), are “homogeneous,” in the
sense that the degrees (for example) tend to be concentrated around a typical value. Many …

Recently there has been much interest in studying large-scale real-world networks and
attempting to model their properties using random graphs. Although the study of real-world …

We present new semi-honest and malicious secure PSI protocols that outperform all prior
works by several times in both communication and running time. Our semi-honest protocol …

Limiting distributions are derived for the sparse connected components that are present
when a random graph on n vertices has approximately 1/2n edges. In particular, we show …

“Explosive percolation” is said to occur in an evolving network when a macroscopic
connected component emerges in a number of steps that is much smaller than the system …