Concentration inequalities are fundamental tools in probabilistic combinatorics and
theoretical computer science for proving that functions of random variables are typically near …

For a given graph G, each partition of the vertices has a modularity score, with higher values
indicating that the partition better captures community structure in G. The modularity q∗(G) of …

We prove that there exists a constant γ crit≈ 0.17566 such that if G∼ G (n, 1/2), then for any
ε> 0 with high probability G has a equipartition such that each vertex has (γ crit− ε) n more …

Consider n= ℓ+ m individuals, where ℓ≤ m, with ℓ individuals holding an opinion A and m
holding an opinion B. Suppose that the individuals communicate via an undirected network …

We survey results on counting graphs with given degree sequence, focusing on asymptotic
results, and mentioning some of the applications of these results. The main recent …

We provide asymptotic formulae for the numbers of bipartite graphs with given degree
sequence, and of loopless digraphs with given in‐and out‐degree sequences, for a wide …

In this letter, we investigate the randomized gossip (RG) algorithm by taking the power
consumption over wireless sensor networks (WSNs) into account for distributed averaging …

Let J and J^* be subsets of N such that 0,1∈J and 0∈J^*. For infinitely many n, let
k=(k_1,...,k_n) be a vector of nonnegative integers whose sum M is even. We find an …

We prove an asymptotic formula for the number of orientations with given out-degree (score)
sequence for a graph $ G $. The graph $ G $ is assumed to have average degrees at least …

Let $ V $ be an $ n $-set, and let $ X $ be a random variable taking values in the powerset of
$ V $. Suppose we are given a sequence of random coupons $ X_1, X_2,\ldots $, where the …