With the advent of big data and the information age, the data magnitude of various complex
networks is growing rapidly. Many real-life situations cannot be portrayed by ordinary …

Complex networks encoding the topological architecture of real-world complex systems
have recently been undergoing a fundamental transition beyond pairwise interactions …

We study the probability that the random graph $ G (n, p) $ is triangle-free. When $ p= o (n^{-
1/2}) $ or $ p=\omega (n^{-1/2}) $ the asymptotics of the logarithm of this probability are …

For a‐regular connected graph H the problem of determining the upper tail large deviation
for the number of copies of H in, an Erdős‐Rényi graph on n vertices with edge probability p …

In practical applications of hypergraph theory, we are usually surrounded by the state of
indeterminacy. This paper employs uncertainty theory to address indeterministic information …

We develop a quantitative large deviations theory for random hypergraphs, which rests on
tensor decomposition and counting lemmas under a novel family of cut-type norms. As our …

We initiate a study of large deviations for block model random graphs in the dense regime.
Following Chatterjee-Varadhan (2011), we establish an LDP for dense block models …

Building on the techniques from the breakthrough paper of Harel, Mousset and Samotij,
which solved the upper tail problem for cliques, we compute the asymptotics of the upper tail …

What is the probability that a sparse n-vertex random d-regular graph G nd, n 1-c< d= o (n)
contains many more copies of a fixed graph K than expected? We determine the behavior of …

We consider general exponential random graph models (ergms) where the sufficient
statistics are functions of homomorphism counts for a fixed collection of simple graphs F k …