Approximating clustering coefficient and transitivity.
Asymptotic equipartition properties for simple hierarchical and networked structures
We prove asymptotic equipartition properties for simple hierarchical structures (modelled as multitype Galton-Watson trees) and networked structures (modelled as randomly coloured random graphs). For example, for large n, a networked data structure consisting of n units connected by an average number of links of order n / log n can be coded by about H × n bits, where H is an explicitly defined entropy. The main technique in our proofs are large deviation principles for suitably defined empirical...
Asymptotic equipartition properties for simple hierarchical and networked structures
We prove asymptotic equipartition properties for simple hierarchical structures (modelled as multitype Galton-Watson trees) and networked structures (modelled as randomly coloured random graphs). For example, for large n, a networked data structure consisting of n units connected by an average number of links of order n / log n can be coded by about H × n bits, where H is an explicitly defined entropy. The main technique in our proofs are large deviation principles for suitably defined empirical...
Asymptotic evolution of acyclic random mappings.
Asymptotic properties of random graphs [Book]
Asymptotic spectral analysis of generalized Erdős-Rényi random graphs
Motivated by the Watts-Strogatz model for a complex network, we introduce a generalization of the Erdős-Rényi random graph. We derive a combinatorial formula for the moment sequence of its spectral distribution in the sparse limit.
Asymptotics for rooted bipartite planar maps and scaling limits of two-type spatial trees.
Average properties of random walks on Galton-Watson trees
Balanced online Ramsey games in random graphs.
Bootstrap percolation and diffusion in random graphs with given vertex degrees.
Chebyshev inequality for random graphs.
Chvátal's Condition cannot hold for both a graph and its complement
Chvátal’s Condition is a sufficient condition for a spanning cycle in an n-vertex graph. The condition is that when the vertex degrees are d₁, ...,dₙ in nondecreasing order, i < n/2 implies that or . We prove that this condition cannot hold in both a graph and its complement, and we raise the problem of finding its asymptotic probability in the random graph with edge probability 1/2.
Coloring the edges of a random graph without a monochromatic giant component.
Component evolution in random intersection graphs.
Constrainted graph processes.
Continuity of the percolation threshold in randomly grown graphs.
Counting and selecting at random bipartite graphs with fixed degrees
Counting triangulations of planar point sets.
Critical subgraphs of a random graph.
Cycle structure of percolation on high-dimensional tori
In the past years, many properties of the largest connected components of critical percolation on the high-dimensional torus, such as their sizes and diameter, have been established. The order of magnitude of these quantities equals the one for percolation on the complete graph or Erdős–Rényi random graph, raising the question whether the scaling limits of the largest connected components, as identified by Aldous (1997), are also equal. In this paper, we investigate the cycle structureof the largest...