In this paper, we describe a methodology for comparing networks represented as weighted graphs. The key idea is to associate a probability density function derived from the graph Laplacian, and then compute the Wasserstein distance between the derived densities of the respective graphs. This has wide applications to various networks including biological and financial.

Motivated by applications of Gabriel graphs andYao graphs in wireless ad-hoc networks, we show that the maximum degree of a random Gabriel graph or Yao graph defined on n points drawn uniformly at random from a unit square grows as (log n/ log log n) in probability.

We determine the probability thresholds for the existence of monotone paths, of finite and infinite length, in random oriented graphs with vertex set N, the set of all increasing k-tuples in N. These graphs appear as line graph of uniform hypergraphs with vertex set N.

This paper deals with chain graphs under the Andersson-Madigan-Perlman (AMP) interpretation. In particular, we present a constraint based algorithm for learning an AMP chain graph a given probability distribution is faithful to. Moreover, we show that the extension of Meek’s conjecture to AMP chain graphs does not hold, which compromises the development of efficient and correct score+search lea...

We establish the conditions under which several algorithmically exploitable structural features hold for random intersection graphs, a natural model for many real-world networks where edges correspond to shared attributes. Specifically, we fully characterize the degeneracy of random intersection graphs, and prove that the model asymptotically almost surely produces graphs with hyperbolicity at ...

Various types of graph statistics for Bernoulli graphs are represented as numerators of incomplete U-statistics. Asymptotic normality of these statistics is proved for Bernoulli graphs in which the edge probability is constant. In addition it is shown that subgraph counts asymptotically are linear functions of the number of edges in the graph. AMS Subject Classification: Primary 05C99; Secondar...

We derive a formula for the level spacing probability distribution in quantum graphs. We apply it to simple examples and we discuss its relation with previous work and its possible application in more general cases. Moreover, we derive an exact and explicit formula for the level spacing distribution of integrable quantum graphs.

We introduce a new class of countably infinite random geometric graphs, whose vertices V are points in a metric space, and vertices are adjacent independently with probability p ∈ (0, 1) if the metric distance between the vertices is below a given threshold. If V is a countable dense set in R equipped with the metric derived from the L∞-norm, then it is shown that with probability 1 such infini...

We introduce a new class of countably infinite random geometric graphs, whose vertices V are points in a metric space, and vertices are adjacent independently with probability p ∈ (0, 1) if the metric distance between the vertices is below a given threshold. If V is a countable dense set in R equipped with the metric derived from the L∞-norm, then it is shown that with probability 1 such infini...

reliability wiener number is a modification of the original wiener number in which probabilities are assigned to edges yielding a natural model in which there are some (or all) bonds in the molecule that are not static. various probabilities naturally allow modelling different types of chemical bonds because chemical bonds are of different types and it is well-known that under certain condition...