Related papers: Weights and degrees in a random graph model based …
We describe the asymptotic behaviour of large degrees in random hyperbolic graphs, for all values of the curvature parameter $ \alpha$. We prove that, with high probability, the node degrees satisfy the following ordering property: the…
We show for a model of scale-free graphs with biased partner choice that knowing the exponent for the degree distribution is in general not sufficient to decide epidemic threshold properties for exponents less than three.We show that the…
We consider complete graphs with edge weights and/or node weights taking values in some set. In the first part of this paper, we show that a large number of graphs are completely determined, up to isomorphism, by the distribution of their…
Subgraphs reveal information about the geometry and functionalities of complex networks. For scale-free networks with unbounded degree fluctuations, we obtain the asymptotics of the number of times a small connected graph occurs as a…
We enumerate rooted 2-connected and 3-connected surface maps with respect to vertices and edges. We also derive the bivariate version of the large face-width result for random 3-connected maps. These results are then used to derive…
We show the asymptotic degree distribution of the typical vertex of a sparse inhomogeneous random intersection graph.
We introduce a random intersection graph process aimed at modeling sparse evolving affiliation networks that admit tunable (power law) degree distribution and assortativity and clustering coefficients. We show the asymptotic degree…
We consider Markov logic networks and relational logistic regression as two fundamental representation formalisms in statistical relational artificial intelligence that use weighted formulas in their specification. However, Markov logic…
We revisit the problem of counting the number of copies of a fixed graph in a random graph or multigraph, for various models of random (multi)graphs. For our proofs we introduce the notion of \emph{patchworks} to describe the possible…
We find an asymptotic enumeration formula for the number of simple $r$-uniform hypergraphs with a given degree sequence, when the number of edges is sufficiently large. The formula is given in terms of the solution of a system of equations.…
A hypergraph is simple if it has no loops and no repeated edges, and a hypergraph is linear if it is simple and each pair of edges intersects in at most one vertex. For $n\geq 3$, let $r= r(n)\geq 3$ be an integer and let $\boldsymbol{k} =…
Inspired by applications to theories of coding and communication in networks of nervous tissue, we study maximum entropy distributions on weighted graphs with a given expected degree sequence. These distributions are characterized by…
We study a general model of random dynamical simplicial complexes and derive a formula for the asymptotic degree distribution. This asymptotic formula encompasses results for a number of existing models, including random Apollonian networks…
We consider a class of scale-free inhomogeneous random graphs, which includes some long-range percolation models. We study the maximum degree in such graphs in a growing observation window and show that its limiting distribution is Frechet.…
We address problem of determining edge weights on a graph using non-backtracking closed walks from a vertex. We show that the weights of all of the edges can be determined from any starting vertex exactly when the graph has minimum degree…
We study a family of directed random graphs whose arcs are sampled independently of each other, and are present in the graph with a probability that depends on the attributes of the vertices involved. In particular, this family of models…
We consider uniform random cographs (either labeled or unlabeled) of large size. Our first main result is the convergence towards a Brownian limiting object in the space of graphons. We then show that the degree of a uniform random vertex…
Various kinds of spread of influence occur in real world social and virtual networks. These phenomena are formulated by activation processes and irreversible dynamic monopolies in combinatorial graphs representing the topology of the…
Many biological networks have been labelled scale-free as their degree distribution can be approximately described by a powerlaw distribution. While the degree distribution does not summarize all aspects of a network it has often been…
The bivariate distribution of degrees of adjacent vertices (degree-degree distribution) is an important network characteristic defining the statistical dependencies between degrees of adjacent vertices. We show the asymptotic degree-degree…