Models of random graphs and their applications - Cannings, Penman - 2003 () Citation Context ...ng on the colours a, b ∈ X of the two vertices. This model, which comprises the simple Erdős-Rényi graph with independent colours as a special case, was introduced by Penman in his ...
Pim van der Hoorn and Nelly Litvak. Degree-degree dependencies in directed networks with heavy-tailed degrees. Internet Mathematics, 11(2):155-179, 2015.Litvak, N., van der Hofstad, R.: Degree-degree correlations in random graphs with heavy- tailed degrees. ArXiv e-prints (2012)...
Most random graph generators aim at modelling global properties of the graphs, such as degree distribution, clustering coefficient, or effective diameter. Hence, models such asErdős and Rényi (1959),Albert and Barabási (2002), or the Forest fire model (Leskovec et al. 2005) do not generate...
with and without a constraint on the time needed for the complete activation. this problem encompasses in special cases many extremal characteristics of graphs like their independence, decycling or domination number, and can also be seen as a packing problem of repulsive particles. we use the cavit...
Randomized On-Line Matching, a representative of a class of algorithms, is a sequential algorithm that exploits a randomized efficient on-line matching algorithm that calculates maximal matchings in bipartite graphs, named the Ranking algorithm [86], as its basis. The Ranking algorithm considers that...
This monograph sets out a body of mathematical theory for finite graphs with nodes placed randomly in Euclidean space and edges added to connect points that are close to each other. As an alternative to classical random graph models, these geometric graphs are relevant to the modelling of real-...
Graph representation learning methods opened new avenues for addressing complex, real-world problems represented by graphs. However, many graphs used in these applications comprise millions of nodes and billions of edges and are beyond the capabilities o
We establish rapid mixing of the random-cluster Glauber dynamics on random -regular graphs for all and , where the threshold corresponds to a uniqueness/non-uniqueness phase transition for the random-cluster model on the (infinite) -regular tree. It is expected that this threshold is sharp, and...
(Note that while both planar and geometric graphs are embedded in space, the latter allows for edge-crossings and therefore broader degree distributions and larger number of edges for the sameN. In light of this difference, the similarity between the two ostensibly different classes of graphs is ...
small complete graphs – then adds a layer representing the connections between households – this can be either a complete graph, as in the original household model, or a random graph with a more inhomogeneous structure, closer to real-world networks. In such models there are many interesting ...