title: Fast Generation of Sparse Random Kernel Graphs.
abstract: The development of kernel-based inhomogeneous random graphs has provided models that are flexible enough to capture many observed characteristics of real networks, and that are also mathematically tractable. We specify a class of inhomogeneous random graph models, called random kernel graphs, that produces sparse graphs with tunable graph properties, and we develop an efficient generation algorithm to sample random instances from this model. As real-world networks are usually large, it is essential that the run-time of generation algorithms scales better than quadratically in the number of vertices n. We show that for many practical kernels our algorithm runs in time at most 𝒪(n(logn)2). As a practical example we show how to generate samples of power-law degree distribution graphs with tunable assortativity.
authors.affiliation: Center for Nonlinear Studies, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico, United States of America.
authors.forename: Aric
authors.initials: A
authors.lastname: Hagberg
authors.affiliation: Applied Mathematics and Plasma Physics, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico, United States of America.
authors.forename: Nathan
authors.initials: N
authors.lastname: Lemons
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical; D013997:Time Factors