I. Derenyi | Searcharxiv

arXiv2004

A Tractable Complex Network Model based on the Stochastic Mean-field Model of Distance

Much recent research activity has been devoted to empirical study and theoretical models of complex networks (random graphs) with three qualitative features: power-law degree distribution, local clustering of edges, and small diameter. We point out a new (in this context) platform for such models -- the stochastic mean-field model of distance -- and within this platform study a simple two-parameter proportional attachment model. The model is mathematicallly natural, permits a wide variety of explicit calculations, has the desired three qualitative features, and fits the complete range of degree scaling exponents and clustering parameters; in these respects it compares favorably to existing models.

cond-mat.dis-nn↗

arXiv2003

Networks in life: Scaling properties and eigenvalue spectra

We analyse growing networks ranging from collaboration graphs of scientists to the network of similarities defined among the various transcriptional profiles of living cells. For the explicit demonstration of the scale-free nature and hierarchical organization of these graphs, a deterministic construction is also used. We demonstrate the use of determining the eigenvalue spectra of sparse random graph models for the categorization of small measured networks.

cond-mat.stat-mech↗