Directed Random Geometric Graphs
Abstract
Many realworld networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet, and the network of followers on Twitter among many others. The challenge, however, is to create a network model that has many of the properties of realworld networks such as powerlaw degree distributions and the smallworld property. To meet these challenges, we introduce the \textit{Directed} Random Geometric Graph (DRGG) model, which is an extension of the random geometric graph model. We prove that it is scalefree with respect to the indegree distribution, has binomial outdegree distribution, has a high clustering coefficient, has few edges and is likely smallworld. These are some of the main features of aforementioned real world networks. We empirically observe that word association networks have many of the theoretical properties of the DRGG model.
 Publication:

arXiv eprints
 Pub Date:
 August 2018
 arXiv:
 arXiv:1808.02046
 Bibcode:
 2018arXiv180802046M
 Keywords:

 Computer Science  Social and Information Networks;
 Condensed Matter  Disordered Systems and Neural Networks;
 Physics  Physics and Society
 EPrint:
 14+5 pages, 5 figures, 3 tables