Directed Random Geometric Graphs
Jesse Michel, Sushruth Reddy, Rikhav Shah, Sandeep Silwal, and Ramis, Movassagh

TL;DR
The paper introduces the Directed Random Geometric Graph (DRGG) model, capturing key properties of real-world directed networks like scale-free degree distributions, high clustering, and small-world characteristics.
Contribution
It presents a novel directed geometric graph model with proven properties matching real-world network features, supported by empirical observations.
Findings
DRGG is scale-free in indegree distribution
DRGG exhibits high clustering coefficient
Empirical word association networks resemble DRGG properties
Abstract
Many real-world 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 real-world networks such as powerlaw degree distributions and the small-world 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 scale-free with respect to the indegree distribution, has binomial outdegree distribution, has a high clustering coefficient, has few edges and is likely small-world. 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.
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Taxonomy
TopicsComplex Network Analysis Techniques · Bioinformatics and Genomic Networks · Topological and Geometric Data Analysis
