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Abstract
Random graph generators are necessary tools for many network science applications. For example, the evaluation of graph analysis algorithms requires methods for generating realistic synthetic graphs. Typically random graph generators are generating graphs that satisfy certain global criteria, such as degree distribution or diameter. If the generated graph is to be used to evaluate community detection and mining algorithms, however, the generator must produce realistic community structure, as well. Recent research has shown that a clique is not necessarily a realistic community structure, necessitating the development of new graph generators. We propose HyGen, a random graph generator that leverages the recent research on non-clique-like communities to produce realistic random graphs with hyperbolic community structure, degree distribution, and clustering coefficient. Our generator can also be used to accurately model time-evolving communities.
Highlights
Modular structure is a characteristic of real-world networks
We propose the HYGEN random graph generator that is based on the hyperbolic community model of Metzler et al (2016)
For each of the graph generators, stochastic block model (SBM), Lancichinetti– Fortunato–Radicchi (LFR), and R-MAT, we learn the respective parameters with these communities as input and generate new graphs according to those parameters
Summary
Modular structure is a characteristic of real-world networks. Its constituents, or communities, typically display specific patterns of connectivity. The majority of members only have ties to the core and not to each other (Laumann and Pappi 1976; Alba and Moore 1978; Morgan et al 1997; Reed and Selbee 2001; Panzarasa et al 2009; Metzler et al 2019) This kind of intra-community structure is well described by a hyperbolic model (Araujo et al 2014; Metzler et al 2016). The hyperbolic model can express the particular core-tail structure which is frequently observed in real-world networks. It encompasses power law-like connectivity and is suitably general to represent clique-like as well as star-like patterns of connectivity (see Fig. 1b)
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