2015
DOI: 10.1016/j.cpc.2015.05.028
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Hyperbolic graph generator

Abstract: Networks representing many complex systems in nature and society share some common structural properties like heterogeneous degree distributions and strong clustering. Recent research on network geometry has shown that those real networks can be adequately modeled as random geometric graphs in hyperbolic spaces. In this paper, we present a computer program to generate such graphs. Besides real-world-like networks, the program can generate random graphs from other well-known graph ensembles, such as the soft co… Show more

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Cited by 52 publications
(63 citation statements)
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References 12 publications
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“…The iterations in the BA model cease when the graph has attained the requisite number n of vertices. The HGG model [41,42] produces a random graph of n vertices by initially fixing n vertices to n points on a hyperbolic disk. In the HGG model, the probability of existence of an edge between two vertices is proportional to the hyperbolic distance between the two points on the hyperbolic disk that correspond to these two vertices.…”
Section: Network Datasetsmentioning
confidence: 99%
See 1 more Smart Citation
“…The iterations in the BA model cease when the graph has attained the requisite number n of vertices. The HGG model [41,42] produces a random graph of n vertices by initially fixing n vertices to n points on a hyperbolic disk. In the HGG model, the probability of existence of an edge between two vertices is proportional to the hyperbolic distance between the two points on the hyperbolic disk that correspond to these two vertices.…”
Section: Network Datasetsmentioning
confidence: 99%
“…In the HGG model, the probability of existence of an edge between two vertices is proportional to the hyperbolic distance between the two points on the hyperbolic disk that correspond to these two vertices. By tuning the input parameter γ, the HGG model can produce either a hyperbolic or a spherical random graph [41,42]. Specifically, the HGG model produces hyperbolic random graphs for γ ∈ [2, ∞) whereas spherical random graphs for γ = ∞.…”
Section: Network Datasetsmentioning
confidence: 99%
“…In Section 3.1, we review existing approaches in Euclidean space (Section 3.1.1); elliptic space, such as the surface of a three-dimensional sphere (Section 3.1.2); and other spaces (Section 3.1.3). In Section 3.2, we highlight properties of hyperbolic space and detail its promising potential application in the class of continuous latent space models for network data, inspired by recent network analysis methods which take advantage of a hyperbolic latent space (Krioukov et al, 2010;Asta and Shalizi, 2014;Aldecoa, Orsini and Krioukov, 2015). We will discuss various interesting aspects of the different choices for the geometry of the latent space in each subsection, but we also have provided a summary of some of the most important differences between Euclidean, elliptic, and hyperbolic space in Table 1.…”
Section: Latent Space Geometriesmentioning
confidence: 99%
“…Similarity has also been proposed as a second mechanism, that together with popularity or preferential attachment, may result into complex networks with an hyperbolic topology [38]. In [2] it is described an hyperbolic graph generator. When SAT instances are modeled as graphs, many graph properties can be analyzed, such as the small-world property [43], the scale-free structure [5,6], the eigenvector centrality [26], or the self-similarity [3].…”
Section: Introductionmentioning
confidence: 98%