entropy maximizing distribution with absolute power constraint

We, therefore, introduce a differerent statistic, weighted triangles, which weighs triangles based on their evidence for geometry. In this paper we show that triangle counts or clustering coefficients are insufficient because they fail to detect geometry induced by hyperbolic spaces. Currently, triangle counts and clustering coefficients are the standard statistics to signal the presence of geometry. Nevertheless, if one observes only the network connections, the presence of geometry is not always evident. Indeed, many real-world networks can be accurately modeled by positioning vertices of a network graph in hyperbolic spaces. Because of that, these models are able to adequately capture many common structural properties of real-world networks, such as scale invariance and high clustering. These models formalize the natural idea that similar vertices are likely to connect. Since more dimensions also increase the number of nearest neighbors for angular clusters representing communities, considering only one more dimension allows us to generate more realistic and diverse community structures.read more read lessĪbstract: In the past decade, geometric network models have received vast attention in the literature. We show that there is an important qualitative difference between the lowest-dimensional model and its higher-dimensional counterparts with respect to how similarity between nodes restricts connection probabilities. Although a few studies have shown that hyperbolic models can generate community structures, another salient feature observed in real networks, we argue that the current models are overlooking the choice of the latent space dimensionality that is required to adequately represent clustered networked data. These properties are ubiquitous in systems as varied as the internet, transportation, brain or epidemic networks, which are thus unified under the hyperbolic network interpretation on a surface of constant negative curvature. Abstract: Abstract Over the last decade, random hyperbolic graphs have proved successful in providing geometric explanations for many key properties of real-world networks, including strong clustering, high navigability, and heterogeneous degree distributions.

Entropy maximizing distribution with absolute power constraint