168 citations · 236 across the 16 of their papers we have counts for
14 papers · 1 filter
Limiting Behavior of Degree-Degree Metrics under Local Convergence in Probability
Andrei-Eugeniu Patularu, Pim van der Hoorn
This paper investigates the limiting behaviour of degree-degree correlation metrics for sequences of random graphs under a general assumption of local convergence in probability. W…
Flexible random graph modeling for cell-cell interactions
Mike van Santvoort, Pim van der Hoorn
In this paper we explore generalisations to a random digraph model designed for modelling cell-cell interactions (RaCInG). In its baseline model -- tested both theoretically and in…
Condensation in scale-free geometric graphs with excess edges
Remco van der Hofstad, Pim van der Hoorn, Céline Kerriou +2
We identify the upper large deviation probability for the number of edges in scale-free geometric random graph models as the space volume goes to infinity. Our result covers the mo…
From inhomogeneous random digraphs to random graphs with fixed arc counts
Mike van Santvoort, Pim van der Hoorn
Consider a random graph model with vertices where each vertex has a vertex-type drawn from some discrete distribution. Suppose that the number of arcs to be placed between each…
Scaling of the clustering function in spatial inhomogeneous random graphs
Remco van der Hofstad, Pim van der Hoorn, Neeladri Maitra
We consider an infinite spatial inhomogeneous random graph model with an integrable connection kernel that interpolates nicely between existing spatial random graph models. Key exa…
Local limits of spatial inhomogeneous random graphs
Remco van der Hofstad, Pim van der Hoorn, Neeladri Maitra
Consider a set of vertices, where each vertex has a location in that is sampled uniformly from the unit cube in , and a weight associated to it. Co…
Ollivier curvature of random geometric graphs converges to Ricci curvature of their Riemannian manifolds
Pim van der Hoorn, Gabor Lippner, Carlo Trugenberger +1
Curvature is a fundamental geometric characteristic of smooth spaces. In recent years different notions of curvature have been developed for combinatorial discrete objects such as…
Clustering in a hyperbolic model of complex networks
Nikolaos Fountoulakis, Pim van der Hoorn, Tobias Müller +1
In this paper we consider the clustering coefficient and clustering function in a random graph model proposed by Krioukov et al.~in 2010. In this model, nodes are chosen randomly i…
Limit theorems for assortativity and clustering in null models for scale-free networks
Remco van der Hofstad, Pim van der Hoorn, Nelly Litvak +1
An important problem in modeling networks is how to generate a randomly sampled graph with given degrees. A popular model is the configuration model, a network with assigned degree…
Sparse Maximum-Entropy Random Graphs with a Given Power-Law Degree Distribution
Pim van der Hoorn, Gabor Lippner, Dmitri Krioukov
Even though power-law or close-to-power-law degree distributions are ubiquitously observed in a great variety of large real networks, the mathematically satisfactory treatment of r…
Average nearest neighbor degrees in scale-free networks
Dong Yao, Pim van der Hoorn, Nelly Litvak
The average nearest neighbor degree (ANND) of a node of degree is widely used to measure dependencies between degrees of neighbor nodes in a network. We formally analyze ANND i…
Typical distances in the directed configuration model
Pim van der Hoorn, Mariana Olvera-Cravioto
We analyze the distribution of the distance between two nodes, sampled uniformly at random, in digraphs generated via the directed configuration model, in the supercritical regime.…
Upper bounds for number of removed edges in the Erased Configuration Model
Pim van der Hoorn, Nelly Litvak
Models for generating simple graphs are important in the study of real-world complex networks. A well established example of such a model is the erased configuration model, where e…
Degree-degree dependencies in directed networks with heavy-tailed degrees
Pim van der Hoorn, Nelly Litvak
In network theory, Pearson's correlation coefficients are most commonly used to measure the degree assortativity of a network. We investigate the behavior of these coefficients in…