192 citations · 529 across the 38 of their papers we have counts for
17 papers · 1 filter
Stationary distribution of node2vec random walks on household models
Lars Schroeder, Clara Stegehuis
The node2vec random walk has proven to be a key tool in network embedding algorithms. These random walks are tuneable, and their transition probabilities depend on the previous vis…
Optimal subgraphs in geometric scale-free random graphs
Riccardo Michielan, Clara Stegehuis, Matthias Walter
Geometric scale-free random graphs are popular models for networks that exhibit as heavy-tailed degree distributions, small-worldness and high clustering. In these models, vertices…
On the distances within cliques in a soft random geometric graph
Ercan Sönmez, Clara Stegehuis
We study the distances of edges within cliques in a soft random geometric graph on a torus, where the vertices are points of a homogeneous Poisson point process, and far-away point…
Large deviations for triangles in scale-free random graphs
Clara Stegehuis, Bert Zwart
We provide large deviations estimates for the upper tail of the number of triangles in scale-free inhomogeneous random graphs where the degrees have power law tails with index $-α,…
Scale-free graphs with many edges
Clara Stegehuis, Bert Zwart
We develop tail estimates for the number of edges in a Chung-Lu random graph with regularly varying weight distribution. Our results show that the most likely way to have an unusua…
Cliques in geometric inhomogeneous random graph
Riccardo Michielan, Clara Stegehuis
Many real-world networks were found to be highly clustered, and contain a large amount of small cliques. We here investigate the number of cliques of any size k contained in a geom…
Degree distributions in AB random geometric graphs
Clara Stegehuis, Lotte Weedage
In this paper, we provide degree distributions for random geometric graphs, in which points of type connect to the closest points of type . The motivating example t…
Counting triangles in power-law uniform random graphs
Pu Gao, Remco van der Hofstad, Angus Southwell +1
We count the asymptotic number of triangles in uniform random graphs where the degree distribution follows a power law with degree exponent . We also analyze the local c…
Subgraphs in preferential attachment models
Alessandro Garavaglia, Clara Stegehuis
We consider subgraph counts in general preferential attachment models with power-law degree exponent . For all subgraphs , we find the scaling of the expected number of sub…
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…
Switch chain mixing times through triangle counts
Tom Bannink, Remco van der Hofstad, Clara Stegehuis
Sampling uniform simple graphs with power-law degree distributions with degree exponent is a non-trivial problem. We propose a method to sample uniform simple graphs th…
Triadic closure in configuration models with unbounded degree fluctuations
Remco van der Hofstad, Johan S. H. van Leeuwaarden, Clara Stegehuis
The configuration model generates random graphs with any given degree distribution, and thus serves as a null model for scale-free networks with power-law degrees and unbounded deg…
Optimal subgraph structures in scale-free configuration models
Remco van der Hofstad, Johan S. H. van Leeuwaarden, Clara Stegehuis
Subgraphs reveal information about the geometry and functionalities of complex networks. For scale-free networks with unbounded degree fluctuations, we obtain the asymptotics of th…
Degree correlations in scale-free null models
Clara Stegehuis
We study the average nearest neighbor degree of vertices with degree . In many real-world networks with power-law degree distribution falls off in , a property…
Mesoscopic scales in hierarchical configuration models
Remco van der Hofstad, Johan S. H. van Leeuwaarden, Clara Stegehuis
To understand mesoscopic scaling in networks, we study the hierarchical configuration model (HCM), a random graph model with community structure. The connections between the commun…
Local clustering in scale-free networks with hidden variables
Remco van der Hofstad, A. J. E. M. Janssen, Johan S. H. van Leeuwaarden +1
We investigate the presence of triangles in a class of correlated random graphs in which hidden variables determine the pairwise connections between vertices. The class rules out s…
Hierarchical Configuration Model
Remco van der Hofstad, Johan S. H. van Leeuwaarden, Clara Stegehuis
We introduce a class of random graphs with a community structure, which we call the hierarchical configuration model. On the inter-community level, the graph is a configuration mod…