7 papers
The rank and layer distributions in random recursive trees
Huck Stepanyants, P. L. Krapivsky, Harrison Hartle +1
The distribution of node depths in a network is crucial for analyzing network structure. Two measures, rank and layer, quantify how deep inside a network a node is. The rank is the…
Leaves of preferential attachment trees
Harrison Hartle, P. L. Krapivsky
We provide a local probabilistic description of the limiting statistics of large preferential attachment trees in terms of the ordinary degree (number of neighbors) but augmented w…
Deterministic construction of typical networks in network models
Narayan G. Sabhahit, Moritz Laber, Harrison Hartle +4
It is often desirable to assess how well a given dataset is described by a given model. In network science, for instance, one often wants to say that a given real-world network app…
Statistics of leaves in growing random trees
Harrison Hartle, P. L. Krapivsky
Leaves, i.e., vertices of degree one, can play a significant role in graph structure, especially in sparsely connected settings in which leaves often constitute the largest fractio…
Growing unlabeled networks
Harrison Hartle, Brennan Klein, Dmitri Krioukov +1
Models of growing networks are a central topic in network science. In these models, vertices are usually labeled by their arrival time, distinguishing even those node pairs whose s…
The Metric Dimension of Sparse Random Graphs
Josep DÃaz, Harrison Hartle, Cristopher Moore
In 2013, Bollobás, Mitsche, and Pralat at gave upper and lower bounds for the likely metric dimension of random ErdÅs-Rényi graphs for a large range of expected degrees…