6 papers · 1 filter
Note on edge expansion and modularity in preferential attachment graphs
Colin McDiarmid, Katarzyna Rybarczyk, Fiona Skerman +1
Edge expansion is a parameter indicating how well-connected a graph is. It is useful for designing robust networks, analysing random walks or information flow through a network and…
Modularity and random graphs
Colin McDiarmid, Fiona Skerman
This work will appear as a chapter in a forthcoming volume titled `Topics in Probabilistic Graph Theory'. For a given graph , each partition of the vertices has a modularity sco…
A branching process with deletions and mergers that matches the threshold for hypercube percolation
Laura Eslava, Sarah Penington, Fiona Skerman
We define a graph process based on a discrete branching process with deletions and mergers, which is inspired by the 4-cycle structure of both the hypercube $Q_d…
The modularity of random graphs on the hyperbolic plane
Jordan Chellig, Nikolaos Fountoulakis, Fiona Skerman
Modularity is a quantity which has been introduced in the context of complex networks in order to quantify how close a network is to an ideal modular network in which the nodes for…
Random tree recursions: which fixed points correspond to tangible sets of trees?
Tobias Johnson, Moumanti Podder, Fiona Skerman
Let be the set of rooted trees containing an infinite binary subtree starting at the root. This set satisfies the metaproperty that a tree belongs to it if and only i…
K-cut on paths and some trees
Xing Shi Cai, Luc Devroye, Cecilia Holmgren +1
We define the (random) -cut number of a rooted graph to model the difficulty of the destruction of a resilient network. The process is as the cut model of Meir and Moon except n…