The statistical physics of real-world networks
In the past 15 years, statistical physics has been successful as a framework for modelling
complex networks. On the theoretical side, this approach has unveiled a variety of physical …
complex networks. On the theoretical side, this approach has unveiled a variety of physical …
Quantifying randomness in real networks
Represented as graphs, real networks are intricate combinations of order and disorder.
Fixing some of the structural properties of network models to their values observed in real …
Fixing some of the structural properties of network models to their values observed in real …
Structure of networks that evolve under a combination of growth and contraction
We present analytical results for the emerging structure of networks that evolve via a
combination of growth (by node addition and random attachment) and contraction (by …
combination of growth (by node addition and random attachment) and contraction (by …
Analysis of the convergence of the degree distribution of contracting random networks towards a Poisson distribution using the relative entropy
We present analytical results for the structural evolution of random networks undergoing
contraction processes via generic node deletion scenarios, namely, random deletion …
contraction processes via generic node deletion scenarios, namely, random deletion …
Convergence towards an Erdős-Rényi graph structure in network contraction processes
In a highly influential paper twenty years ago, Barabási and Albert [Science 286, 509 (1999)
SCIEAS 0036-8075 10.1126/science. 286.5439. 509] showed that networks undergoing …
SCIEAS 0036-8075 10.1126/science. 286.5439. 509] showed that networks undergoing …
Random graph ensembles with many short loops
ES Roberts, ACC Coolen - ESAIM: Proceedings and Surveys, 2014 - esaim-proc.org
Networks observed in the real world often have many short loops. This violates the tree-like
assumption that underpins the majority of random graph models and most of the methods …
assumption that underpins the majority of random graph models and most of the methods …
The distribution of first hitting times of random walks on directed Erdős–Rényi networks
We present analytical results for the distribution of first hitting times of random walkers (RWs)
on directed Erdős–Rényi (ER) networks. Starting from a random initial node, a random …
on directed Erdős–Rényi (ER) networks. Starting from a random initial node, a random …
Generating random networks that consist of a single connected component with a given degree distribution
We present a method for the construction of ensembles of random networks that consist of a
single connected component with a given degree distribution. This approach extends the …
single connected component with a given degree distribution. This approach extends the …
Tailored random graph ensembles
ES Roberts, A Annibale… - Journal of Physics …, 2013 - iopscience.iop.org
Tailored graph ensembles are a developing bridge between biological networks and
statistical mechanics. The aim is to use this concept to generate a suite of rigorous tools that …
statistical mechanics. The aim is to use this concept to generate a suite of rigorous tools that …
Entropies of tailored random graph ensembles: bipartite graphs, generalized degrees, and node neighbourhoods
ES Roberts, ACC Coolen - Journal of Physics A: Mathematical …, 2014 - iopscience.iop.org
We calculate explicit formulae for the Shannon entropies of several families of tailored
random graph ensembles for which no such formulae were as yet available, in leading …
random graph ensembles for which no such formulae were as yet available, in leading …