Entropy distribution and condensation in random networks with a given degree distribution
The entropy of network ensembles characterizes the amount of information encoded in the
network structure and can be used to quantify network complexity and the relevance of given …
network structure and can be used to quantify network complexity and the relevance of given …
Variational principle for scale-free network motifs
For scale-free networks with degrees following a power law with an exponent τ∈(2, 3), the
structures of motifs (small subgraphs) are not yet well understood. We introduce a method …
structures of motifs (small subgraphs) are not yet well understood. We introduce a method …
Statistical mechanics of random geometric graphs: Geometry-induced first-order phase transition
M Ostilli, G Bianconi - Physical Review E, 2015 - APS
Random geometric graphs (RGGs) can be formalized as hidden-variables models where the
hidden variables are the coordinates of the nodes. Here we develop a general approach to …
hidden variables are the coordinates of the nodes. Here we develop a general approach to …
Scale-free network clustering in hyperbolic and other random graphs
C Stegehuis, R van Der Hofstad… - Journal of Physics A …, 2019 - iopscience.iop.org
Random graphs with power-law degrees can model scale-free networks as sparse
topologies with strong degree heterogeneity. Mathematical analysis of such random graphs …
topologies with strong degree heterogeneity. Mathematical analysis of such random graphs …
Parameter estimators of sparse random intersection graphs with thinned communities
J Karjalainen, JSH van Leeuwaarden… - Algorithms and Models for …, 2018 - Springer
This paper studies a statistical network model generated by a large number of randomly
sized overlapping communities, where any pair of nodes sharing a community is linked with …
sized overlapping communities, where any pair of nodes sharing a community is linked with …
Optimal subgraph structures in scale-free configuration models
R Van der Hofstad, JSH Van Leeuwaarden… - 2021 - projecteuclid.org
Subgraphs reveal information about the geometry and functionalities of complex networks.
For scale-free networks with unbounded degree fluctuations, we obtain the asymptotics of …
For scale-free networks with unbounded degree fluctuations, we obtain the asymptotics of …
Degree correlations in scale-free random graph models
C Stegehuis - Journal of Applied Probability, 2019 - cambridge.org
We study the average nearest-neighbour degree a (k) of vertices with degree k. In many real-
world networks with power-law degree distribution, a (k) falls off with k, a property ascribed …
world networks with power-law degree distribution, a (k) falls off with k, a property ascribed …
When is a scale-free graph ultra-small?
R van der Hofstad, J Komjáthy - Journal of Statistical Physics, 2017 - Springer
In this paper we study typical distances in the configuration model, when the degrees have
asymptotically infinite variance. We assume that the empirical degree distribution follows a …
asymptotically infinite variance. We assume that the empirical degree distribution follows a …
Switch chain mixing times and triangle counts in simple random graphs with given degrees
T Bannink, R van der Hofstad… - Journal of Complex …, 2019 - academic.oup.com
Sampling uniform simple graphs with power-law degree distributions with degree exponent
is a non-trivial problem. Firstly, we propose a method to sample uniform simple graphs that …
is a non-trivial problem. Firstly, we propose a method to sample uniform simple graphs that …
Characterizing the intrinsic correlations of scale-free networks
JB De Brito, CIN Sampaio Filho, AA Moreira… - … Journal of Modern …, 2016 - World Scientific
When studying topological or dynamical properties of random scale-free networks, it is tacitly
assumed that degree–degree correlations are not present. However, simple constraints …
assumed that degree–degree correlations are not present. However, simple constraints …