Nonparametric weighted stochastic block models

TP Peixoto - Physical Review E, 2018 - APS
We present a Bayesian formulation of weighted stochastic block models that can be used to
infer the large-scale modular structure of weighted networks, including their hierarchical …

Statistical inference of assortative community structures

L Zhang, TP Peixoto - Physical Review Research, 2020 - APS
We develop a principled methodology to infer assortative communities in networks based on
a nonparametric Bayesian formulation of the planted partition model. We show that this …

Clustering via hypergraph modularity

B Kamiński, V Poulin, P Prałat, P Szufel, F Théberge - PloS one, 2019 - journals.plos.org
Despite the fact that many important problems (including clustering) can be described using
hypergraphs, theoretical foundations as well as practical algorithms using hypergraphs are …

Modularity of the ABCD random graph model with community structure

B Kamiński, B Pankratz, P Prałat… - Journal of Complex …, 2022 - academic.oup.com
Abstract The Artificial Benchmark for Community Detection (ABCD) graph is a random graph
model with community structure and power-law distribution for both degrees and community …

Modularity of Erdős‐Rényi random graphs

C McDiarmid, F Skerman - Random Structures & Algorithms, 2020 - Wiley Online Library
For a given graph G, each partition of the vertices has a modularity score, with higher values
indicating that the partition better captures community structure in G. The modularity q∗(G) of …

Modularity of Complex Networks Models.

LO Prokhorenkova, P Pralat, AM Raigorodskii - WAW, 2016 - Springer
Modularity is designed to measure the strength of division of a network into clusters (known
also as communities). Networks with high modularity have dense connections between the …

Graph fractal dimension and the structure of fractal networks

P Skums, L Bunimovich - Journal of Complex Networks, 2020 - academic.oup.com
Fractals are geometric objects that are self-similar at different scales and whose geometric
dimensions differ from so-called fractal dimensions. Fractals describe complex continuous …

Separating polarization from noise: comparison and normalization of structural polarization measures

A Salloum, THY Chen, M Kivelä - Proceedings of the ACM on human …, 2022 - dl.acm.org
Quantifying the amount of polarization is crucial for understanding and studying political
polarization in political and social systems. Several methods are used commonly to measure …

The modularity of random graphs on the hyperbolic plane

J Chellig, N Fountoulakis… - Journal of Complex …, 2022 - academic.oup.com
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 form …

Modularity in several random graph models

LO Prokhorenkova, P Prałat, A Raigorodskii - Electronic Notes in Discrete …, 2017 - Elsevier
Modularity is a graph characteristic which measures the strength of division of a network into
clusters (or communities). Networks with high modularity usually have distinguishable …