ID: 1608.06135

Resolution of ranking hierarchies in directed networks

August 22, 2016

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Random Irregular Block-hierarchical Networks: Algorithms for Computation of Main Properties

October 14, 2015

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Svetlana Avetisyan, Mikayel Samvelyan, Martun Karapetyan
Data Structures and Algorith...

In this paper, the class of random irregular block-hierarchical networks is defined and algorithms for generation and calculation of network properties are described. The algorithms presented for this class of networks are more efficient than known algorithms both in computation time and memory usage and can be used to analyze topological properties of such networks. The algorithms are implemented in the system created by the authors for the study of topological and statistic...

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Random walk hierarchy measure: What is more hierarchical, a chain, a tree or a star?

August 31, 2015

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Dániel Czégel, Gergely Palla
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Signs of hierarchy are prevalent in a wide range of systems in nature and society. One of the key problems is quantifying the importance of hierarchical organisation in the structure of the network representing the interactions or connections between the fundamental units of the studied system. Although a number of notable methods are already available, their vast majority is treating all directed acyclic graphs as already maximally hierarchical. Here we propose a hierarchy m...

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Hierarchical Block Structures and High-resolution Model Selection in Large Networks

October 16, 2013

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Tiago P. Peixoto
physics.data-an
cond-mat.dis-nn
cond-mat.stat-mech
cs.SI
physics.soc-ph
stat.ML

Discovering and characterizing the large-scale topological features in empirical networks are crucial steps in understanding how complex systems function. However, most existing methods used to obtain the modular structure of networks suffer from serious problems, such as being oblivious to the statistical evidence supporting the discovered patterns, which results in the inability to separate actual structure from noise. In addition to this, one also observes a resolution lim...

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Hierarchical Models for Independence Structures of Networks

May 15, 2016

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Kayvan Sadeghi, Alessandro Rinaldo
Methodology
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We introduce a new family of network models, called hierarchical network models, that allow us to represent in an explicit manner the stochastic dependence among the dyads (random ties) of the network. In particular, each member of this family can be associated with a graphical model defining conditional independence clauses among the dyads of the network, called the dependency graph. Every network model with dyadic independence assumption can be generalized to construct memb...

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Community Detection and Classification in Hierarchical Stochastic Blockmodels

March 7, 2015

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Vince Lyzinski, Minh Tang, Avanti Athreya, ... , Priebe Carey E.
Machine Learning
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We propose a robust, scalable, integrated methodology for community detection and community comparison in graphs. In our procedure, we first embed a graph into an appropriate Euclidean space to obtain a low-dimensional representation, and then cluster the vertices into communities. We next employ nonparametric graph inference techniques to identify structural similarity among these communities. These two steps are then applied recursively on the communities, allowing us to de...

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Model-based clustering of multiple networks with a hierarchical algorithm

November 4, 2022

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Tabea LPSM Rebafka
Statistics Theory
Statistics Theory

The paper tackles the problem of clustering multiple networks, directed or not, that do not share the same set of vertices, into groups of networks with similar topology. A statistical model-based approach based on a finite mixture of stochastic block models is proposed. A clustering is obtained by maximizing the integrated classification likelihood criterion. This is done by a hierarchical agglomerative algorithm, that starts from singleton clusters and successively merges c...

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Geometric detection of hierarchical backbones in real networks

June 5, 2020

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Elisenda Ortiz, Guillermo García-Pérez, M. Ángeles Serrano
Physics and Society
Social and Information Netwo...

Hierarchies permeate the structure of real networks, whose nodes can be ranked according to different features. However, networks are far from tree-like structures and the detection of hierarchical ordering remains a challenge, hindered by the small-world property and the presence of a large number of cycles, in particular clustering. Here, we use geometric representations of undirected networks to achieve an enriched interpretation of hierarchy that integrates features defin...

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The Hierarchy of Block Models

February 7, 2020

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Majid Noroozi, Marianna Pensky
Machine Learning
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There exist various types of network block models such as the Stochastic Block Model (SBM), the Degree Corrected Block Model (DCBM), and the Popularity Adjusted Block Model (PABM). While this leads to a variety of choices, the block models do not have a nested structure. In addition, there is a substantial jump in the number of parameters from the DCBM to the PABM. The objective of this paper is formulation of a hierarchy of block model which does not rely on arbitrary identi...

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The Highest Dimensional Stochastic Blockmodel with a Regularized Estimator

June 11, 2012

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Karl Rohe, Tai Qin, Haoyang Fan
Statistics Theory
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In the high dimensional Stochastic Blockmodel for a random network, the number of clusters (or blocks) K grows with the number of nodes N. Two previous studies have examined the statistical estimation performance of spectral clustering and the maximum likelihood estimator under the high dimensional model; neither of these results allow K to grow faster than N^{1/2}. We study a model where, ignoring log terms, K can grow proportionally to N. Since the number of clusters must b...

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Hierarchical structure and the prediction of missing links in networks

November 4, 2008

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Aaron Clauset, Cristopher Moore, M. E. J. Newman
Machine Learning
Physics and Society
Molecular Networks

Networks have in recent years emerged as an invaluable tool for describing and quantifying complex systems in many branches of science. Recent studies suggest that networks often exhibit hierarchical organization, where vertices divide into groups that further subdivide into groups of groups, and so forth over multiple scales. In many cases these groups are found to correspond to known functional units, such as ecological niches in food webs, modules in biochemical networks (...

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