# Structural Inference of Hierarchies in Networks

@inproceedings{Clauset2006StructuralIO, title={Structural Inference of Hierarchies in Networks}, author={Aaron Clauset and Cristopher Moore and Mark E. J. Newman}, booktitle={SNA@ICML}, year={2006} }

One property of networks that has received comparatively little attention is hierarchy, i.e., the property of having vertices that cluster together in groups, which then join to form groups of groups, and so forth, up through all levels of organization in the network. Here, we give a precise definition of hierarchical structure, give a generic model for generating arbitrary hierarchical structure in a random graph, and describe a statistically principled way to learn the set of hierarchical…

## 134 Citations

Detecting hierarchical structure in networks

- Computer Science2012 3rd International Workshop on Cognitive Information Processing (CIP)
- 2012

This work proposes a generative Bayesian model that is able to infer whether hierarchies are present or not from a hypothesis space encompassing all types of hierarchical tree structures, and proposes a collapsed Gibbs sampling procedure that jointly infers a partition and its hierarchical structure.

Detectability of ranking hierarchies in directed networks

- Mathematics, Computer ScienceArXiv
- 2016

It is found that agony may fail to identify hierarchies when the structure is not strong enough and the size of the classes is small with respect to the whole network.

Community Structure in Large Networks: Natural Cluster Sizes and the Absence of Large Well-Defined Clusters

- Computer Science, MathematicsInternet Math.
- 2009

This paper employs approximation algorithms for the graph-partitioning problem to characterize as a function of size the statistical and structural properties of partitions of graphs that could plausibly be interpreted as communities, and defines the network community profile plot, which characterizes the "best" possible community—according to the conductance measure—over a wide range of size scales.

Resolution of ranking hierarchies in directed networks

- Computer Science, PhysicsPloS one
- 2018

It is found that agony may fail to identify hierarchies when the structure is not strong enough and the size of the classes is small with respect to the whole network.

Mixture models and exploratory analysis in networks

- Computer Science, PhysicsProceedings of the National Academy of Sciences
- 2007

A general technique for detecting structural features in large-scale network data that works by dividing the nodes of a network into classes such that the members of each class have similar patterns of connection to other nodes is described.

Finding Statistically Significant Communities in Networks

- Physics, MedicinePloS one
- 2011

OSLOM (Order Statistics Local Optimization Method), the first method capable to detect clusters in networks accounting for edge directions, edge weights, overlapping communities, hierarchies and community dynamics, is presented.

Detecting the overlapping and hierarchical community structure in complex networks

- Physics, Mathematics
- 2009

Many networks in nature, society and technology are characterized by a mesoscopic level of organization, with groups of nodes forming tightly connected units, called communities or modules, that are…

Hierarchical Random Graphs for Networks with Weighted Edges and Multiple Edge Attributes

- 2011

Network analysis has proven a useful tool for analyzing properties of complex systems. Many real-world systems exhibit hierarchical structure and analysis tools should leverage that knowledge in…

Hierarchical block structures and high-resolution model selection in large networks

- Computer Science, PhysicsArXiv
- 2013

A nested generative model is constructed that, through a complete description of the entire network hierarchy at multiple scales, enables the detection of modular structure at levels far beyond those possible with current approaches, and is based on the principle of parsimony.

Statistical properties of community structure in large social and information networks

- Computer ScienceWWW
- 2008

It is found that a generative model, in which new edges are added via an iterative "forest fire" burning process, is able to produce graphs exhibiting a network community structure similar to that observed in nearly every network dataset examined.

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