Sparse Networks with Core-Periphery Structure

  title={Sparse Networks with Core-Periphery Structure},
  author={Cian Naik and Franccois Caron and Judith Rousseau},
We propose a statistical model for graphs with a core-periphery structure. To do this we define a precise notion of what it means for a graph to have this structure, based on the sparsity properties of the subgraphs of core and periphery nodes. We present a class of sparse graphs with such properties, and provide methods to simulate from this class, and to perform posterior inference. We demonstrate that our model can detect core-periphery structure in simulated and real-world networks. 

Core-periphery structure in networks: a statistical exposition

The current research landscape is presented by reviewing the most popular metrics and models that have been used for quantitative studies on core-periphery structure, and various inferential problems in this context are explored, such as estimation, hypothesis testing, and Bayesian inference.

Variability in higher order structure of noise added to weighted networks

The results demonstrate that noise does not present as a monolithic nuisance, but rather as a nuanced, topology-dependent, and even useful entity in characterizing higher-order network interactions.



Identification of core-periphery structure in networks

The method is found to be efficient, scaling easily to networks with a million or more nodes, and it is demonstrated that the method is immune to the detectability transition observed in the related community detection problem, which prevents the detection of community structure when that structure is too weak.

Core-periphery organization of complex networks.

  • P. Holme
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2005
This study proposes a coefficient to measure if the network has such a clear-cut core-periphery dichotomy and measures this coefficient for a number of real-world and model networks and finds that different classes of networks have their characteristic values.

Core-Periphery Structure in Networks (Revisited)

This paper develops a new method to investigate the meso-scale feature known as core-periphery structure, which entails identifying densely connected core nodes and sparsely connected peripheral nodes in a network.

Models of core/periphery structures

Exchangeable random measures for sparse and modular graphs with overlapping communities

  • A. TodeschiniF. Caron
  • Computer Science
    Journal of the Royal Statistical Society: Series B (Statistical Methodology)
  • 2020
It is shown that the approach proposed can recover interpretable structure of real world networks and can handle graphs with thousands of nodes and tens of thousands of edges.

Detection of core–periphery structure in networks using spectral methods and geodesic paths

Several novel and computationally efficient methods for detecting “core–periphery structure” in networks, which aggregates information from many geodesic paths in a network and yields a score for each vertex that reflects the likelihood that that vertex is a core vertex.

Random Clique Covers for Graphs with Local Density and Global Sparsity

A Bayesian nonparametric graph model based on random edge clique covers is developed, and it is shown that this model can capture power law degree distribution, global sparsity and non-vanishing local clustering coefficient.

Finding multiple core-periphery pairs in networks

This work proposes a scalable algorithm to detect multiple nonoverlapping groups of core-periphery structure in a network and illustrates the algorithm using synthesized and empirical networks.

Detecting Core-Periphery Structures by Surprise

A novel method to detect statistically significant bimodular structures, i.e., either bipartite or core-periphery ones, based on a modification of the surprise, recently proposed for detecting communities is proposed.

Profiling core-periphery network structure by random walkers

It is shown that the core-periphery structure can effectively be profiled by elaborating the behaviour of a random walker, providing a global topological portrait.