# Statistical inference for network samples using subgraph counts

@article{Maugis2017StatisticalIF, title={Statistical inference for network samples using subgraph counts}, author={Pierre-Andr{\'e} G. Maugis and Carey E. Priebe and Sofia C. Olhede and Patrick J. Wolfe}, journal={ArXiv}, year={2017}, volume={abs/1701.00505} }

We consider that a network is an observation, and a collection of observed networks forms a sample. In this setting, we provide methods to test whether all observations in a network sample are draw...

## 15 Citations

Testing for Global Network Structure Using Small Subgraph Statistics

- Computer ScienceArXiv
- 2017

This work proposes a simple test for the existence of communities based only on the frequencies of three-node subgraphs, and demonstrates how the method can be effective for detecting structure in social networks, citation networks for scientific articles, and correlations of stock returns between companies on the S\&P 500.

Nonparametric regression for multiple heterogeneous networks

- Computer Science, Mathematics
- 2020

A multi- graphon model is proposed which allows node-level as well as network-level heterogeneity, and it is shown how information from multiple networks can be leveraged to enable estimation of the multi-graphon via standard nonparametric regression techniques, e.g. kernel regression, orthogonal series estimation.

Bootstrapping Networks with Latent Space Structure

- Computer Science
- 2019

The first method generates bootstrap replicates of network statistics that can be represented as U-statistics in the latent positions, and avoids actually constructing new bootstrapped networks.

Central limit theorems for local network statistics

- MathematicsArXiv
- 2020

This work derives the asymptotic joint distribution of rooted subgraph counts in inhomogeneous random graphs, a model which generalizes many popular statistical network models and enables a shift in the statistical analysis of large graphs, from estimating network summaries, to estimating models linking local network structure and vertex-specific covariates.

Identifying networks with common organizational principles

- Computer ScienceJ. Complex Networks
- 2018

This paper introduces a new network comparison methodology that is aimed at identifying common organizational principles in networks that is simple, intuitive and applicable in a wide variety of settings ranging from the functional classification of proteins to tracking the evolution of a world trade network.

Subgraphs in preferential attachment models

- MathematicsAdvances in Applied Probability
- 2019

Abstract We consider subgraph counts in general preferential attachment models with power-law degree exponent $\tau > 2$ . For all subgraphs H, we find the scaling of the expected number of subgraphs…

Testing Network Structure Using Relations Between Small Subgraph Probabilities

- MathematicsArXiv
- 2017

The results show how global structural characteristics of networks can be inferred from local subgraph frequencies, without requiring the global community structure to be explicitly estimated.

Degree‐based goodness‐of‐fit tests for heterogeneous random graph models: Independent and exchangeable cases

- Mathematics, Computer ScienceScandinavian Journal of Statistics
- 2019

This paper introduces goodness‐of‐fit tests for two classes of models such as the heterogeneous Erdös‐Rényi model and a generic model for exchangeable random graphs called the W‐graph and proves the asymptotic normality under specific sparsity regimes.

Preferential attachment models for dynamic networks

- Materials Science
- 2019

• A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of…

Optimal adaptivity of signed-polygon statistics for network testing

- Computer ScienceThe Annals of Statistics
- 2021

This work proposes the Signed Polygon as a class of new tests and shows that both the SgnT and SgnQ tests satisfy (a)-(d), and especially, they work well for both very sparse and less sparse networks.

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