# Systematic assessment of the quality of fit of the stochastic block model for empirical networks

arXiv: https://arxiv.org/abs/2201.01658 · HTML: https://mlsanity.com/paper/2201.01658/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 175 references that are in the map.
- First posted on arXiv 5 Jan 2022.

## Builds on (most cited first, 30 of 31)

- [Cooperative Game Theory Approaches for Network Partitioning](https://mlsanity.com/paper/1707.03587/) (2017)
- [Contact patterns in a high school: a comparison between data collected using wearable sensors, contact diaries and friendship surveys](https://mlsanity.com/paper/1506.03645/) (2015)
- [Hierarchical Block Structures and High-resolution Model Selection in Large Networks](https://mlsanity.com/paper/1310.4377/) (2013)
- [Stacking Models for Nearly Optimal Link Prediction in Complex Networks](https://mlsanity.com/paper/1909.07578/) (2019)
- [Layer aggregation and reducibility of multilayer interconnected networks](https://mlsanity.com/paper/1405.0425/) (2014)
- [Efficient Monte Carlo and greedy heuristic for the inference of stochastic block models](https://mlsanity.com/paper/1310.4378/) (2013)
- [Bayesian stochastic blockmodeling](https://mlsanity.com/paper/1705.10225/) (2017)
- [The Anatomy of a Scientific Rumor](https://mlsanity.com/paper/1301.2952/) (2013)
- [Nonparametric Bayesian inference of the microcanonical stochastic block model](https://mlsanity.com/paper/1610.02703/) (2016)
- [Network histograms and universality of blockmodel approximation](https://mlsanity.com/paper/1312.5306/) (2013)
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- [Data on face-to-face contacts in an office building suggests a low-cost vaccination strategy based on community linkers](https://mlsanity.com/paper/1409.7017/) (2014)
- [Evaluating Overfit and Underfit in Models of Network Community Structure](https://mlsanity.com/paper/1802.10582/) (2018)
- [Configuring Random Graph Models with Fixed Degree Sequences](https://mlsanity.com/paper/1608.00607/) (2016)
- [Random Walks on Multiplex Networks](https://mlsanity.com/paper/1306.0519/) (2013)
- [Clustering Network Layers With the Strata Multilayer Stochastic Block Model](https://mlsanity.com/paper/1507.01826/) (2015)
- [Merge-split Markov chain Monte Carlo for community detection](https://mlsanity.com/paper/2003.07070/) (2020)
- [Combinatorial Analysis of Multiple Networks](https://mlsanity.com/paper/1303.4986/) (2013)
- [Detectability thresholds and optimal algorithms for community structure in dynamic networks](https://mlsanity.com/paper/1506.06179/) (2015)
- [Corruption Risk in Contracting Markets: A Network Science Perspective](https://mlsanity.com/paper/1909.08664/) (2019)
- [Disentangling homophily, community structure and triadic closure in networks](https://mlsanity.com/paper/2101.02510/) (2021)
- [Cover time for random walks on arbitrary complex networks](https://mlsanity.com/paper/1706.02356/) (2017)
- [Latent Poisson models for networks with heterogeneous density](https://mlsanity.com/paper/2002.07803/) (2020)
- [MIGRAINE: MRI Graph Reliability Analysis and Inference for Connectomics](https://mlsanity.com/paper/1312.4875/) (2013)
- [Organization Mining Using Online Social Networks](https://mlsanity.com/paper/1303.3741/) (2013)
- [Percolation on sparse networks](https://mlsanity.com/paper/1405.0483/) (2014)
- [Analysing Scientific Collaborations of New Zealand Institutions using Scopus Bibliometric Data](https://mlsanity.com/paper/1709.02897/) (2017)
- [City-wide Analysis of Electronic Health Records Reveals Gender and Age Biases in the Administration of Known Drug-Drug Interactions](https://mlsanity.com/paper/1803.03571/) (2018)
- [Data Mining of Online Genealogy Datasets for Revealing Lifespan Patterns in Human Population](https://mlsanity.com/paper/1311.4276/) (2013)
- [The Budapest Reference Connectome Server v2.0](https://mlsanity.com/paper/1412.3151/) (2014)

## Built on by (most cited first, 1 of 1)

- [Clustered Graph Matching for Label Recovery and Graph Classification](https://mlsanity.com/paper/2205.03486/) (2022)

## Abstract (arXiv)

We perform a systematic analysis of the quality of fit of the stochastic block model (SBM) for 275 empirical networks spanning a wide range of domains and orders of size magnitude. We employ posterior predictive model checking as a criterion to assess the quality of fit, which involves comparing networks generated by the inferred model with the empirical network, according to a set of network descriptors. We observe that the SBM is capable of providing an accurate description for the majority of networks considered, but falls short of saturating all modeling requirements. In particular, networks possessing a large diameter and slow-mixing random walks tend to be badly described by the SBM. However, contrary to what is often assumed, networks with a high abundance of triangles can be well described by the SBM in many cases. We demonstrate that simple network descriptors can be used to evaluate whether or not the SBM can provide a sufficiently accurate representation, potentially pointing to possible model extensions that can systematically improve the expressiveness of this class of models.