Inverse Complexity Blog

Higher orders need higher standards
hypergraphs
higher-order
hype
mean-field
TL;DR — Contrary to widespread claims in recent years, it’s not true that graphs encode “pairwise” interactions. Graphs encode neighborhoods—sets of nodes incident to other…
Tiago P. Peixoto
Feb 23, 2026

The perplexing “connected cluster axiom”
community detection
heuristics
overfitting
memes
TL;DR — There’s no good reason to always expect communities in networks to be made of strictly connected nodes. On the contrary, doing so leads to conceptual inconsistencies…
Tiago P. Peixoto
Dec 4, 2025

Untangling the hairball using statistical inference
network visualization
inference
hairball
apophenia
ridiculogram
methodological imperialism
TL;DR — Network visualization is often done in the wrong way: first a network layout is produced using a heuristic, and then follow-up analyses are performed and evaluated…
Tiago P. Peixoto
May 20, 2024

Hidden models and latent compression in community detection
community detection
Bayes
compression
MDL
overfitting
free lunch
This is an overdue post on a paper published last year with Alec Kirkley, named “Implicit Models, Latent Compression, Intrinsic Biases, and Cheap Lunches in Community…
Tiago P. Peixoto
Apr 1, 2024

Is Bayesian inference subjective?
community detection
Bayes
compression
MDL
subjectivity
In a previous blog post (covering [1]) I discussed how inferential approaches to community detection are based on the formulation of generative models, via the definition of…
Tiago P. Peixoto
Jan 4, 2022

Significant community structure via statistical tests?
community detection
modularity
overfitting
statistical significance
In a previous blog post I explained how modularity maximization tends to overfit and find spurious community structure even in random graphs.
Tiago P. Peixoto
Dec 13, 2021

Do we need to believe in generative models?
community detection
Bayes
compression
MDL
In two previous blog posts (first and second) I advocated for the use of statistical inference for community detection in networks, whenever our objective is of an…
Tiago P. Peixoto
Dec 8, 2021

No free lunch in community detection?
community detection
free lunch
inference
compression
Bayes
For a wide class of optimization and learning problems there exist so-called “no-free-lunch” (NFL) theorems, which broadly state that when averaged over all possible problem…
Tiago P. Peixoto
Dec 7, 2021

Modularity maximization considered harmful
community detection
modularity
inference
Bayes
SBM
The most widespread method for community detection is modularity maximization  [2], which happens also to be one of the most problematic. This method is based on the…
Tiago P. Peixoto
Dec 6, 2021

Inferring, explaining, and compressing
community detection
description
inference
Bayes
MDL
SBM
Inferential approaches to community detection (see  [2] for a detailed introduction) are designed to provide explanations for network data in a principled manner. They are…
Tiago P. Peixoto
Dec 3, 2021

Descriptive vs. inferential community detection
community detection
description
inference
Bayes
SBM
Community detection is the task of dividing a network — typically one which is large — into many smaller groups of nodes that have a similar contribution to the overall…
Tiago P. Peixoto
Dec 2, 2021

Is network reconstruction impossible?
inference
reconstruction
Bayes
SBM
I have been getting some questions about a 2018 paper  [1] by Jinyuan Chang, Eric D. Kolaczyk, and Qiwei Yao that deals with reconstruction of noisy networks, i.e. networks…
Tiago P. Peixoto
Oct 29, 2021
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