# Micro, Meso, Macro: the effect of triangles on communities in networks

## TL;DR

This paper demonstrates that micro-structures like triangles can induce community detection in networks, even when using algorithms designed to avoid such structures, highlighting their fundamental role in network organization.

## Contribution

It reveals that triangles alone can cause community-like structures to appear, challenging assumptions about community detection and the role of micro-structures in networks.

## Key findings

- Triangles induce communities in random networks.
- Community detection methods are affected by micro-structures.
- Micro-level motifs can spontaneously generate communities.

## Abstract

Meso-scale structures (communities) are used to understand the macro-scale properties of complex networks, such as their functionality and formation mechanisms. Micro-scale structures are known to exist in most complex networks (e.g., large number of triangles or motifs), but they are absent in the simple random-graph models considered (e.g., as null models) in community-detection algorithms. In this paper we investigate the effect of micro-structures on the appearance of communities in networks. We find that alone the presence of triangles leads to the appearance of communities even in methods designed to avoid the detection of communities in random networks. This shows that communities can emerge spontaneously from simple processes of motiff generation happening at a micro-level. Our results are based on four widely used community-detection approaches (stochastic block model, spectral method, modularity maximization, and the Infomap algorithm) and three different generative network models (triadic closure, generalized configuration model, and random graphs with triangles).