# Motif Conservation Laws for the Configuration Model

arXiv: https://arxiv.org/abs/1408.6303 · HTML: https://mlsanity.com/paper/1408.6303/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Aug 2014.

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

- [Studying and Improving Graph Neural Network-based Motif Estimation](https://mlsanity.com/paper/2506.15709/) (2025)

## Abstract (arXiv)

The observation that some subgraphs, called motifs, appear more often in real networks than in their randomized counterparts has attracted much attention in the scientific community. In the prevalent approach the detection of motifs is based on comparing subgraph counts in a network with their counterparts in the configuration model with the same degree distribution as the network. In this short note we derive conservation laws that relate motif counts in the configuration model.