# Motifs for processes on networks

arXiv: https://arxiv.org/abs/2007.07447 · HTML: https://mlsanity.com/paper/2007.07447/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jul 2020.

## Built on by (most cited first, 6 of 6)

- [Capturing Graphs with Hypo-Elliptic Diffusions](https://mlsanity.com/paper/2205.14092/) (2022)
- [Generative Graph Pattern Machine](https://mlsanity.com/paper/2505.16130/) (2025)
- [Demystifying Higher-Order Graph Neural Networks](https://mlsanity.com/paper/2406.12841/) (2024)
- [Learning low-rank latent mesoscale structures in networks](https://mlsanity.com/paper/2102.06984/) (2021)
- [odeN: Simultaneous Approximation of Multiple Motif Counts in Large Temporal Networks](https://mlsanity.com/paper/2108.08734/) (2021)
- [Network inference via process motifs for lagged correlation in linear stochastic processes](https://mlsanity.com/paper/2208.08871/) (2022)

## Abstract (arXiv)

The study of motifs in networks can help researchers uncover links between the structure and function of networks in biology, sociology, economics, and many other areas. Empirical studies of networks have identified feedback loops, feedforward loops, and several other small structures as "motifs" that occur frequently in real-world networks and may contribute by various mechanisms to important functions in these systems. However, these mechanisms are unknown for many of these motifs. We propose to distinguish between "structure motifs" (i.e., graphlets) in networks and "process motifs" (which we define as structured sets of walks) on networks and consider process motifs as building blocks of processes on networks. Using the steady-state covariances and steady-state correlations in a multivariate Ornstein--Uhlenbeck process on a network as examples, we demonstrate that the distinction between structure motifs and process motifs makes it possible to gain quantitative insights into mechanisms that contribute to important functions of dynamical systems on networks.