# Causal motifs and existence of endogenous cascades in directed networks with application to company defaults

arXiv: https://arxiv.org/abs/2011.08148 · HTML: https://mlsanity.com/paper/2011.08148/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Nov 2020.

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

- [LimiX-2: A Contextual Mechanism Network Towards General Structured-Data Intelligence](https://mlsanity.com/paper/2609.17488/) (2026)

## Abstract (arXiv)

Motivated by the detection of cascades of defaults in economy, we developed a detection framework for an endogenous spreading based on causal motifs we define in this paper. We assume that the change of state of a vertex can be triggered by an endogenous or an exogenous event, that the underlying network is directed and that times when vertices changed their states are available. In addition to the data of company defaults, we also simulate cascades driven by different stochastic processes on different synthetic networks. We show that some of the smallest motifs can robustly detect endogenous spreading events. Finally, we apply the method to the data of defaults of Croatian companies and observe the time window in which an endogenous cascade was likely happening.