ariel-flint-ashery / causal-dags

Investigation of network geometry and percolation in directed acyclic graphs (MSci Thesis). Maintained by Ariel Flint Ashery and Kevin Teo. Supervisor: Timothy Evans

Causal-DAGs

Investigation of topological phase transitions in Directed Acyclic Graphs (MSci Thesis). Maintained by Ariel Flint Ashery and Kevin Teo. Supervisor: Timothy Evans.

This repository contains code for a project investigating causal structure and network geometry of Directed Acyclic Graphs. This work contributes towards the final year project theses of Ariel Flint Ashery and Kevin Teo as part of their MSci in Physics at Imperial College London, and is supervised by Tim Evans.

We investigate two types of topological phase transition in DAGs:

1. Evolution of a random geometric (DAG) network in Lp space. We show there is a critical expected average degree (or equivalently, a critical radius) for which any geometric DAG in Lp space is connected from source to sink nodes.
2. Pseudo-geodesic path phase transition. We show that p=1 is a critical point, at which the network approximation of the geodesic between two points in the geometry swaps between the longest and shortest path in the network, for both network and geometric length.

Link to the Google drive https://drive.google.com/drive/folders/1UI8xaAQ8xHoKJCY27nZSfuTtwNtkoVvS?usp=sharing