# Path abstraction

## TL;DR

This paper introduces the concept of path abstraction in directed graphs, showing how certain vertex deletions and identifications produce a new digraph with a related set of paths, and explores its theoretical properties and connections.

## Contribution

It formalizes the construction of path abstractions, providing detailed methods, fundamental results, and discussing potential generalizations and links to random digraphs.

## Key findings

- Path abstractions preserve path structures under specific vertex operations
- Basic properties and results of path abstractions are established
- Connections with random digraphs are illustrated

## Abstract

Given the set of paths through a digraph, the result of uniformly deleting some vertices and identifying others along each path is coherent in such a way as to yield the set of paths through another digraph, called a \emph{path abstraction} of the original digraph. The construction of path abstractions is detailed and relevant basic results are established; generalizations are also discussed. Connections with random digraphs are also illustrated.