Passages in Graphs

TL;DR

This paper explores the properties of passages in directed graphs, showing their closure under set operations and their composition from minimal passages, aiding graph decomposition tasks.

Contribution

It introduces key properties of passages, including closure under set operations and their composition from minimal passages, facilitating graph analysis and decomposition.

Findings

Passages are closed under union, intersection, and difference.

Any passage can be decomposed into minimal passages.

Properties enable improved graph decomposition methods.

Abstract

Directed graphs can be partitioned in so-called passages. A passage P is a set of edges such that any two edges sharing the same initial vertex or sharing the same terminal vertex are both inside $P$ or are both outside of P. Passages were first identified in the context of process mining where they are used to successfully decompose process discovery and conformance checking problems. In this article, we examine the properties of passages. We will show that passages are closed under set operators such as union, intersection and difference. Moreover, any passage is composed of so-called minimal passages. These properties can be exploited when decomposing graph-based analysis and computation problems.