Simplification for Graph-like Objects

TL;DR

This paper explores the categorical framework for simplifying complex graph-like structures into simpler forms, introducing a dual concept called antisimplification that involves removing isolated elements.

Contribution

It generalizes graph simplification within a categorical context and introduces the dual notion of antisimplification, expanding theoretical understanding.

Findings

Categorical abstraction of graph simplification

Introduction of antisimplification as a dual process

General conditions for simplification in comma categories

Abstract

The simplification of a multigraph into a simple graph can be abstracted to a more general comma category under some common conditions. When using the identity functor, the category of simple objects in a comma category generalizes the functor-structured category. Seated in categorical terms, simplification can be dualized to "antisimplification", which manifests as removal of isolated vertices and loose edges.