Graph Algebras and Derived Graph Operations

Round 1

Reviewer 1 Report

The research reported in this paper stems from pioneering work conducted in the '90s on generalized sketches. It is a natural, substantial, and welcome development of some of the authors' previous results presented in [1,2]. There are two major contributions here: First, a reframing of basic definitions, constructions, and properties from universal algebra in a category-theoretic setting, which then paves the way to generalizations of those concepts and results from traditional set-based algebras to graph algebras. Second, a detailed presentation of derived graph operations; these supersede graph terms to accommodate complex graph outputs instead of lone vertices or edges; in addition, they are conceptually independent of typical term algebras, so they can also be used in much more general category-theoretic settings where terms aren't available.

All in all, I think this is an interesting and carefully written paper. I did find it a bit overly verbose at times, and I would have appreciated a more concise presentation that gets to graph operations more swiftly; but I understand other readers may prefer the current style, so this observation does not affect my recommendation at all. Unfortunately, I couldn't devote as much time to examining the paper as I would have liked; nonetheless, based on what I have seen thus far, I can confidently support its acceptance: compared to previous approaches, relying for example on monoidal categories, the ideas presented here are fresh and with great potential for development.

Author Response

Many thanks for the encouraging review. We have to confess that the paper is indeed "a bit overly verbose" since we probably exaggerated in presenting the process of finding an appropriate approach to Derived Graph Operations. Another reason is that we intended to reach out to diverse communities like Universal Algebra, Algebraic Specifications, Graph Transformations, Category Theory, Type Theory and Monoidal Categories, for example. 

Reviewer 2 Report

Although the article is very long, it is an important study in terms of the benefits it provides.

They adapted existing graph structures in their own areas. 

They worked on graph algebras using graph operations.

Work is successful in itself but It's too long for just one article (57 pages).

Author Response

Many thanks for the positive review. We have to confess that the paper is indeed a bit too long since we probably exaggerated in presenting the process of finding an appropriate approach to Derived Graph Operations. Another reason is that we intended to reach out to diverse communities like Universal Algebra, Algebraic Specifications, Graph Transformations, Category Theory, Type Theory and Monoidal Categories, for example.