Algebraic geometric software to investigate polynomials with graph theoretical origin?

Question

My teacher uses Singular and Macaulay2 for specific problems in Algebraic geometry but she was unaware which software would be best suited to investigate polynomial basis problems where their origin are graph theoretical: need to construct parallel graphs, series graphs, their different combinations, ready commands for specific graphs and commands for graph properties such as eccentricity and other distances. The idea is to generate different structure functions from the graphs and then analyse them with the softwares.

Which software(s) would you recommend to do algebraic geometric research on polynomials originating from grahs?

Answer 1

Recommendations for Commutative Algebra Software?

• CoCoa
• Singular
• Macaulay2

where the example usage about CoCoa is GR basis like How to analyse a sparse adjacency matrix.

Graphs visualised with examples

• Atlas visualisation like here with NetworkX for different polynomials

• Random geometric graph with NetworkX

• giant component here

• ego graph (neighbourhood graph) where one vertex as the center

• concept maps with CmapTools to visualise different aspects about the polynomials here or graphs

and more examples

• NetworkX here
• Sage examples.

Different matrix presentations for the graphs

• incidence matrix (vertex to edge)

• adjacency matrix (vertex to vertex)

• integer matrix

• Kircchoff matrix D-A (i.e. diagonal matrix minus adjacency matrix)

General questions for analysing graphs

Most popluar threads

• Online tool for making graphs (vertices and edges)?

• Graph theory software?

and less known

• Software for drawing and analyzing a graph?

• Software to find out adjacency matrix of a graph.