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Graph theory -- using Metanet/Scilab

(Learn Metanet/Scilab using graph theory)

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Credibility      Competence      Commitment	About the author What is graph theory ? What is Metanet ? What is Scilab ? (short intro -- pdf file -- 14 pages) What is Scilab ? (full manual -- pdf file -- 700 pages) Teach yourself graph theory, with Scilab and Metalab	Misc. Social contribution Contact Administrivia
An important social message Why is Linux good for me ? Teach yourself graph theory Teach yourself graph theory. Experiment with and explore graph theory, using Metanet. The Metanet toolbox for graph theory, is included with Scilab. Scilab itself is included with this CDROM, along with a whole lot of documentation. You also get some good e-books on graph theory, in this CDROM. This CDROM is organised as a series of exercises on Graph theory. For each exercise, you will get : The problem statement The Metanet/Scilab code for solving the problem The solution Annotations and commentaries The exercises are also grouped together in convenient groups, according to their focus. You can reach each exercise, by just clicking on the title of the exercise.

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Teach yourself graph theory

Teach yourself Metanet/Scilab

A -- Graph operations

1. Create a undirected graph G , with v vertices and e edges
2. Create a directed graph G , with v vertices and e edges
3. Add a vertex x, to G. Add edges to x
4. Add an edge to G between two given vertices x and y
5. Remove a vertex of G. Detect and remove all edges incident on that vertex
6. Remove an edge from G

B -- Graph properties

1. Is G connected ? How many components does G have ?
2. Are there any isolated nodes in G ? What are they ?
3. Compute the incidence matrix of G
4. Compute the adjacency matrix of G
5. Is G a planar graph ?
6. Is G a complete graph ?
7. Is G a regular graph ?

C -- Trees

1. Compute all the spanning trees of G -- use a depth-first-search
2. Compute all the spanning trees of G -- use a breadth-first-search
3. Is G a tree ?

D -- Paths

1. Is G an Euler graph ?
2. Compute all Euler paths in G
3. Compute all Euler circuits in G
4. Compute all hamiltonian paths in G
5. Compute all Hamiltonian circuits in G
6. Given vertices x and y of G. Is there a pateh from x to y ?
7. How many paths are there from x to y ?
8. Compute all paths from x to y
9. Compute the length of each path
10. Model the Koeningsburg Bridges (KBP) problem, and answer the above questions about Koenigsburg bridges
11. Would deleting any bridges, solve teh KBP ? Which ones ?
12. Would adding any bridges, solve the KBP ? Where should they be added (between which landmassess) ?