Undirected weighted graph matching in matlab

Iam having two matrix as shown below.In my project iam using graph matching technique.Below are my 3 questions:

 4     2     3     1     4
 2     2     3     1     4
 2     3     3     1     4
 1     2     3     1     4
 4     2     3     1     5

 4     1     4     2     3
 1     1     2     3     4
 4     1     5     2     3
 2     1     3     2     4
 3     1     4     2     3

1.How these 2 matrices can be made as 2 graphs.i.e how it can be represented as G(V,E,W) where V is Vetex set,E is edge set and W is weight of edges.Is matrix itself is a graph or what?

2.After that how 2 graphs should be matched.(i.e Is there any function in matlab to match 2 graphs)

3.There are 2 graph matching algorithm spectral graph matching and Error Correcting Graph Matching algorithm which one is best.

Answer 1

[Basheer Alwaely]

Hi Prashanth,

1- To generate any gragh, you need vertices, which means you need positions of these nodes to draw your graph.

2. There is no single command to do so. However, there are some online Matlab codes.

3- There are many studies on graph matching, including spectral matching, binary matching, tree matching, node range matching, error correction, etc. The best algorithm actually depends on the type of graphs you have.

Kind regards,

Basheer

[Walter Roberson]

You do not need node positions to generate a graph object or a digraph object. You can attach node positions, but the node positions are only of interest to plot() and there are various layout hints you can give for plot purposes.

What you do need, though, is an interpretation of those matrices. It is not clear to me what those matrices mean. The 4 at index (1,1) could potentially mean that node 1 has a directional connection to node 4, or it could potentially mean that the weight of node 1 connecting to itself is 4, or it could mean something else.