MATLAB: Delete and add new edges in a graph

graphgraph theoryincidenceMATLAB

Hello,
I am trying to add new nodes between two nodes that already exist in a graph.
For example, I have a graph with two nodes labelled '1' and '2'
If I have to add 4 nodes between nodes labelled '1' and '2' , the edge between nodes 1 and 2 is deleted, new nodes are added to the graph,
new edges are added.
The following code performs the above-mentioned steps.
NNode = 2;
tail = 1:NNode-1;
head = 2:NNode;
Graph = graph(tail,head);
plot(Graph);
Graph.Nodes.Name = cellstr(string(1:height(Graph.Nodes))');
% Add new nodes
nnew = 4 % number of new nodes
Graph = rmedge(Graph,1,2)
Graph = addnode(Graph, nnew)
Graph.Nodes.Name
 
to_add = vertcat('1',Graph.Nodes.Name(end-nnew+1:end),'2')
for node = 1:length(to_add)-1
    head = to_add(node)
    tail = to_add(node+1)
    Graph = addedge(Graph,head,tail);
end
plot(Graph)
Graph.Nodes
Graph.Edges
I_inv = full(incidence(Graph))'
The following is the output of Graph.Edges
         EndNodes     
    __________________
    '1'        'Node3'
    '2'        'Node6'
    'Node3'    'Node4'
    'Node4'    'Node5'
    'Node5'    'Node6'
There is a problem that occurs while adding new edges. I am adding the last edge as addedge(Graph, 'Node6', '2').
However, in the above table we can see the head node is '2' and tail node is 'Node6'. Whereas, the edge was added the other way round.
Because of this the way in which incidence matrix is computed differs.
For example, the incidencematrix of the following graph is different from the above,
NNode = 6;
tail = 1:NNode-1;
head = 2:NNode;
Graph = graph(tail,head);
Although both graphs are the same and have 6 nodes.
Any suggestions on how to aviod this problem ? I would like to retain the result of Graph.Edges to be in the order in which the head and tail nodes are added to the Graph.

Best Answer

A graph object is undirected. A digraph object is directed.
Construct your network graph using digraph instead of graph on the fourth line of your code.
By the way, the addedge function has two capabilities you might find useful.
  1. The s (source) and t (target) inputs can be vectors to add multiple edges at once.
  2. If the source and/or target inputs reference nodes that don't yet exist, addedge adds them.
So you could do this with something like:
% Make a digraph and plot it for later reference
G = digraph(triu(ones(3)));
figure;
plot(G)
% How many nodes does G have?
N = numnodes(G);
% Add 2 new nodes
newnodes = [N+1 N+2];
% Add the edges between 1 and N+1, N+1 and N+2, and N+2 and 2
%

% I'm doing this in a copy of G, rather than G itself so you can go back
% and compare G and G2. But you can modify G itself if you want.
%
% Because of the way I created G, it's a weighted digraph, so I need
% to give the new edges weights. I chose to weight them all pi.
% Scalar expansion lets me specify a scalar weight to be used for each new edge.
G2 = addedge(G, [1 newnodes], [newnodes 2], pi);
% Eliminate the edge from 1 to 2
G2 = rmedge(G2, 1, 2);
% Plot the new digraph
figure;
plot(G2)
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