MATLAB: Is there an easy (automated) way to determine if vertices are ‘mutually adjacent’ in a directed graph

directed graphmutual adjacency

I am comparing two directed graphs containing 253 vertices. The first graph contains around 1100 edges, the second graph contains around 1800 edges.

For each graph, I would like to know the number of 'mutually adjacent' vertices. When I say mutually adjacent I mean that one directed edge connects Vertex A to Vertex B and a second directed edge connects Vertex B to Vertex A.

Essentially I am trying to quantify how many pairs of directed edges effectively constitute an directed edge.

I don't need to know which specific vertices are mutually adjacent, just the quantity.

Thank you.

Best Answer

For a square adjacency matrix A that contains non-zero values to indicate links (not necessarily 1), then

nnz(tril(A & A.'))

Related Solutions

MATLAB: How to label all the edges in a graph the euclidean distance between two adjacent nodes??

I think one possible solution would be like this:

% Make Graph object
rng('default');
s = [1 1 3];
t = [2 3 4];
G = graph(s,t);
% Calculate pair-wise Euclidian distance between every node
X = 10*rand(4,1);
Y = 10*rand(4,1);
d = pdist([X,Y]);
d = squareform(d);
% Label Euclidian distance for each edge
G.Edges.Wieght =...
  arrayfun(@(j,k) d(j,k),G.Edges.EndNodes(:,1),G.Edges.EndNodes(:,2));
% Visualize the Graph
plot(G,'XData',X,'YData',Y,'EdgeLabel',G.Edges.Wieght)

MATLAB: How to convert graph to digraph

I'm afraid it's not possible to have both directed and undirected edges in the same graph. To convert a graph to a digraph, you could use

 gDirected = digraph(adjacency(gUndirected));

This will replace every undirected edge with two directed edges going in opposing directions. You could then use rmedge to remove the edges that go in the direction you don't want.

Within most graph algorithms, these two edges will behave the same way as the undirected edge did - but of course, the plot will look very different.

Best Answer

Related Solutions

MATLAB: How to label all the edges in a graph the euclidean distance between two adjacent nodes??

MATLAB: How to convert graph to digraph

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