# How to map points in Vector A with many points in vector B?

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Rayan Glus on 14 Mar 2021
Commented: Rayan Glus on 18 Mar 2021
Hi,
I have two row vectors with the same size.
A = randi(100,1,100); % Elements of A represent cities
B = randi([101, 200],1,100); % Elements of B represent some other cities
Is it possible to map each element in A with many elements in B ? For example, I want to connect A (i) with, let's say, three cities in B. Where i is a city in vector A.
Is it doable under some constraints?
Thanks!
Waseem AL Aqqad on 16 Mar 2021
Hi Rayan,
For the case of one to many structure or mapping, the two networks or graphs cannot have the same number of nodes. Otherwise, half the number of nodes in one of the graphs would be considered autonomous nodes, that is, independent nodes.
So, if graph G has 8 nodes, graph H should have c * numnodes(G) nodes, where c is a positive integer. Let's assume that c = 2, then numnodes(H) = 16. Another constraint would be that each node i in G should be mapped to the same number of nodes in H. In our example, each node i in G should be mapped to two nodes in H.
The staff at Mathworks developed an amazing toolbox for graph theory, so you might want to check this page to help you have a better understanding.
Rayan Glus on 17 Mar 2021
Thanks for your nice explanation, Waseem.
So, I've been trying to map between A and B based on your explanation
A = 1:8;
B = 9:24;
But nothing works. I'm getting lots of errors. How should AB look like? a matrix?

Steven Lord on 17 Mar 2021
You can do this using an adjacency matrix:
A = [1 1 0; 0 0 1; 1 0 1];
D = digraph(A);
D.Nodes.Name = ["Boston"; "New York"; "Los Angeles"]
D =
digraph with properties: Edges: [5×2 table] Nodes: [3×1 table]
plot(D)
Or you could build an empty graph or digraph and use addedges and addnodes to built it up incrementally.
D2 = digraph;
D2 = addedge(D2, "Boston", "New York");
D2 = addedge(D2, "New York", "Los Angeles");
D2 = addedge(D2, "Los Angeles", "Boston");
D2 = addedge(D2, "Los Angeles", "Los Angeles")
D2 =
digraph with properties: Edges: [5×1 table] Nodes: [3×1 table]
plot(D2)
Rayan Glus on 18 Mar 2021
Thank you so much, Steven!
I tried your code while I was in the lab today, and it's just amzing.
But what I was looking for is how can I map the nodes of the digraph D you created with another digraph E's nodes. Is it via another adjacency Matrix?
A = [0 1 1; 1 0 1; 1 1 0];
E = digraph(A);
E.Nodes.Name = {'Las Vegas'; 'Miami'; 'Dallas'}
plot(E)
Thanks again.