To print the n nodes of maximum degree with Matlab - matlab

Question

I need a matlab script that is going to return the n nodes of maximum degree in a graph.
For exemple:
N = maxnodes(Graph,n)
Graph is a matrix
n the number of nodes that we need
N is a vector that conatains the n nodes.
Here is my source code (script). But it doesn't work well.
M = [0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0;
1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0;
0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0;
0 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0;
1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0;
1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0;
0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0;
0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1;
0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0;
0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0;
0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0;
0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0;
0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1;
0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0;];
n = 5; % The number of nodes that we want
G=[]; % I'll store here the n nodes of maximum degree
for i=1:size(M)
G1(1,i)=sum(M(i,:)); % I'm storing each node with its degree in G1
G1(2,i)=i;
C(1,i)=G1(1,i); %I store only degree of nodes
end
C1 = sort(C,'descend'); % I sort "descendly" the degrees of nodes
for i=1:n %We want to take only the n nodes that we need and save it in C2
C2(1,i) = C1(1,i);
end
C2; % This vector stores the n descend maximum degrees that I need.
%My actual problem is here. How could I find the node that correspond to each degree?
%I tried to do it with the following loop:
for j=1:n
for i=1:size(M)
if C2(1,j) == G1(1,i)
G2(1,j)=G1(2,i);
end
end
end %But this loop doesn't store well the nodes in G2 because it repeats nodes.
G2

Answer 1

You have absolutely shown no effort so you actually shouldn't be getting any help from anyone.... but I love graph problems, so I'll throw you a bone.
I'm going to assume that Graph is an adjacency matrix, where each element (i,j) in the matrix corresponds to an edge connected between the two nodes i and j. I also am assuming that you have an undirected graph as input. If you examine the nature of the adjacency matrix (that Wikipedia article has a great example), it's not hard to see that the degree of a node i is simply the sum over all of the columns of row i in the adjacency matrix. Recall that the degree is defined as the total number of edges connected to a particular node. As such, all you have to do is sum over all of the columns for each row, and determine the rows that have the largest degree in your graph. Once we do this, we simply return the nodes that have this largest degree, which is up to n.
However, we will put in a safeguard where if we specify n to be larger than number of nodes having this maximum degree, we will cap it so that we only show up to this many nodes rather than n.
Therefore:
function [N] = maxnodes(Graph, n)
%// Find degrees of each node
degs = sum(Graph, 2);
%// Find those nodes that have the largest degree
locs = find(degs == max(degs));
%// If n is larger than the total number of nodes
%// having this maximum degree, then cap it
if n > numel(locs)
n = numel(locs);
end
%// Return those nodes that have this maximum degree
N = locs(1:n);

Answer 2

Here is a script that works very well and solves my problem. Otherwise, I would have liked well that my source code above would be debug.
function N = maxnodes(M,n)
nb1_rows= sum(M,2);
[nbs,is] = sort(nb1_rows,'descend');
N = transpose(is(1:n));