无需使用 Matlab 内置函数即可在无向图中查找节点的唯一邻居的有效方法

Question

I have an undirected graph of N nodes and L links, whose structure is typically described by its adjacency matrix A with N rows and N columns. In this adjacency matrix, the value '1' denotes a link between two nodes and, conversely, '0' denotes no links.

I work in Matlab and want to avoid all the sophistications provided by the built-in graph() functions such as N = neighbors(G, NODEID) where G is G = graph(adjm); and adjm the adjacency matrix.

In this graph, I need to identify which unique nodes (neighbors) are connected to one or several starting nodes, labelled idx . I'm currently using the following line of code:

fidx = unique(ceil(find(adjm(idx,:)) / numel(idx)));

where fidx contains the neighbors (connected nodes) of a set of idx starting nodes. This operation is repeated a large number of times for different nodes and after some profiling, I found that the instruction find(adjm(idx,:)) is really hindering the overall runtime. My first attempt was to try to avoid find() . For example using:

A = adjm(idx,:);
A = A(:) == 1;
V = 1:size(A,1);
idx = unique(ceil(V(A) / numel(idx)));

However, this still remains too slow for my application.

What are you suggestions to reduce the runtime associated with this specific section of code?

Here is a minimal example:

%Minimal example:
f = @() get_neighb();
timeit(f)

function get_neighb()
%generate a graph with a large number of nodes N, in order to have
%computations times large enough:
N = 2e4; %number of nodes
G = round( rand(N) / 1.5 );
G = triu(G) + triu(G,1)';
adjm = G - diag(diag(G));

%for visualisation purposes:
%plot(graph(adjm));

s = size(adjm,1);

%list of some nodes to search for (randomly chosen):
n_nodes_test = 2000; %number of couples to test
%In this minimal example, we focus on searching for the neighbors of each couple (2-tuple) of
%nodes only. But 'snodes' can be single nodes or n-tuples, i.e. containing more
%than 2 nodes
snodes = [ round(linspace(1, s/2, n_nodes_test)); round(linspace(s/2, s, n_nodes_test))]';

%This section is the critical one:
for i=1:n_nodes_test
    
    idx = snodes(i,:); %assign current couple of starting nodes to 'idx'.
    
    %fidx = unique(ceil(find(adjm(idx,:)) / numel(idx)));
    %can be replaced by the following:
    A = adjm(idx,:);
    A = A(:) == 1;
    V = 1:size(A,1);
    idxf = unique(ceil(V(A) / numel(idx)));
    
    %which is similar to (using Matlab built-in 'graph' functions):
    % G = graph(adjm);
    % T = unique([neighbors(G, snodes(1,1)); neighbors(G, snodes(1,2))]);
    % here idxf' == T
end


end

Answer 1

You can use any , so the code will be reduced to:

idxf = find(any(adjm(idx, :)));

Explanation:
Assume that you have two logical row vectors A and B and you want to find a vector C that contains 1 where any of elements of A or B are 1 . In other words we want to find the unique indices of A or B where they that contain 1 . We simply can use logical OR operator:

C = A | B;

Equivalently you can use any function to compute C :

C = any([A;B]);

When we use idx = find(C) the indices will be unique and there is no need to use the unique function.

A second solution

idxf = find(idx * adjm);

Here we can use vector by matrix multiplication idx * adjm that is equivalent to sum(adjm(idx, :)) .