# One hop nearest neighbor in a graph

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aasha verghese on 27 Jun 2022
Answered: Steven Lord on 27 Jun 2022
Hi,
nodeIDs = nearest( G , s , d ) returns all nodes in graph G that are within distance d from node s. But how do we find out one hop away neighbors (just closest nodes only) within a distance, in a graph? I mean the nearest neighbour of a vertex in a graph within a distance must be connected through an edge. (only one edge)
thanks!

Chunru on 27 Jun 2022
% Example graph
s = [1 1 1 1 1 2 2 2 3 3 3 3 3];
t = [2 4 5 6 7 3 8 9 10 11 12 13 14];
weights = randi([1 10],1,13);
G = graph(s,t,weights);
p = plot(G,'Layout','force','EdgeLabel',G.Edges.Weight); % All edges from node 1
eid = outedges(G, 1)
eid = 5×1
1 2 3 4 5
% info for edges from the node
e = G.Edges(eid, :)
e = 5×2 table
EndNodes Weight ________ ______ 1 2 8 1 4 8 1 5 3 1 6 4 1 7 8
% min distance
[~, idx] = min(e.Weight)
idx = 3
e(idx, :)
ans = 1×2 table
EndNodes Weight ________ ______ 1 5 3
min_node = e(idx, 1).EndNodes(2)
min_node = 5
min_dist = e.Weight(idx, 1)
min_dist = 3

Steven Lord on 27 Jun 2022
Find the neighbors of the node in the undirected graph then compute the distances between the specified node and its neighbors. Let's take an example: the buckyball graph.
b = bucky;
Update the adjacency matrix with some random weights and make it symmetric.
b = b.*randi(10, size(b));
b = (b + b.')/2;
Make the graph.
g = graph(b);
Find the neighbors of node 42.
n = neighbors(g, 42)
n = 3×1
8 41 43
Find the distances from node 42 to the neighbor nodes.
d = distances(g, 42, n)
d = 1×3
6.0000 1.5000 7.0000
Check with the original sparse matrix.
b(n, 42)
ans =
(1,1) 6.0000 (2,1) 1.5000 (3,1) 7.0000
If you later want to use a directed graph you may need to use successors or predecessors instead of neighbors.