Problem 45261. List every vertices neighbor indices

Created by Nicolas Douillet

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Input T is a triangulation.
The purpose of this function is to query at once the cell array N of all vertex neighbor indices... of every vertices, nothing less (!)
Output N must be a cell array since of course each vertex may have a different number of neighbors.
For example, for an input filled octahedron whom triangulation is
T = [1, 2, 3;...
     1, 3, 4;...
     1, 4, 5;...
     1, 2, 5;...
     2, 3, 6;...
     3, 4, 6;...
     4, 5, 6;...
     2, 5, 6;...
     2, 3, 4;...
     2, 4, 5;...
     1, 2, 4;...
     2, 4, 6],
then the output N is a 6x1 cell array of integers row vectors, such that :
N(1,1) = {[2, 3, 4, 5]};
N(2,1) = {[1, 3, 4, 5, 6]};
N(3,1) = {[1, 2, 4, 6]};
N(4,1) = {[1, 2, 3, 5, 6]};
N(5,1) = {[1, 2, 4, 6]};
N(6,1) = {[2, 3, 4, 5]};
Indeed vertex #2 is part of triangles [1, 2, 3], [1, 2, 5], [2, 3, 6], [2, 5, 6], [2, 3, 4], [2, 4, 5], [1, 2, 4], and [2, 4, 6], it then admit all the other vertices as neighbors ([1, 3, 4, 5, 6]).
Hypothesis / conditions :
a vertex is the neighbor of another if they are linked with an edge in at least one same triangle. A vertex is not neighbor of itself.
Output N row order is crucial since row number actually corresponds to the vertex id / index.
Output N cells content order doesn't matter, but it doesn't admit any duplicated index / value.
Tip : solving my previous problems, and especially query_vertex_neighbors will help you to fully understand and solve this one.
NB : the question of unreferenced vertices is not tacled here. We just supposed there are not.
See also
Mesh generation
Mesh processing toolbox

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Last Solution submitted on Jun 22, 2025

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Nicolas Douillet on 10 Jan 2020

Pedagogic solution is available in position 2 (commented, same as solution 1 but more explicit thus suboptimal).

Lloyd Stagg on 10 Mar 2025

In problem 45261, my solution produces a cell array with the correct contents except that my vectors are columns not rows as required in the solution tests. How do I change the contents of each cell from a column to row vector?

Nicolas Douillet on 13 Aug 2025 at 5:03

Hi Lloyd, I am sorry I discover your comment only now. Maybe use rowfiun instead of cellfun. Else, just transpose your column vector inside its cell.

Christian Schröder on 14 Aug 2025 at 12:58

@Lloyd cellfun(@transpose, ca, UniformOutput = false) when ca is your cell array, but as you've already found the best choice is often to construct ca such that this step is not even necessary.

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Problem 45261. List every vertices neighbor indices

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Problem 45261. List every vertices neighbor indices

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