Data_Elementos =[...
1 1 7;
2 7 8;
3 8 2;
4 7 9;
5 8 10;
6 4 9;
7 9 13;
8 9 10;
9 13 14;
10 14 10;
11 10 3;
12 6 11;
13 11 9;
14 11 15;
15 12 5;
16 10 12;
17 12 16;
18 16 14;
19 15 13;
20 15 16;
21 11 12];
G = graph(Data_Elementos(:, 2), Data_Elementos(:, 3));
plot(G)
This doesn't look like the picture you posted, but that's because I don't have the coordinates of the vertices. If you did have those coordinates, you could specify them in the plot call (like plot(G, 'XData', xcoords, 'YData', ycoords) or plot(G, 'XData', xcoords, 'YData', ycoords, 'ZData', zcoords)).
Now to determine if all the points in a set are connected you could check if the distance matrix between points in that set is all finite.
pointsInSet = [1,7,4,9,13,6,11,15];
d = distances(G, pointsInSet, pointsInSet);
all(isfinite(d), 'all')
If I remove the edge [1 7] node 1 is no longer connected to the rest of the graph.
G2 = rmedge(G, 1, 7);
d2 = distances(G2, pointsInSet, pointsInSet);
all(isfinite(d2), 'all')
