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Provide MATLAB representation for the following two graphs using adjacency matrices: Edges
have uniform length 1. How to find in MATLAB a shortest path from Node 4 to Node 6 (in both
graphs)?
Solution
Adjancy Matrix
function W = getAdjacencyMatrix(I)
[m, n] = size(I);
I_size = m*n;
V = repmat([ones(m-1,1); 0],n, 1);
V = V(1:end-1); % remove last zero
U = ones(m*(n-1), 1);
W = sparse(1:(I_size-1),   2:I_size, V, I_size, I_size)...
+ sparse(1:(I_size-m),(m+1):I_size, U, I_size, I_size);
W = W + W';
Shorest Path
function D = dijkstra(G, pairs)
p = size(pairs, 1); % Number of pairs
v = size(G, 1); % Number of vertices
D = [];
for i = 1:v
for j = 1:v
if G(i,j) <= esp
G(i,j) = inf
end
end
end
for i = 1:p
dist = inf(1, v);
seen = ones(1, v);
not_seen = v;
dist(1, pairs(i,1)) = 0;
while not_seen > 0
[distance index] = min(dist .* seen);
if distance == inf
break;
end
if index == pairs(i,2)
break;
end
seen(index) = inf;
not_seen = not_seen - 1;
for n = 1:v
if seen(n) == 1
alt = distance + G(index, n);
if alt < dist(n)
dist(n) = alt;
end
end
end
end
D = [D ; dist(pairs(i,2))];
end
end
Provide MATLAB representation for the following two graphs using adjac.docx

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Provide MATLAB representation for the following two graphs using adjac.docx

  • 1. Provide MATLAB representation for the following two graphs using adjacency matrices: Edges have uniform length 1. How to find in MATLAB a shortest path from Node 4 to Node 6 (in both graphs)? Solution Adjancy Matrix function W = getAdjacencyMatrix(I) [m, n] = size(I); I_size = m*n; V = repmat([ones(m-1,1); 0],n, 1); V = V(1:end-1); % remove last zero U = ones(m*(n-1), 1); W = sparse(1:(I_size-1),   2:I_size, V, I_size, I_size)... + sparse(1:(I_size-m),(m+1):I_size, U, I_size, I_size); W = W + W'; Shorest Path function D = dijkstra(G, pairs) p = size(pairs, 1); % Number of pairs v = size(G, 1); % Number of vertices D = []; for i = 1:v for j = 1:v if G(i,j) <= esp G(i,j) = inf
  • 2. end end end for i = 1:p dist = inf(1, v); seen = ones(1, v); not_seen = v; dist(1, pairs(i,1)) = 0; while not_seen > 0 [distance index] = min(dist .* seen); if distance == inf break; end if index == pairs(i,2) break; end seen(index) = inf; not_seen = not_seen - 1; for n = 1:v if seen(n) == 1 alt = distance + G(index, n); if alt < dist(n) dist(n) = alt; end end end end D = [D ; dist(pairs(i,2))]; end end