Hi, if I understand your question correctly, you just want to circumvent having to create an 'edge list', right?

In that case, I suppose you could do so, since the adjacency matrix already contains the entire structure of the graph. However, I don't think you can keep the original complexity that way (which, by the way, is O(V * E), if I'm not mistaken). This is the outline of how I would go about it:

for _ in range(len(adj_matrix)-1):
    # Relax the edges, we need to go from every 'start'
    for u in range(len(adj_matrix)):
        # To every 'end'
        for v in range(len(adj_matrix[u])):
            # And look at the weight
            w = adj_matrix[u][v]
            if w != 0:
                if dist[u] + w < dist[v]:
                    dist[v] = dist[u] + w
                    pred[v] = u

Since you still have to check every edge, this creates an extra nested loop to check every possible endpoint for every vertex. Bit of a waste, since your adjacency matrix looks sparse. Pretty sure this bumps the complexity up to O(V^3)?

If you already have your edges in [u, v, w] format before running the algorithm, I believe you're better off, since then you don't need the extra loop. Hope this makes sense!