// Graph: Graph with vertices v and edges e
// source: starting vertex
ModifiedDijkstra (Graph, source)
    foreach vertex v in Graph G
        dist[v] := infinity
        previous[v] := undefined
        biggestEdge[v] := infinity
    dist[source] = 0
    biggestEdge[source] = 0
    Q := the set of all vertices in G
    while Q is not empty
        u = vertices in Q with smallest dist[v]
        remove u from Q
        foreach neightbour v of u
            old = dist[u] + dist_between(u,v)
            size = max(biggestEdge[u], dist_between(u,v))
            if (size < biggestEdge[v])
                dist[v] = old
                previous[u] = u
                biggestEdge[v] = size
    return previous[]