用邻接矩阵表示图

Question

# Creating the graph as an adjacency matrix
vertices = [[0, 1, 1, 0],
            [0, 0, 1, 0],
            [0, 0, 0, 1],
            [0, 0, 0, 0]]
edges =  [[0, 3, 4, 0],
          [0, 0, 0.5, 0],
          [0, 0, 0, 1],
          [0, 0, 0, 0]]

So I am trying to understand Dijkstra's algorithm in python but I don't understand the graph clearly since I don't understand the real meaning of each sublist, I understand that certain numbers like 3, 4, 1 and 0.5 are the distances of certain vericles but thats really it. I am attaching the image of what the graph looks like visually.

Answer 1

Adjacency matrices show information between pairs of vertices. In this example, you should interpret the lists like a matrix where the elements in each row and column corresponds to a pair of vertices:

  a b c d
a 0 1 1 0
b 0 0 1 0
c 0 0 0 1
d 0 0 0 0

Here, a 0 in the a column and a row, or at the position (0, 0) signifies that there is no edge from the a node to the a node and a 1 in the b column and the a row or position (0, 1) signifies that there is an edge from the a node to the b node. In other words, anywhere there is a 1, it signifies that there is an edge starting at the node corresponding to the row and ending at the node corresponding to the column, whereas a 0 signifies that there isn't an edge.

Apply similar logic to the edges list, which instead marks the weight of the edge rather than just marking whether an edge exists or not. As @misha mentioned, this list is not enough to represent the interconnectedness of nodes, because edges between nodes may have a weight of 0, which would be indistinguishable from an edge not existing at all, so both the edges and the vertices matrices are necessary