You can have the edge weights influence the layout of the graph or digraph but it is possible to specify edge weights such that drawing the network with edges of exactly those lengths is impossible. One such example that violates the triangle inequality is:
EndNodes = [1 2; 1 3; 2 3];
Weights = [5; 5; 20]; %
E = table(EndNodes, Weights);
g = graph(E);
plot(g)
See the example "Graph Layout Based on Edge Weights" on the documentation page for the layout function for an example. In the case of this simple a graph the layout using 'force' with or without a WeightEffect looks the same, but for a more complicated graph (like a randomly weighted buckyball) it may not.
B = graph(bucky);
B.Edges.Weight = randi(20, numedges(B), 1);
figure
plot(B); % No weight effect
figure
h = plot(B);
layout(h, 'force', 'WeightEffect', 'direct') % Higher weighted edges tend to be longer
figure
plot(B, 'layout', 'force', 'WeightEffect', 'inverse') % higher weight, shorter edge
