If you only need an unscaled version of your graph, it is simply possible to plot the graph in MATLAB with unweighted edges, and it can look like the following. The distances plotted here are just strings labels, the graph is basically plotted without notion of edge-distance.
It should be simplest for you to populate the data as a list of lines/edges (or an edge-list). I hope the following code is self explanatory:
labelarray = {'Station1', 'Station2', 'Station3', 'Station4', 'Station5'};
% example edge list
% replace this with your real data.
% each number corresponds to the names above.
edges = [1 2; 1 3; 2 3; 2 4; 3 4; 4 5];
edgeLabels = {'100 km', '50 km', '80 km', '6 km', '100 km', '2 km'}; % replace with your desired labels
% create graph
G = graph(edges(:,1), edges(:,2));
% plot the graph
p = plot(G);
p.NodeLabel = labelarray;
highlight(p, [1 3], [2 4], 'LineStyle', '--'); % bonus: you can change lines to dashed for specific edges
labeledge(p, 1:numedges(G), edgeLabels);
You can find more about graph and plot in the official MATLAB documentation:
