I would like to know a good program for drawing graphs and analyzing them (finding Eulerian circuits, Hamilton cycles, etc.). I would also like to export the drawing to Word.
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Why don't you try Sage -- it's free and should do as good a job anything else. You just type in
G = Graph (M)
for M an adjacency matrix to create your graph, then you can do
G.eulerian_circuit()
G.hamiltonian_cycle()
to find these things, and
plot(G)
draws your graph as a .png file which shouldn't be too hard to open in Word.
maxymoo
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graph_editor. – fidbc Apr 24 '13 at 21:29