TITLE: Software for drawing and analyzing a graph?
QUESTION [9 upvotes]: 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.

REPLY [11 votes]: 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.