Try Sage (sagemath.org)... you can use 'graphs' to get the list of all graphs of the given order... then you can test if they are of the given size... something like

for G in graphs(5):

    if G.size() == 10:

        do something

They even have an online version (sagemathcloud) so you don't have to install the whole library

send me the data in excel format and graph by hand made in pdf form. 

Use nauty for graph generation and dot (from the graphviz package) for drawing. You could do it within sage, which gives you a nice environment to string those together.

Try Sage (sagemath.org)... you can use 'graphs' to get the list of all graphs of the given order... then you can test if they are of the given size... something like

for G in graphs(5):

    if G.size() == 10:

        do something

They even have an online version (sagemathcloud) so you don't have to install the whole library

try this:

glist = [ G for G in graphs(5) if G.size() == 3 ]

graphs_list.show_graphs(glist)

of course beware of the size (I have put 5...). graphs(n) generates the list of all graphs (up to isomorphism) of the given order

Thanks to all for their helpful comments and suggestions. I found Sage (suggested by Professor Álvaro Lozano-Rojo) very convenient.