### Maximum algebraic connectivity from a given collection of graphs

~~for g in graphs.nauty_geng("8 -c"):~~

if g.size()==9:

g.show()

h=g.laplacian_matrix().eigenvalues()

h.sort()

show(h)

g.show()

Using this The following code ~~I have generate ~~runs through all connected graphs on 8 vertices and 9 ~~edges. ~~edges,
and shows each graph as well as the sorted list of its laplacian eigenvalues.

```
for g in graphs.nauty_geng("8 -c"):
```~~Now among all these collection I need ~~ if g.size() == 9:
g.show()
h = g.laplacian_matrix().eigenvalues()
h.sort()
show(h)

How could one list only ~~those graph or ~~the graphs ~~(if it is more than one) on 9 edges, ~~whose algebraic ~~connectivity ~~connectivity
(i.e ~~the ~~second smallest laplacian eigenvalue) is maximum among ~~all other ~~all
bicyclic graphs on 8 vertices and 9 edges. Here the ~~maximum ~~maximum
algebraic connectivity attained by the class is ~~1. Now how to find those graphs [having algebraic connectivity=1] from the entire collection?~~1.