Regarding the proposal for
*Enumeration of Paths *
*In the graph module of Sagemath, we currently have a method in Python for 
enumerating all paths from a source to a destination in an undirected graph 
by increasing length (number of edges). We also have methods for 
enumerating all (simple) paths and cycles in a directed graph by increasing 
length (number of edges). The following tasks are intended to speed up 
these methods and offer more functionalities: *

using all_paths(start,end)
we get the simple paths between starting and ending vertices for both 
directed and undirected graphs however not in order of increasing length as 
heap implementation is not used here.

But using all_simple_paths(startingv_vertices,ending_vertices) 
a method in Digraph is do able to provide all possible paths in a Digraph 
in order of increasing length(edge)

So currently missing thing is enumerating paths in order of increasing 
length(edge) in Undirected Graphs and the Cythonic implementation of the 
above methods.
So should I begin by implementing the Cythonic version of the above methods 
under c_graph.pyx file under the CGraphBackened class or somewhere else?



Thanks
Rajat Mittal

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