Write an algorithm to find cycle in a Graph

Given the following directed graph, how many cycles are there from B? E в D O 15 21 O 13

If there is an Euler path that starts at AA and ends at some other vertex, give it. Otherwise enter DNE.This should be a list of letters, from A to the other vertex: e.g. ACBDEAD (if that were even possible!). Path:  Since this is a planar graph, the number of regions - arcs + nodes equals what number?

Draw the adjacency list for the given undirected graph. No need for any program or something.