define a function that returns whether a graph is eulerian or not in python

To check if a graph is eulerian, we can use the following steps:

1. Check if every vertex of the graph has even degree. If not, the graph cannot be eulerian.
2. Check if the graph is connected. If not, the graph cannot be eulerian.
3. If the above two conditions are met, the graph is eulerian.

We can implement this algorithm in Python with the help of the NetworkX library. Here's the code:

main.py
import networkx as nx

def is_eulerian(G):
    # Check if every vertex has even degree
    for v in G.nodes():
        if G.degree(v) % 2 != 0:
            return False
    # Check if the graph is connected
    if not nx.is_connected(G):
        return False
    # If both conditions are met, the graph is eulerian
    return True
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Here, G represents the input graph as a NetworkX graph object. The degree function of NetworkX returns the degree of a vertex. The is_connected function checks if the graph is connected.

You can call this function with your graph object as the argument and it will return True if the graph is eulerian or False otherwise.