Connectivity

A graph is connected if there is a route between every pair of nodes. Your task is to determine if a given graph is connected.

For example, the following graph is connected, because there is a route from any node to any other node.

The graph below is not connected, because there is no route from the node $1$ to the node $4$.

In a file connectivity.py, implement the function connected, whose parameters are the lists of the nodes and the edges of a graph. The function should return True if the graph is connected and False otherwise.

def connected(nodes, edges):
    # TODO

if __name__ == "__main__":
    nodes = [1, 2, 3, 4, 5]
    edges = [(1, 2), (1, 3), (1, 4), (2, 4), (2, 5), (3, 4), (4, 5)]
    print(connected(nodes, edges)) # True

    nodes = [1, 2, 3, 4, 5, 6, 7, 8]
    edges = [(1, 2), (1, 3), (2, 3), (4, 5), (4, 6), (5, 7), (6, 7)]
    print(connected(nodes, edges)) # False

    nodes = [1, 2, 3, 4, 5]
    edges = []
    print(connected(nodes, edges)) # False

    nodes = [1, 2, 3, 4, 5]
    edges = [(1, 2), (1, 3), (1, 4), (1, 5)]
    print(connected(nodes, edges)) # True