def graph_is_connected(edges, players):
    """
    Test if the set of edges defines a graph in which each player is connected
    to at least one other player. This function does not test if the graph is
    fully connected in the sense that each node is reachable from every other
    node.

    Parameters:
    -----------
    edges : a list of 2 tuples
    players : a list of player names

    Returns:
    --------
    boolean : True if the graph is connected as specified above.
    """
    # Check if all players are connected.
    player_indices = set(range(len(players)))
    node_indices = set()
    for edge in edges:
        for node in edge:
            node_indices.add(node)

    return player_indices == node_indices