import random


def prune_graph_at_given_percentage(graph, percentage):
    """
    Randomly selects percentage% of edges and removes them 
    """
    new_graph = graph.copy()
    edges = graph.edges()
    count = int(round(len(edges) * float(percentage) / 100))
    random.shuffle(edges)
    for edge in edges[:count]:
        new_graph.remove_edge(edge[0], edge[1])
    return new_graph