def graph_add(node, node_set, sub_G, G):
    """
    Add node, and links between node and node_set that exist in Graph that to sub-graph
    """
    sub_G.add_node(node, x=G.nodes[node]['x'])
    for v in node_set:
        if (node, v) in G.edges():
            sub_G.add_edge(node, v)
    return sub_G