Python networkx.closeness_centrality函数代码示例

def closeness_component(seed_num, graph_json_filename=None, graph_json_str=None):
  if graph_json_filename is None and graph_json_str is None:
    return []

  G = None
  if graph_json_str is None:
    G = util.load_graph(graph_json_filename=graph_json_filename)
  else:
    G = util.load_graph(graph_json_str=graph_json_str)

  components = list(nx.connected_components(G))
  components = filter(lambda x: len(x) > 0.1 * len(G), components)
  total_size = sum(map(lambda x: len(x), components))
  total_nodes = 0
  rtn = []
  for comp in components[1:]:
    num_nodes = int(float(len(comp)) / total_size * seed_num)
    component = G.subgraph(list(comp))
    clse_cent = nx.closeness_centrality(component)
    collector = collections.Counter(clse_cent)
    clse_cent = collector.most_common(num_nodes)
    rtn += map(lambda (x, y): x, clse_cent)
    total_nodes += num_nodes

  num_nodes = seed_num - total_nodes
  component = G.subgraph(list(components[0]))
  clse_cent = nx.closeness_centrality(component)
  collector = collections.Counter(clse_cent)
  clse_cent = collector.most_common(num_nodes)
  rtn += map(lambda (x, y): x, clse_cent)
  return rtn

def closeness_fracture(infile, outfile, fraction, recalculate = False):
    """
    Removes given fraction of nodes from infile network in reverse order of 
    closeness centrality (with or without recalculation of centrality values 
    after each node removal) and saves the network in outfile.
    """

    g = networkx.read_gml(infile)
    m = networkx.closeness_centrality(g)
    l = sorted(m.items(), key = operator.itemgetter(1), reverse = True)
    largest_component = max(networkx.connected_components(g), key = len)
    n = len(g.nodes())
    for i in range(1, n):
        g.remove_node(l.pop(0)[0])
        if recalculate:
            m = networkx.closeness_centrality(g)
            l = sorted(m.items(), key = operator.itemgetter(1), 
                       reverse = True)
        largest_component = max(networkx.connected_components(g), key = len)
        if i * 1. / n >= fraction:
            break
    components = networkx.connected_components(g)
    component_id = 1
    for component in components:
        for node in component:
            g.node[node]["component"] = component_id
        component_id += 1
    networkx.write_gml(g, outfile)

def compute_static_graph_statistics(G,start_time,end_time):
    verts = G.vertices
    n = len(verts)
    m = float(end_time - start_time)
    agg_statistics = [dict.fromkeys(verts,0),dict.fromkeys(verts,0),dict.fromkeys(verts,0)]*3
    avg_statistics = [dict.fromkeys(verts,0),dict.fromkeys(verts,0),dict.fromkeys(verts,0)]*3

    aggregated_graph = nx.Graph()
    aggregated_graph.add_nodes_from(verts)
    start_time = max(1,start_time)
    for t in xrange(start_time,end_time+1):
        aggregated_graph.add_edges_from(G.snapshots[t].edges_iter())
         
        dc = G.snapshots[t].degree()
        cc = nx.closeness_centrality(G.snapshots[t])
        bc = nx.betweenness_centrality(G.snapshots[t])
        for v in verts:
            avg_statistics[0][v] += dc[v]/(n-1.0)
            avg_statistics[1][v] += cc[v]
            avg_statistics[2][v] += bc[v]
    for v in verts:
        avg_statistics[0][v] = avg_statistics[0][v]/m
        avg_statistics[1][v] = avg_statistics[1][v]/m
        avg_statistics[2][v] = avg_statistics[2][v]/m
    
    dc = nx.degree_centrality(aggregated_graph)
    cc = nx.closeness_centrality(aggregated_graph)
    bc = nx.betweenness_centrality(aggregated_graph)
    for v in verts:
        agg_statistics[0][v] = dc[v]
        agg_statistics[1][v] = cc[v]
        agg_statistics[2][v] = bc[v]
    return (agg_statistics, avg_statistics)

def closeness_removal(g, recalculate=False):
    """
    Performs robustness analysis based on closeness centrality,
    on the network specified by infile using sequential (recalculate = True)
    or simultaneous (recalculate = False) approach. Returns a list
    with fraction of nodes removed, a list with the corresponding sizes of
    the largest component of the network, and the overall vulnerability
    of the network.
    """

    m = nx.closeness_centrality(g)
    l = sorted(m.items(), key=operator.itemgetter(1), reverse=True)
    x = []
    y = []

    dimension = fd.fractal_dimension(g, iterations=100, debug=False)
    n = len(g.nodes())
    x.append(0)
    y.append(dimension)

    for i in range(1, n-1):
        g.remove_node(l.pop(0)[0])
        if recalculate:
            m = nx.closeness_centrality(g)
            l = sorted(m.items(), key=operator.itemgetter(1),
                       reverse=True)
        dimension = fd.fractal_dimension(g, iterations=100, debug=False)
        x.append(i * 1. / n)
        y.append(dimension)

    return x, y

def closeness(infile, recalculate = False):
    """
    Performs robustness analysis based on closeness centrality,  
    on the network specified by infile using sequential (recalculate = True) 
    or simultaneous (recalculate = False) approach. Returns a list 
    with fraction of nodes removed, a list with the corresponding sizes of 
    the largest component of the network, and the overall vulnerability 
    of the network.
    """

    g = networkx.read_gml(infile)
    m = networkx.closeness_centrality(g)
    l = sorted(m.items(), key = operator.itemgetter(1), reverse = True)
    x = []
    y = []
    largest_component = max(networkx.connected_components(g), key = len)
    n = len(g.nodes())
    x.append(0)
    y.append(len(largest_component) * 1. / n)
    R = 0.0
    for i in range(1, n):
        g.remove_node(l.pop(0)[0])
        if recalculate:
            m = networkx.closeness_centrality(g)
            l = sorted(m.items(), key = operator.itemgetter(1), 
                       reverse = True)
        largest_component = max(networkx.connected_components(g), key = len)
        x.append(i * 1. / n)
        R += len(largest_component) * 1. / n
        y.append(len(largest_component) * 1. / n)
    return x, y, 0.5 - R / n

 def test_digraph(self):
     G = nx.path_graph(3, create_using=nx.DiGraph())
     c = nx.closeness_centrality(G)
     cr = nx.closeness_centrality(G.reverse())
     d = {0: 0.0, 1: 0.500, 2: 0.667}
     dr = {0: 0.667, 1: 0.500, 2: 0.0}
     for n in sorted(self.P3):
         assert_almost_equal(c[n], d[n], places=3)
         assert_almost_equal(cr[n], dr[n], places=3)

def closeness_centrality_distribution(G, return_dictionary=False):
    """Return a distribution of unweighted closeness centralities, as used in
    Borges, Coppersmith, Meyer, and Priebe 2011.
    If return_dictionary is specified, we return a dictionary indexed by
    vertex name, rather than just the values (as returned by default).
    """
    if return_dictionary:
        return nx.closeness_centrality(G)
    else:
        return nx.closeness_centrality(G).values()

 def test_wf_improved(self):
     G = nx.union(self.P4, nx.path_graph([4, 5, 6]))
     c = nx.closeness_centrality(G)
     cwf = nx.closeness_centrality(G, wf_improved=False)
     res = {0: 0.25, 1: 0.375, 2: 0.375, 3: 0.25,
            4: 0.222, 5: 0.333, 6: 0.222}
     wf_res = {0: 0.5, 1: 0.75, 2: 0.75, 3: 0.5,
               4: 0.667, 5: 1.0, 6: 0.667}
     for n in G:
         assert_almost_equal(c[n], res[n], places=3)
         assert_almost_equal(cwf[n], wf_res[n], places=3)

def closeness_apl(g, recalculate=False):
    """
    Performs robustness analysis based on closeness centrality,
    on the network specified by infile using sequential (recalculate = True)
    or simultaneous (recalculate = False) approach. Returns a list
    with fraction of nodes removed, a list with the corresponding sizes of
    the largest component of the network, and the overall vulnerability
    of the network.
    """

    m = networkx.closeness_centrality(g)
    l = sorted(m.items(), key=operator.itemgetter(1), reverse=True)
    x = []
    y = []

    average_path_length = 0.0
    number_of_components = 0
    n = len(g.nodes())

    for sg in networkx.connected_component_subgraphs(g):
        average_path_length += networkx.average_shortest_path_length(sg)
        number_of_components += 1

    average_path_length = average_path_length / number_of_components
    initial_apl = average_path_length

    x.append(0)
    y.append(average_path_length * 1. / initial_apl)

    r = 0.0
    for i in range(1, n):
        g.remove_node(l.pop(0)[0])
        if recalculate:
            m = networkx.closeness_centrality(g)
            l = sorted(m.items(), key=operator.itemgetter(1),
                       reverse=True)

        average_path_length = 0.0
        number_of_components = 0

        for sg in networkx.connected_component_subgraphs(g):
            if len(sg.nodes()) > 1:
                average_path_length += networkx.average_shortest_path_length(sg)
            number_of_components += 1

        average_path_length = average_path_length / number_of_components

        x.append(i * 1. / initial_apl)
        r += average_path_length * 1. / initial_apl
        y.append(average_path_length * 1. / initial_apl)
    return x, y, r / initial_apl

	def closeness_centrality(self, withme=False, node=None, average=False):
		if node==None:
			if withme:
				my_dict = nx.closeness_centrality(self.mynet)
				new = {}
				new2={}
				for i in my_dict:
					new[self.id_to_name(i)] = my_dict[i]
					new2[i] = my_dict[i]
				if average:
					print "The average is " + str(round(sum(new.values())/float(len(new.values())),4))
				else:
					for i,j in new.items():
						print i, round(j,4)
					return new2
			else:
				my_dict = nx.closeness_centrality(self.no_ego_net)

				new = {}
				new2={}
				for i in my_dict:
					new[self.id_to_name(i)] = my_dict[i]
					new2[i] = my_dict[i]
				if average:
					print "The average is " + str(round(sum(new.values())/float(len(new.values())),4))
				else:
					for i,j in new.items():
						print i, round(j,4)
					return new2
		else:
			if withme:
				my_dict = nx.closeness_centrality(self.mynet)
				try:
					print "The coefficient for node "+str(node)+ "is "+ str(round(my_dict[node],4))
				except:
					try:
						print "The coefficient for node "+str(node)+ "is "+ str(my_dict[[self.name_to_id(node)]])
					except:
						print "Invalid node name"
			else:
				my_dict = nx.closeness_centrality(self.no_ego_net)
				try:
					print "The coefficient for node "+str(node)+ "is "+ str(round(my_dict[node],4))
				except:
					try:
						print "The coefficient for node "+str(node)+ "is "+ str(round(my_dict[[self.name_to_id(node)]],4))
					except:
						print "Invalid node name"

def attack_based_max_closeness(G):
    """ Recalcuat closeness attack
    """
    n = G.number_of_nodes()
    tot_ND = [0] * (n+1)
    tot_T = [0] * (n+1)

    ND, ND_lambda = ECT.get_number_of_driver_nodes(G)
    tot_ND[0] = ND
    tot_T[0] = 0

    # remember when all the closeness have been zero for all nodes
    for i in range(1, n+1):
        all_closeness = nx.closeness_centrality(G)
        # get node with max betweenness       
        node = max(all_closeness, key=all_closeness.get)
        
        # remove all the edges adjacent to node
        if not nx.is_directed(G):   # undirected graph
            for key in G[node].keys():
                G.remove_edge(node, key)
        else:   # directed graph
            for x in [v for u, v in G.out_edges_iter(node)]:
                G.remove_edge(node, x)
            for x in [u for u, v in G.in_edges_iter(node)]:
                G.remove_edge(x, node)
        # calculate driver node number ND
        ND, ND_lambda = ECT.get_number_of_driver_nodes(G)
        tot_ND[i] = ND
        tot_T[i]  = i
    return (tot_ND, tot_T, Max_Betweenness_Zero_T)

def plot_closeness_dist (graph, path):
    """Plot distribution of closeness centrality of the graph and save the figure
       at the given path. On X-axis we have closeness centrality values and on
       Y-axis we have percentage of the nodes that have that closeness value"""

    N = float(graph.order())
    node_to_closeness = nx.closeness_centrality(graph)
    closeness_to_percent = {}

    # calculate percentages of nodes with certain closeness value
    for node in node_to_closeness:
        closeness_to_percent[node_to_closeness[node]] = 1 + \
                closeness_to_percent.get(node_to_closeness[node], 0)
    for c in closeness_to_percent:
        closeness_to_percent[c] = closeness_to_percent[c] / N * 100

    x = sorted(closeness_to_percent.keys(), reverse = True)
    y = [closeness_to_percent[i] for i in x]

    plt.loglog(x, y, 'b-', marker = '.')
    plt.title("Closeness Centrality Distribution")
    plt.ylabel("Percentage")
    plt.xlabel("Closeness value")
    plt.axis('tight')
    plt.savefig(path)

def computeLeague(libSNA, session):
    d = nx.degree(libSNA.graph)
    c = nx.closeness_centrality(libSNA.graph)
    b = nx.betweenness_centrality(libSNA.graph)
    
    ds = sorted_map(d)
    cs = sorted_map(c)
    bs = sorted_map(b)
    
    weights = [.50, .30, .20]
    
    names1 = [x[0] for x in ds[:10]]
    names2 = [x[0] for x in cs[:10]]
    names3 = [x[0] for x in bs[:10]]
    
    names = list(set(names1) | set(names2) | set(names3))
    names = sorted(names, key = lambda name: (float(d[name])/ds[0][1])*weights[0] + (float(c[name])/cs[0][1])*weights[1] + (float(b[name])/bs[0][1])*weights[2], reverse = True)
    
    result = fbutils.fql(
        "SELECT uid, name FROM user WHERE uid IN ( " \
        "SELECT uid2 FROM friend WHERE uid1 = me() )",
        session['access_token'])
    
    nodes = {}
    for node in result:
        nodes[str(node['uid'])] = node['name']
    
    return [[name, nodes[name], str(d[name]), str(c[name]), str(b[name])] for name in names]

def closeness_neighbors(seed_num, graph=None, graph_json_filename=None, graph_json_str=None):
  if graph_json_filename is None and graph_json_str is None and graph is None:
    return []

  G = None
  if graph is not None:
    G = graph
  elif graph_json_str is None:
    G = util.load_graph(graph_json_filename=graph_json_filename)
  else:
    G = util.load_graph(graph_json_str=graph_json_str)

  clse_cent = nx.get_node_attributes(G, "centrality")
  if len(clse_cent) == 0:
    clse_cent = nx.closeness_centrality(G)
    nx.set_node_attributes(G, "centrality", clse_cent)
    print "closeness neighbors"

  collector = collections.Counter(clse_cent)
  clse_cent = collector.most_common(SURROUND_TOP)
  nodes = map(lambda (x, y): x, clse_cent)

  current_seed = 0
  rtn = []
  while current_seed < seed_num:
    current_node = nodes[current_seed % len(nodes)]
    current_neighbors = G.neighbors(current_node)
    rtn += random.sample(set(current_neighbors) - set(rtn) - set(nodes), 1)
    current_seed += 1

  return rtn

def centrality_scores(vote_matrix, season_graph):
    deg = nx.degree(season_graph)
    deg = {k: round(v,1) for k,v in deg.iteritems()}

    close = nx.closeness_centrality(season_graph)
    close = {k: round(v,3) for k,v in close.iteritems()}

    btw = nx.betweenness_centrality(season_graph)
    btw = {k: round(v,3) for k,v in btw.iteritems()}

    eig = nx.eigenvector_centrality_numpy(season_graph)
    eig = {k: round(v,3) for k,v in eig.iteritems()}
    
    page = nx.pagerank(season_graph)
    page = {k: round(v,3) for k,v in page.iteritems()}

    # Add contestant placement (rank)
    order = list(vote_matrix.index)
    place_num = list(range(len(order)))
    place = {order[i]:i+1 for i in place_num}
    
    names = season_graph.nodes()

    # Build a table with centralities 
    table=[[name, deg[name], close[name], btw[name], eig[name], page[name], place[name]] for name in names]

    # Convert table to pandas df
    headers = ['name', 'deg', 'close', 'btw', 'eig', 'page', 'place']
    df = pd.DataFrame(table, columns=headers)
    df = df.sort_values(['page', 'eig', 'deg'], ascending=False)
    
    return df