def test_random_seed(self):
"""Tests that each call with the same random seed generates the
same graph.
"""
deg_seq = [3] * 12
G1 = nx.configuration_model(deg_seq, seed=1000)
G2 = nx.configuration_model(deg_seq, seed=1000)
assert_true(nx.is_isomorphic(G1, G2))
G1 = nx.configuration_model(deg_seq, seed=10)
G2 = nx.configuration_model(deg_seq, seed=10)
assert_true(nx.is_isomorphic(G1, G2))
def get_corr_rand_set(G,disease_seeds,num_reps=5,alpha=.5,num_its=20,conserve_heat=True):
'''
Calculate the dot-product of heat propagated on N disease gene sets (disease_seeds: dict with keys disease names and values lists of disease genes), on an edge-shuffled, degree-preserving random matrix, with number of repetitions = num_reps, alpha=alpha, num_its = num_its.
Return the mean of the dot-product averaged over num_reps, and the standard deviation over num_reps, over all pairs of gene sets in disease_seeds. This way we only have to create one random matrix for each pair, which will speed up processing time a bit.
'''
num_Ds = len(disease_seeds)
dnames = disease_seeds.keys()
dname_pairs = list(itertools.combinations(dnames, 2))
dot_rand=dict()
dot_rand_mean = dict()
dot_rand_std = dict()
for d in dname_pairs:
# initialize dictionaries
dot_rand[d] = []
dot_rand_mean[d] = []
dot_rand_std[d] = []
for r in range(num_reps):
G_temp = nx.configuration_model(G.degree().values())
G_rand = nx.Graph() # switch from multigraph to digraph
G_rand.add_edges_from(G_temp.edges())
# remove self-loops
#G_rand.remove_edges_from(G_rand.selfloop_edges())
G_rand = nx.relabel_nodes(G_rand,dict(zip(range(len(G_rand.nodes())),G.degree().keys())))
Wprime_rand = normalized_adj_matrix(G_rand,conserve_heat=conserve_heat)
for i in range(len(dname_pairs)):
seeds_D1 = disease_seeds[dname_pairs[i][0]]
seeds_D2 = disease_seeds[dname_pairs[i][1]]
Fnew_D1 = network_propagation(G_rand,Wprime_rand,seeds_D1,alpha=alpha,num_its=num_its)
Fnew_D1_norm = Fnew_D1/np.linalg.norm(Fnew_D1)
rand_seeds = seeds_D2 #set(random.sample(G.nodes(),size_rand_set))
Fnew_D2 = network_propagation(G_rand,Wprime_rand,seeds_D2,alpha=alpha,num_its=num_its)
Fnew_D2_norm = Fnew_D2/np.linalg.norm(Fnew_D2)
idx_g0 = list(Fnew_D1[(Fnew_D1>0)&(Fnew_D2>0)].index)
idx_ND1ND2 = list(np.setdiff1d(list(Fnew_D1.index),np.union1d(seeds_D1,seeds_D2)))
dot_D1_D1 = np.dot(Fnew_D1_norm,Fnew_D2_norm)
dot_rand[dname_pairs[i]].append(dot_D1_D1)
for d in dname_pairs:
dot_rand_mean[d] = np.mean(dot_rand[d])
dot_rand_std[d] = np.std(dot_rand[d])
return dot_rand_mean,dot_rand_std
def powerlaw_degree_sequence(n, a):
"""
Create a graph without self-loops or parallel edges; having power law degree
distribution with an exponent 'around' a.
Parameters
----------
n : int
Number of nodes in graph.
a : float
Ideal exponent.
Returns
-------
G : networkx.Graph
The constructed graph.
"""
dsq = nx.create_degree_sequence(n, nx.utils.powerlaw_sequence, exponent = a)
G = nx.Graph(nx.configuration_model(dsq))
G.remove_edges_from(G.selfloop_edges())
# Check for a disconnected graph just in case...
if not nx.is_connected(G):
emsg = "The generated power-law graph is not connected!"
logger.error(emsg)
raise NepidemiXBaseException(emsg)
return G
def scale_free_network(n=100, gamma=2.5, avrdeg=8):
"""
Generates a scale free network by configuration model,
which is shown in :cite:`Wu2011`
:param int n: The number of nodes
:param float gamma: Exponent of degree distribution
:param float avrdeg: Average degree
:return: Scale-free network
:rtype: networkx.Graph
Generates degree sequence from calling
:func:`~.powerlaw_sequence` and
:func:`networkx.utils.random_sequence.create_degree_sequence`
then, build network by configuration model
(see :func:`networkx.generators.degree_seq.configuration_model`)
finally, remove self-loop and parallel edge to simplify.
.. Note:: Actual average degree is smaller than `avrdeg`
"""
seq = create_degree_sequence(
n, powerlaw_sequence, gamma=gamma, avrdeg=avrdeg)
G = configuration_model(seq)
# multigraph -> graph
G.remove_edges_from(G.selfloop_edges())
return nx.Graph(G)
def normaliseNodeWise(G, func, n=500, retNorm=True, inVal=None):
"""
This function normalises the function G by generating a series of n random
graphs and averaging the results. If retNorm is specified, the normalised
value is returned, else a list of n values for a random graph are returned.
"""
nodesDict = {v:[] for v in G.nodes()}
for i in range(n):
rand = configuration_model(G.degree().values())
rand = nx.Graph(rand) # convert to simple graph from multigraph
nodeList = [v for v in rand.nodes() if rand.degree(v)==0]
rand.remove_nodes_from(nodeList)
try:
res = func(rand) # collect values using the function
except KeyError: # exception raised if the spatial information is missing
print "Adding spatial info"
nx.set_node_attributes(rand, 'xyz', {rn:G.node[v]['xyz'] for rn,v in enumerate(G.nodes())}) # copy across spatial information
res = func(rand) # collect values using the function
for x,node in enumerate(nodesDict):
nodesDict[node].append(res[x])
if retNorm: # return the normalised values
if not inVal:
inVal = func(G)
for node in nodesDict:
nodesDict[node] = inVal[node]/np.mean(nodesDict[node])
return(nodesDict)
else: # return a list of the values from the random graph
return(nodesDict)
def normalise(G, func, n=500, retNorm=True, inVal=None, printLCC=False):
"""
This function normalises the function G by generating a series of n random
graphs and averaging the results. If retNorm is specified, the normalised
value is returned, else a list of n values for a random graph are returned.
"""
vals = []
for i in range(n):
rand = configuration_model(G.degree().values())
if nx.components.number_connected_components(rand)>1:
graphList = ccs(rand)
rand = graphList.next()
if printLCC:
print "Selecting largest connected components of "+str(len(rand.nodes()))+" nodes"
try:
vals.append(func(rand)) # collect values using the function
except KeyError: # exception raised if the spatial information is missing
nx.set_node_attributes(rand, 'xyz', {rn:G.node[v]['xyz'] for rn,v in enumerate(G.nodes())})
vals.append(func(rand)) # collect values using the function
if retNorm: # return the normalised values
if not inVal:
inVal = func(G)
return(inVal/np.mean(vals))
else: # return a list of the values from the random graph
return(vals)
def initScaleFreeGraph(self,N,k,e): s = [] while len(s) < N: nextval = int(nx.utils.powerlaw_sequence(k, e)[0]) if nextval != 0: s.append(nextval) #TODO: s must be scaled s = s/np.mean(s) * k s = np.around(s) s = s.astype(int) # Sum of degrees must be even. One way to solve this is to add a single node with degree 1 if sum(s) % 2: s[len(s)-1] = s[len(s)-1] + 1 print "length s:", len(s) print "Sum:", sum(s) G = nx.configuration_model(s) G = nx.Graph(G) # Remove self-loops G.remove_edges_from(G.selfloop_edges()) return G
def test_configuration():
seeds = [2718183590, 2470619828, 1694705158, 3001036531, 2401251497]
for seed in seeds:
deg_seq = nx.random_powerlaw_tree_sequence(20, seed=seed, tries=5000)
G = nx.Graph(nx.configuration_model(deg_seq, seed=seed))
G.remove_edges_from(nx.selfloop_edges(G))
_check_augmentations(G)
def createGraph(self):
""" Calculate the basic data for the graph """
""" Generate everything for the scale free network """
# Create a graph with degrees following a power law distribution
s = []
count = 0
while len(s) < self.N:
nextval = int(nx.utils.powerlaw_sequence(int(self.k), self.e)[0])
if nextval != 0:
count += nextval
s.append(nextval)
# s scaled and rounded such that the average degree equals k
s = s / np.mean(s) * self.k
s = np.around(s).astype(int)
# Sum of degrees must be even. I added one edge to the first node to fix this
if sum(s) % 2:
s[0] += 1
G = nx.configuration_model(s)
G = nx.Graph(G)
# Remove self-loops
G.remove_edges_from(G.selfloop_edges())
self.G = G
self.generateInfected()
def generate_graph(type = 'PL', n = 100, seed = 1.0, parameter = 2.1):
if type == 'ER':
G = nx.erdos_renyi_graph(n, p=parameter, seed=seed, directed=True)
G = nx.DiGraph(G)
G.remove_edges_from(G.selfloop_edges())
elif type == 'PL':
z = nx.utils.create_degree_sequence(n, nx.utils.powerlaw_sequence, exponent = parameter)
while not nx.is_valid_degree_sequence(z):
z = nx.utils.create_degree_sequence(n, nx.utils.powerlaw_sequence, exponent = parameter)
G = nx.configuration_model(z)
G = nx.DiGraph(G)
G.remove_edges_from(G.selfloop_edges())
elif type == 'BA':
G = nx.barabasi_albert_graph(n, 3, seed=None)
G = nx.DiGraph(G)
elif type == 'grid':
G = nx.grid_2d_graph(int(np.ceil(np.sqrt(n))), int(np.ceil(np.sqrt(n))))
G = nx.DiGraph(G)
elif type in ['facebook', 'enron', 'twitter', 'students', 'tumblr', 'facebookBig']:
#print 'start reading'
#_, G, _, _ = readRealGraph(os.path.join("..","..","Data", type+".txt"))
_, G, _, _ = readRealGraph(os.path.join("..","Data", type+".txt"))
print 'size of graph', G.number_of_nodes()
#Gcc = sorted(nx.connected_component_subgraphs(G.to_undirected()), key = len, reverse=True)
#print Gcc[0].number_of_nodes()
#print 'num of connected components', len(sorted(nx.connected_component_subgraphs(G.to_undirected()), key = len, reverse=True))
#exit()
if G.number_of_nodes() > n:
G = getSubgraph(G, n)
#G = getSubgraphSimulation(G, n, infP = 0.3)
#nx.draw(G)
#plt.show()
return G
def randomly_clustering(g, tries = 10): """ Comparing the average clustering coefficient of g with other graphs h which share identical degree sequence. This function returns the comparison ratio. Parameters: ----------- g: NetworkX Graph, NetworkX DiGraph tries: int, optional, (default = 10) number of tries (compared graphs) See also: --------- mean_clustering Returns: -------- float, the ratio of avg clustering coefficient, avg_cc(g) / mean(avg_cc(h)) """ from scipy import average g = to_undirected(g) d = g.degree().values() c = mean_clustering(g, normalized = False) p = list() for t in xrange(tries): ng = nx.configuration_model(d, create_using = nx.Graph()) p.append(mean_clustering(ng)) del ng return(c / average(p))
def generateNetwork():
## use a networkx function to create a degree sequence that follows a power law
degreeSequence=nx.utils.create_degree_sequence(numberOfNodes,powerlaw_sequence, 100)
## use aforementioned degree sequence to configure a pseudograph that contains self-loops & hyper-edges
pseudoGraph=nx.configuration_model(degreeSequence)
## remove hyper (parallel) edges
Graph = nx.Graph(pseudoGraph)
## remove self edges
Graph.remove_edges_from(Graph.selfloop_edges())
## loop through all nodes and set capacity equal to degree
for bankID in range(0, len(Graph.node)):
Graph.node[bankID]['bankID'] = bankID
Graph.node[bankID]['capacity'] = Graph.degree(bankID)
Graph.node[bankID]['solventNeighbors'] = Graph.degree(bankID)
## right now capacity = degree
Graph.node[bankID]['cumulativeShock'] = 0
## solvent = normal
## exposed = cumulative shock is less than capacity
## fail = recently failed, about to spread
## dead = can no longer spread or receive shocks
Graph.node[bankID]['status'] = 'solvent'
## here we set the timestep that the bank becomes insolvent to a big number
Graph.node[bankID]['insolventTimestep'] = 50
## here we set the size of the shock to be propagated (zero at sim start)
Graph.node[bankID]['shockToPropagate'] = 0
return Graph
def test_degree_zero(self):
"""Tests that a degree sequence of all zeros yields the empty
graph.
"""
G = nx.configuration_model([0, 0, 0])
assert_equal(len(G), 3)
assert_equal(G.number_of_edges(), 0)
def test_configuration_directed():
# seeds = [671221681, 2403749451, 124433910, 672335939, 1193127215]
seeds = [67]
for seed in seeds:
deg_seq = nx.random_powerlaw_tree_sequence(20, seed=seed, tries=5000)
G = nx.DiGraph(nx.configuration_model(deg_seq, seed=seed))
G.remove_edges_from(nx.selfloop_edges(G))
_check_edge_connectivity(G)
def measure_connectivity(G,focal_nodes,method='jaccard',num_reps=10):
avg_focal_degree = np.mean(G.degree(focal_nodes).values())
var_focal_degree = np.std(G.degree(focal_nodes).values())
if method=='jaccard':
#focal_sim = jaccard_sim_array(G,focal_nodes)
# select random node set
rand_sim=[]
focal_sim=[]
for r in range(num_reps):
# bootstrap a sample from focal_nodes
focal_subset = np.random.choice(list(focal_nodes),size=len(focal_nodes),replace=True)
focal_sim.append(jaccard_sim_array(G,focal_subset))
print('calculating random set ' + str(r) + ' out of ' + str(num_reps))
G_temp = nx.configuration_model(G.degree().values())
G_rand = nx.Graph() # switch from multigraph to digraph
G_rand.add_edges_from(G_temp.edges())
# remove self-loops
#G_rand.remove_edges_from(G_rand.selfloop_edges())
G_rand = nx.relabel_nodes(G_rand,dict(zip(range(len(G_rand.nodes())),G.degree().keys())))
rand_sim.append(jaccard_sim_array(G_rand,focal_subset)) # measure the jaccard similarity of degree-preserving edge shuffled network
elif method=='edge_overlap':
focal_sim = num_shared_neighbors(G,focal_nodes)
# select random node set
rand_sim=[]
for r in range(num_reps):
print('calculating random set ' + str(r) + ' out of ' + str(num_reps))
G_rand = nx.configuration_model(G.degree().values())
G_rand = nx.relabel_nodes(G_rand,dict(zip(range(len(G_rand.nodes())),G.degree().keys())))
rand_sim.append(num_shared_neighbors(G_rand,focal_nodes)) # rand_sim is array of length num_reps
return focal_sim,rand_sim
def generate_random_graph_powerlaw(n): m = 1 p = 0.7 #H = powerlaw_cluster_graph(n, m, p) gamma = 2.5 powerlaw_gamma = lambda N: nx.utils.powerlaw_sequence(N, exponent=gamma) z = nx.utils.create_degree_sequence(n, powerlaw_gamma, max_tries=1000) G = nx.configuration_model(z) while not nx.is_connected(G): powerlaw_gamma = lambda N: nx.utils.powerlaw_sequence(N, exponent=gamma) z = nx.utils.create_degree_sequence(n, powerlaw_gamma, max_tries=100) G = nx.configuration_model(z) G = [n for n in nx.connected_component_subgraphs(G)][0] G.remove_edges_from(G.selfloop_edges()) return G
def calc_localization(Gint,genes_focal,write_file_name='localization_results',num_reps=5,num_genes=20,
conserve_heat=True, replace=True,subsample=True, savefile=True):
seed_FOCAL = list(np.intersect1d(list(genes_focal),Gint.nodes()))
if subsample:
num_genes_S=num_genes
else:
num_genes_S=len(seed_FOCAL)
Wprime = normalized_adj_matrix(Gint,conserve_heat=conserve_heat)
kurt_FOCAL =[]
kurt_Srand=[]
var_FOCAL, var_Srand=[],[]
sumTop_FOCAL= []
sumTop_Srand= []
for r in range(num_reps):
print(r)
subset_FOCAL = np.random.choice(seed_FOCAL,size=num_genes_S,replace=replace)
Fnew_FOCAL = network_propagation(Gint,Wprime,subset_FOCAL,alpha=.5,num_its=20)
Fnew_FOCAL.sort()
kurt_FOCAL.append(scipy.stats.kurtosis(Fnew_FOCAL))
var_FOCAL.append(np.var(Fnew_FOCAL))
sumTop_FOCAL.append(np.sum(Fnew_FOCAL.head(1000)))
G_temp = nx.configuration_model(Gint.degree().values())
G_rand = nx.Graph() # switch from multigraph to digraph
G_rand.add_edges_from(G_temp.edges())
# remove self-loops
#G_rand.remove_edges_from(G_rand.selfloop_edges())
G_rand = nx.relabel_nodes(G_rand,dict(zip(range(len(G_rand.nodes())),Gint.degree().keys())))
Wprime_rand = normalized_adj_matrix(G_rand,conserve_heat=conserve_heat)
Fnew_Srand = network_propagation(G_rand,Wprime_rand,subset_FOCAL,alpha=.5,num_its=20)
Fnew_Srand.sort()
kurt_Srand.append(scipy.stats.kurtosis(Fnew_Srand))
var_Srand.append(np.var(Fnew_Srand))
sumTop_Srand.append(np.sum(Fnew_Srand.head(1000)))
print(var_FOCAL[-1])
print(var_Srand[-1])
results_dict = {'kurtosis':kurt_FOCAL,'kurt_rand':kurt_Srand,
'var':var_FOCAL,'var_rand':var_Srand,
'sumTop':sumTop_FOCAL, 'sumTop_rand':sumTop_Srand,
'num_reps':num_reps, 'conserve_heat':conserve_heat,
'replace':replace,'subsample':subsample,'num_genes':num_genes}
if savefile:
json.dump(results_dict,open(write_file_name,'w'))
return results_dict
def generate_graph(gamma, kmin, kmax, dk):
# map probability to power law:
p = np.random.random(graph_size)
C = (-gamma+1) / ((kmax+dk)**(-gamma+1) - (kmin+dk)**(-gamma+1))
k = ((-gamma+1)/C * p + (kmin+dk)**(-gamma + 1)) ** (1/(-gamma+1)) - dk
sequence = map(int, sorted(np.round(k))) # map sorted intervalls to int
if np.mod(np.sum(sequence), 2) != 0: # if odd, get rid of last element
sequence[-1]-=1
G = nx.configuration_model(sequence)
G = nx.Graph(G) # remove multiple connections
return G
def test_degree_sequence(self):
"""Tests that the degree sequence of the generated graph matches
the input degree sequence.
"""
deg_seq = [5, 3, 3, 3, 3, 2, 2, 2, 1, 1, 1]
G = nx.configuration_model(deg_seq, seed=12345678)
assert_equal(sorted((d for n, d in G.degree()), reverse=True),
[5, 3, 3, 3, 3, 2, 2, 2, 1, 1, 1])
assert_equal(sorted((d for n, d in G.degree(range(len(deg_seq)))),
reverse=True),
[5, 3, 3, 3, 3, 2, 2, 2, 1, 1, 1])
def connect_configuration(self,N,degseq):
"""
Uses the configuration model to wire up a pulse oscillator network with a given
input degree sequence. The length of degseq must equal N. The resulting network
is pruned of both self loops and parallel (multi) edges.
"""
assert len(degseq) == N, "ERROR. Each node needs an input degree."
self.connect_empty(N)
G = nx.configuration_model(degseq)
G = nx.Graph(G)
G.remove_edges_from(G.selfloop_edges())
self.add_edges_from(G.edges())
def create_star(self,node): sequence = create_degree_sequence(node, powerlaw_sequence, exponent=2.5) graph = nx.configuration_model(sequence) loops = graph.selfloop_edges() graph = nx.Graph(graph) graph.remove_edges_from(loops) components = sorted(nx.connected_components(graph), key=len, reverse=True) lcc = graph.subgraph(components[0]) #pos = nx.spring_layout(lcc) #nx.draw_networkx(lcc, pos) graph = list(nx.generate_edgelist(lcc)) edges = lcc.edges() #print(edges) flat = list(sum(edges, ())) return edges, max(flat,key=flat.count)
def DegreeSequenceConfigurationModel(deg_sequence, seed=None):
"""
Returns a random pseudograph with the given degree sequence. Raises
a NetworkX error if the proposed degree sequence cannot be that of
a graph with multiple edges and loops.
One requirement is that the sum of the degrees must be even, since
every edge must be incident with two vertices.
INPUT:
- ``deg_sequence`` - a list of integers with each entry corresponding to the
expected degree of a different vertex.
- ``seed`` - a ``random.Random`` seed or a Python ``int`` for the random
number generator (default: ``None``).
EXAMPLES::
sage: G = graphs.DegreeSequenceConfigurationModel([1,1])
sage: G.adjacency_matrix()
[0 1]
[1 0]
Note: as of this writing, plotting of loops and multiple edges is
not supported, and the output is allowed to contain both types of
edges.
::
sage: G = graphs.DegreeSequenceConfigurationModel([3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3])
sage: len(G.edges())
30
sage: G.show() # long time
REFERENCE:
[New2003]_
"""
if seed is None:
seed = int(current_randstate().long_seed() % sys.maxsize)
import networkx
return Graph(networkx.configuration_model([int(i) for i in deg_sequence],
seed=seed),
loops=True,
multiedges=True,
sparse=True)
def topology_chars(self):
"""
Calculates clustering coefficient, average shortest path length, small-worldness and
compares them with random graph.
"""
Gcc = sorted(nx.connected_components(self.G), key=len, reverse=True)
G0 = self.G.subgraph(Gcc[0])
H = nx.gnm_random_graph(self.G.number_of_nodes(),
self.G.number_of_edges()) #for clustering
F = nx.configuration_model([d for v, d in self.G.degree()
]) #for shortest path length
Fcc = sorted(nx.connected_components(F), key=len, reverse=True)
F0 = F.subgraph(Fcc[0])
cc = nx.average_clustering(self.G)
cc_r = nx.average_clustering(H)
# cc_r = nx.average_clustering(F)
asph = nx.average_shortest_path_length(G0)
asph_r = nx.average_shortest_path_length(F0)
sigma = (cc / cc_r) / (asph / asph_r)
omega = asph_r / asph - cc / cc_r
title = 'Topological Charateristics.txt'
topol_file = open(self.path + title, 'w')
topol_file.write('Size of the Giant Component is: ' +
str(G0.number_of_nodes()) + ' with ' +
str(G0.number_of_edges()) + ' edges' + '\n')
topol_file.write('Average Shortert Path Length' + '\n')
topol_file.write(str(asph) + '\n')
topol_file.write('Clustering Coeficient' + '\n')
topol_file.write(str(cc) + '\n')
topol_file.write('Small-Worldness Sigma' + '\n')
topol_file.write(str(sigma) + '\n')
topol_file.write('Small-Worldness Omega' + '\n')
topol_file.write(str(omega) + '\n')
topol_file.write('\n')
topol_file.write('The Corresponding Random Graph Has:' + '\n')
topol_file.write('Shortert Path Length: ' + str(asph_r) + '\n')
topol_file.write('Clustering Coeficient: ' + str(cc_r) + '\n' + '\n')
topol_file.write(
'A graph is commonly classified as small-world if Small-Worldness Sigma is bigger than 1. \n\n'
)
topol_file.write(
'The small-world coefficient Omega ranges between -1 and 1.\nValues close to 0 means the G features small-world characteristics.\nValues close to -1 means G has a lattice shape whereas values close to 1 means G is a random graph.'
)
topol_file.close()
return asph, cc, asph_r, cc_r, sigma, omega
def DegreeSequenceConfigurationModel(deg_sequence, seed=None):
"""
Returns a random pseudograph with the given degree sequence. Raises
a NetworkX error if the proposed degree sequence cannot be that of
a graph with multiple edges and loops.
One requirement is that the sum of the degrees must be even, since
every edge must be incident with two vertices.
INPUT:
- ``deg_sequence`` - a list of integers with each
entry corresponding to the expected degree of a different vertex.
- ``seed`` - for the random number generator.
EXAMPLES::
sage: G = graphs.DegreeSequenceConfigurationModel([1,1])
sage: G.adjacency_matrix()
[0 1]
[1 0]
Note: as of this writing, plotting of loops and multiple edges is
not supported, and the output is allowed to contain both types of
edges.
::
sage: G = graphs.DegreeSequenceConfigurationModel([3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3])
sage: sorted(G.edges(labels=False))
[(0, 2), (0, 10), (0, 15), (1, 6), (1, 16), (1, 17), (2, 5), (2, 19),
(3, 7), (3, 14), (3, 14), (4, 9), (4, 13), (4, 19), (5, 6),
(5, 15), (6, 11), (7, 11), (7, 17), (8, 11), (8, 18), (8, 19),
(9, 12), (9, 13), (10, 15), (10, 18), (12, 13), (12, 16), (14, 17),
(16, 18)]
sage: G.show() # long time
REFERENCE:
.. [Newman2003] Newman, M.E.J. The Structure and function of complex
networks, SIAM Review vol. 45, no. 2 (2003), pp. 167-256.
"""
if seed is None:
seed = current_randstate().long_seed()
import networkx
return Graph(networkx.configuration_model([int(i) for i in deg_sequence], seed=seed), loops=True, multiedges=True, sparse=True)
def make_graph_with_same_degree_dist(G):
G_sequence = list(d for n, d in G.degree())
G_sequence.sort()
sorted_G_sequence = list((d, n) for n, d in G.degree())
sorted_G_sequence.sort(key=lambda tup: tup[0])
done = False
while not done:
G_prime = nx.configuration_model(G_sequence)
G_prime = nx.Graph(G_prime)
G_prime.remove_edges_from(G_prime.selfloop_edges())
tries = 10
while tries > 0 and (len(G.edges()) != len(G_prime.edges())):
sorted_G_prime_sequence = list((d, n) for n, d in G_prime.degree())
sorted_G_prime_sequence.sort(key=lambda tup: tup[0])
#print("Sorted G_sequence:")
#print(sorted_G_sequence)
#print("Sorted G_prime_sequence:")
#print(sorted_G_prime_sequence)
missing = []
for i in range(0, len(G.nodes())):
while sorted_G_sequence[i][0] > sorted_G_prime_sequence[i][0]:
missing.append(sorted_G_prime_sequence[i][1])
sorted_G_prime_sequence[i] = (
sorted_G_prime_sequence[i][0] + 1,
sorted_G_prime_sequence[i][1])
missing = np.random.permutation(missing)
if len(missing) % 2 != 0:
print("Sanity issue! Alert!")
#print("Edges before:")
#print(G_prime.edges())
#print("Missing:")
#print(missing)
for i in range(0, int(len(missing) / 2)):
G_prime.add_edge(missing[2 * i], missing[2 * i + 1])
G_prime = nx.Graph(G_prime)
G_prime.remove_edges_from(G_prime.selfloop_edges())
#print("Edges after:")
#print(G_prime.edges())
if not is_connected(G_prime):
# print("Bad: G_prime disconnected")
pass
tries -= 1
if not is_connected(G_prime):
pass
elif len(G.edges()) == len(G_prime.edges()):
#print("Graph creation successful")
done = True
return G_prime
def DegreeSequenceConfigurationModel(deg_sequence, seed=None):
"""
Returns a random pseudograph with the given degree sequence. Raises
a NetworkX error if the proposed degree sequence cannot be that of
a graph with multiple edges and loops.
One requirement is that the sum of the degrees must be even, since
every edge must be incident with two vertices.
INPUT:
- ``deg_sequence`` - a list of integers with each
entry corresponding to the expected degree of a different vertex.
- ``seed`` - for the random number generator.
EXAMPLES::
sage: G = graphs.DegreeSequenceConfigurationModel([1,1])
sage: G.adjacency_matrix()
[0 1]
[1 0]
Note: as of this writing, plotting of loops and multiple edges is
not supported, and the output is allowed to contain both types of
edges.
::
sage: G = graphs.DegreeSequenceConfigurationModel([3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3])
sage: G.edges(labels=False)
[(0, 2), (0, 10), (0, 15), (1, 6), (1, 16), (1, 17), (2, 5), (2, 19), (3, 7), (3, 14), (3, 14), (4, 9), (4, 13), (4, 19), (5, 6), (5, 15), (6, 11), (7, 11), (7, 17), (8, 11), (8, 18), (8, 19), (9, 12), (9, 13), (10, 15), (10, 18), (12, 13), (12, 16), (14, 17), (16, 18)]
sage: G.show() # long time
REFERENCE:
.. [Newman2003] Newman, M.E.J. The Structure and function of complex
networks, SIAM Review vol. 45, no. 2 (2003), pp. 167-256.
"""
if seed is None:
seed = current_randstate().long_seed()
import networkx
return Graph(networkx.configuration_model([int(i) for i in deg_sequence],
seed=seed),
loops=True,
multiedges=True,
sparse=True)
def power_law_graph(x_min, power_law_exponent, size_of_net):
degree_sequence = [1]
#~ G = nx.fast_gnp_random_graph(1, 1)
#~ while min(G.degree().values()) != x_min:
while sum(degree_sequence) % 2 == 1:
degree_sequence = []
for i in range(size_of_net):
degree_sequence.append(
int(pl_gen.random_power_no(x_min, power_law_exponent)))
G = nx.configuration_model(degree_sequence)
G = nx.Graph(G)
G.remove_edges_from(G.selfloop_edges())
return G
def perturbed_graph(seed_graph):
'''
Returns random graph with approximately the same degree
distribution as given seed graph
'''
# Generate new graph with given degree sequence
deg_sequence = shuffle(list(seed_graph.degree))
new_G = nx.configuration_model(list(zip(*deg_sequence))[1])
# Rename graph with nodes in seed_graph with corresponding degrees
deg2names = get_degree_to_names(deg_sequence)
mapping = get_degree_preserving_relabelling(deg2names, new_G)
new_G = nx.relabel_nodes(new_G, mapping)
# Remove self loops and parallel edges and return
return util.simple_two_core(nx.Graph(new_G), verbose=False)
def experiment(n_tries):
samples = 5
G_list = list()
#array to hold the average_clustering coeff for all the n_tries
data = np.zeros(n_tries)
for i in range(n_tries):
for j in range(samples):
G = nx.configuration_model(deg_seq)
G = nx.Graph(G)
G_list.append(G)
G = random.choice(G_list)
average_clustering = nx.average_clustering(G)
data[i] = average_clustering
return data
def generate_graph_mean(degree_start=10, degree_end=15, size=5000):
z=[numpy.random.geometric(0.07) for i in range(size)]
print("Mean degree", numpy.mean(z))
# if sum of degree sequence is odd, make it even
if sum(z) % 2 != 0:
z[random.randint(0, size)] += 1
G=nx.configuration_model(z)
# remove self-loops and parallel edges
G=nx.Graph(G)
G.remove_edges_from(G.selfloop_edges())
return G
def __init__(self,
f,
s,
r,
graph_type="Regular",
rows=-1,
cols=-1,
num_hubs=-1):
self.G = None
self.F = set([])
self.owners_list = []
self.collected = []
self.path = []
self.batch_nums = []
self.fig, self.pos, self.ax = None, None, None
self.ani_title = ""
self.num_times = 0
self.ani = None
self.f = f
self.s = s
self.r = r
self.graph_type = graph_type
self.num_hubs = num_hubs
if graph_type == "Regular":
self.G = self.make_reg_graph(f, s, r)
elif graph_type == "Euclidean":
self.s = rows * cols
self.G = nx.grid_2d_graph(rows, cols)
elif graph_type == "Network":
assert (num_hubs > 0)
# sequence = nx.generators.degree_seq.create_degree_sequence(s, nx.utils.powerlaw_sequence)
# self.G = nx.configuration_model(sequence)
# Check all combinations of feasible degrees to see if we can make a valid graph
hub_degrees = range((2 * s) // num_hubs, (3 * s) // num_hubs)
non_hub_degrees = range(1, 4)
for degree_seq in itertools.product(
*[hub_degrees for _ in range(num_hubs)],
*[non_hub_degrees for _ in range(s - num_hubs)]):
if sum(degree_seq) % 2 != 0:
continue
G_curr = nx.configuration_model(degree_seq)
if nx.is_connected(G_curr):
self.G = G_curr
break
assert (self.G != None)
self.F = set(random.sample(self.G.nodes, f))
def save_power_law(n, exponent, save=False):
sequence = nx.random_powerlaw_tree_sequence(n=n,
gamma=exponent,
tries=50000)
graph = nx.configuration_model(sequence)
print(sequence)
adj = nx.adjacency_matrix(graph)
adj[range(n), range(n)] = 1 #adding self-loops to the adj matrix
# print('avg path length: ', nx.average_shortest_path_length(graph))
print('density: ', nx.density(graph))
if save:
# average_shortest_path_length = nx.average_shortest_path_length(graph)
print('saving...')
adjacency_matrix_file = 'power_law_n_{}_exp_{}.pickle'.format(
n, exponent)
with open(adjacency_matrix_file, 'wb') as handle:
pickle.dump(adj, handle, -1)
def degree_sequence_graphs():
print("Degree sequence")
print("Configuration model")
z = nx.utils.create_degree_sequence(30, powerlaw_sequence)
G = nx.configuration_model(z)
draw_graph(G)
# to remove paralel edges
G = nx.Graph(G)
draw_graph(G)
# to remove self loops
G.remove_edges_from(G.selfloop_edges())
draw_graph(G)
print("Directed configuration model")
D = nx.DiGraph([(0, 1), (1, 2), (2, 3), (1, 3)]) # directed path graph
din = list(D.in_degree().values())
dout = list(D.out_degree().values())
din.append(1)
dout[0] = 2
D = nx.directed_configuration_model(din, dout)
D = nx.DiGraph(D) # to remove paralell edges
D.remove_edges_from(D.selfloop_edges()) # to remove self loops
draw_graph(D)
print("Expected degree graphs")
z = [i for i in range(10)]
G = nx.expected_degree_graph(z)
draw_graph(G)
print("Havel Hakimi graphs")
z = [2, 4, 5, 6, 7, 3]
G = nx.havel_hakimi_graph(z)
draw_graph(G)
print("Directed Havel Hakimi graphs")
inds = [2, 4, 5, 6, 7, 3]
outds = [2, 4, 5, 6, 7, 3]
G = nx.directed_havel_hakimi_graph(in_deg_sequence=inds,
out_deg_sequence=outds)
draw_graph(G)
print("Degree Sequence Tree")
dg = [1, 2, 3, 4, 2, 3]
G = nx.degree_sequence_tree(dg)
draw_graph(G)
print("Random Degree Sequence")
sequence = [1, 2, 2, 3]
G = nx.random_degree_sequence_graph(sequence)
sorted(G.degree().values())
draw_graph(G)
def DegreeSequenceConfigurationModel(deg_sequence, seed=None):
"""
Returns a random pseudograph with the given degree sequence. Raises
a NetworkX error if the proposed degree sequence cannot be that of
a graph with multiple edges and loops.
One requirement is that the sum of the degrees must be even, since
every edge must be incident with two vertices.
INPUT:
- ``deg_sequence`` - a list of integers with each entry corresponding to the
expected degree of a different vertex.
- ``seed`` - a ``random.Random`` seed or a Python ``int`` for the random
number generator (default: ``None``).
EXAMPLES::
sage: G = graphs.DegreeSequenceConfigurationModel([1,1])
sage: G.adjacency_matrix()
[0 1]
[1 0]
Note: as of this writing, plotting of loops and multiple edges is
not supported, and the output is allowed to contain both types of
edges.
::
sage: G = graphs.DegreeSequenceConfigurationModel([3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3])
sage: len(G.edges())
30
sage: G.show() # long time
REFERENCE:
.. [Newman2003] Newman, M.E.J. The Structure and function of complex
networks, SIAM Review vol. 45, no. 2 (2003), pp. 167-256.
"""
if seed is None:
seed = int(current_randstate().long_seed() % sys.maxsize)
import networkx
return Graph(networkx.configuration_model([int(i) for i in deg_sequence], seed=seed), loops=True, multiedges=True, sparse=True)
def buildGraphFromDegreeInfo(self):
if self.read:
self.readGraph()
if self.G != None:
degreeSequence = sorted([d for n, d in self.G.degree()],
reverse=True)
degreeCount = dict(collections.Counter(degreeSequence))
for d in range(1, max(degreeSequence) + 1):
degreeCount[
d] = degreeCount[d] / self.n if d in degreeCount else 0
self.degreeDistribution = degreeCount
return
if self.degreeDistribution != None:
degreeSequence = []
temp = 0
for i in range(self.n - 1):
d = utils.sampleDegreeFromDistribution(self.degreeDistribution)
degreeSequence.append(d)
temp += d
d = utils.sampleDegreeFromDistribution(self.degreeDistribution)
while (temp + d) % 2 != 0:
d = utils.sampleDegreeFromDistribution(self.degreeDistribution)
degreeSequence.append(d)
temp += d
self.degreeSequence = degreeSequence
if self.degreeSequence != None:
self.G = nx.configuration_model(self.degreeSequence)
self.degreeSequence = []
for i in range(self.n):
self.degreeSequence.append(len(self.G[i]))
self.G.nodes[i]["id"] = i
self.G.nodes[i]["products"] = set([0, 1])
self.G.nodes[i]["payoff"] = 0
degreeCount = dict(collections.Counter(self.degreeSequence))
for d in range(1, self.n):
degreeCount[
d] = degreeCount[d] / self.n if d in degreeCount else 0
self.degreeDistribution = degreeCount
print(self.degreeSequence)
print(len(self.degreeSequence))
def pvalue(G, comms, LLRtest, L=3000, plothist=False):
'''
Compute the distribution of the test statistic in a range.
Warning: Enumerating all Null networks is very slow.
Do not call this function in practical community detection.
Use threshold on the LR test statistic directly.
Args:
G: input networkx graph instance
comms: the suggested partiton, list of lists
LLRtest: the log-likelihood ratio test statistics
L: number of synthetic null networks (default 3000)
Returns:
(float): pvalue of LLRtest
'''
node_seq, deg_seq = zip(*list(G.degree()))
index = {n: i for i, n in enumerate(node_seq)}
# nodes should be index-0
comms = [list(map(index.get, c)) for c in comms]
null_distri = []
for niter in range(L):
# debug
if niter % 100 == 1: print("iter", niter, "H0 LLR", LRnull)
# generate configuration network
F = nx.Graph(nx.configuration_model(deg_seq))
# obtain test statistic on null network
LRnull = _2ll(F, comms)
null_distri.append(LRnull)
pval = sum([LLRnull > LLRtest
for LLRnull in null_distri]) / float(len(null_distri))
# plot
if plothist:
print("plotting")
hist(null_distri, LLRtest, "%d_%d" % (len(comms), G.number_of_nodes()),
pval)
return pval
def GraphType(num_nodes, str, p=0.05, m=3):
"""
:param num_nodes: the number of nodes of the graph (if that option is available)
:param str: the type of graph that is used. We have
'erdos' an erdos renyi graph
'powerlaw' a graph with powerlaw degree distribution
'enron' a social network graph loaded from
http://snap.stanford.edu/data/email-Enron.html. (36692 nodes)
'karateclub' some karate club graph
'women' women social network
:return: the graph
"""
if str == 'erdos':
graph = nx.erdos_renyi_graph(num_nodes, p)
elif str == 'powerlaw':
graph = nx.powerlaw_cluster_graph(num_nodes, m, p)
elif str == 'enron':
graph = nx.Graph()
edges = np.loadtxt('Enron.txt',skiprows=4)
graph.add_edges_from(edges)
elif str == 'karateclub':
graph = nx.karate_club_graph()
elif str == 'women':
graph = nx.davis_southern_women_graph()
elif str == 'pair':
graph = nx.DiGraph()
graph.add_edge(0,1)
graph.add_edge(1,0)
elif str == 'star':
graph = nx.star_graph(num_nodes)
elif str == 'cycle':
graph = nx.cycle_graph(num_nodes)
elif str == 'config':
max_degree = int(num_nodes/5)
#Create some degrees
degrees = np.asarray(np.round(np.exp(np.log(max_degree) * np.random.uniform(size=num_nodes))), np.int)
#Ensure the total number of degrees is even
if sum(degrees) % 2 != 0:
degrees[np.random.randint(num_nodes)] += 2 * np.random.randint(2) - 1
#Create a graph and apply the configuration model
graph = nx.Graph()
graph = nx.configuration_model(degrees, graph)
graph = graph.to_directed()
return graph
def DegreeSequenceConfigurationModel(deg_sequence, seed=None):
"""
Return a random pseudograph with the given degree sequence.
This method raises a NetworkX error if the proposed degree sequence cannot
be that of a graph with multiple edges and loops.
One requirement is that the sum of the degrees must be even, since every
edge must be incident with two vertices.
INPUT:
- ``deg_sequence`` -- list of integers with each entry corresponding to the
expected degree of a different vertex
- ``seed`` -- (optional) a ``random.Random`` seed or a Python ``int`` for
the random number generator
EXAMPLES::
sage: G = graphs.DegreeSequenceConfigurationModel([1,1])
sage: G.adjacency_matrix()
[0 1]
[1 0]
The output is allowed to contain both loops and multiple edges::
sage: deg_sequence = [3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3]
sage: G = graphs.DegreeSequenceConfigurationModel(deg_sequence)
sage: G.order(), G.size()
(20, 30)
sage: G.has_loops() or G.has_multiple_edges() # random
True
sage: G.show() # long time
REFERENCE:
[New2003]_
"""
if seed is None:
seed = int(current_randstate().long_seed() % sys.maxsize)
import networkx
deg_sequence = [int(i) for i in deg_sequence]
return Graph(networkx.configuration_model(deg_sequence, seed=seed),
loops=True, multiedges=True, sparse=True)
def _gen(self, gname: str, gen_id: int) -> nx.Graph:
assert 'degree_seq' in self.params, 'imporper parameters for Chung-Lu'
try:
g = nx.configuration_model(
self.params['degree_seq']) # fit the model to the degree seq
except nx.NetworkXError: # config model failed
raise Exception('Generation failed!')
else: # gets called only if the exception is not thrown
g = nx.Graph(g) # make it into a simple graph
g.remove_edges_from(nx.selfloop_edges(g)) # remove self-loops
g.name = gname
g.gen_id = gen_id
return g
def under_weighted_model(G,reps): lmbda=1 old_clustering=nx.clustering(G).values() degree=G.degree().values() clust_mat=np.zeros((reps,G.number_of_nodes())) for i in xrange(reps): C=nx.configuration_model(degree) C=nx.Graph(C) #remove parallel edges C.remove_edges_from(C.selfloop_edges()) #remove self-loops for e in C.edges(): C.edge[e[0]][e[1]]['weight']=np.random.poisson()+1 #start with 1 clustering=nx.clustering(C, weight='weight') clust_mat[i]=clustering.values() means=np.mean(clust_mat, axis=0) #mean over iterations for each node per25=np.percentile(clust_mat, 25, axis=0) per75=np.percentile(clust_mat, 75, axis=0) return [old_clustering-means, old_clustering-per25, old_clustering-per75]
def scale_free_network(number_of_nodes, powerlaw_exponent):
sequence = nx.utils.random_sequence.powerlaw_sequence(
number_of_nodes, powerlaw_exponent)
sequence = np.round(sequence).astype(int)
# Ensure that the total number of stubs is even
if (sequence.sum() % 2) != 0:
sequence[np.random.randint(number_of_nodes)] += 1
# Initiate the network
network = nx.configuration_model(sequence)
adjacency = adjacency_from_edges(list(network.edges()), number_of_nodes)
adjacency = clean_adjacency(adjacency)
adjacency = sparse.csr_matrix(adjacency)
return adjacency
def normalise(G, func, n=500, retNorm=True, inVal=None, weight='weight'):
"""
This function normalises the function G by generating a series of n random
graphs and averaging the results. If retNorm is specified, the normalised
value is returned, else a list of n values for a random graph are returned.
"""
vals = []
for i in range(n):
rand = configuration_model(G.degree().values())
rand = nx.Graph(rand) # convert to simple graph from multigraph
# check whether the graph is weighted
# if so, the algorithm randomly reassigns weights from the input graph to the random graph node by node
# this means that for each node the total weighted degree will be similar
# nb this depends on the random graph having the same or fewer vertices for each node
if isinstance(G.degree(weight=weight)[0], float):
randDegs = rand.degree()
for node in rand.nodes():
edgeVals = [v[2][weight] for v in G.edges(G.nodes()[node],data=True)]
shuffle(edgeVals)
for en,edge in enumerate(rand.edges(node)):
rand.edge[edge[0]][edge[1]]['weight'] = edgeVals[en]
# remove unconnected nodes
nodeList = [rand.degree()[v] for v in rand.nodes() if rand.degree(v)==0]
rand.remove_nodes_from(nodeList)
# add spatial information if necessary
if spatial:
print "Adding spatial info"
nx.set_node_attributes(rand, 'xyz', {rn:G.node[v]['xyz'] for rn,v in enumerate(G.nodes())}) # copy across spatial information
try:
vals.append(func(rand),weight='weight') # collect values using the function
except:
vals.append(func(rand)) # collect values using the function
if retNorm: # return the normalised values
if not inVal:
inVal = func(G)
return(inVal/np.mean(vals))
else: # return a list of the values from the random graph
return(vals)
def from_degree_distribution(N, degree_dist, return_pos=False):
number_of_nodes = N * np.array(degree_dist)
degree_sequence = []
for i in range(int(math.floor(len(number_of_nodes)))):
number_with_that_degree = number_of_nodes[i]
for k in range(int(math.floor(number_with_that_degree))):
degree_sequence.append(i)
graphical = nx.is_graphical(degree_sequence)
if not graphical:
degree_sequence.append(1)
G = nx.configuration_model(degree_sequence)
try:
G.remove_edges_from(nx.selfloop_edges(G))
except RuntimeError:
print('No self loops to remove')
if return_pos:
pos = nx.spring_layout(G)
return G, pos
return G, None
def power_law_graph_cuts(size_of_net, x_min, power_law_exponent):
degree_sequence = []
norm_const = float(size_of_net) / sum(
[var**(-power_law_exponent) for var in range(x_min, size_of_net)]
) #The maximum degree fo an undirected simple graph is N-1 where N is size_of_net.
for i in range(x_min, size_of_net):
for j in range(int(round(norm_const * i**(-power_law_exponent)))):
degree_sequence.append(i)
if sum(degree_sequence) % 2 != 0:
if x_min % 2 != 0:
degree_sequence.append(x_min)
else:
degree_sequence.append(x_min + 1)
G = nx.configuration_model(degree_sequence)
G = nx.Graph(G)
G.remove_edges_from(G.selfloop_edges())
return G
def randomized_graph(G,num_randomization=None):
'''
Input:
G: an undirected weighted network
IR_weight_cutoff: threshold on the minimum weight to reach
Output:
E: an undirected weighted graph with the same degree and weight
sequence of G.
'''
if num_randomization==None:
num_randomization=G.number_of_edges();
max_index=0;
print('Begin creation corresponding configuration model...');
weight_dictionary=nx.get_edge_attributes(G,'weight');
weight_sequence=list(weight_dictionary.values());
degree_sequence=list(nx.degree(G).values());
#preliminary scan of edge weights to define filtration steps
print('Preliminary scan of edge weights to define filtration steps...');
edge_weights=[];
edge_weights=list(set(nx.get_edge_attributes(G,'weight').values()));
edge_weights=sorted(edge_weights, reverse=True);
print('Preliminary scan and sorting completed.')
rn.seed(rn.randint(0,1000000)+time.time());
E=nx.configuration_model(degree_sequence);
E=nx.Graph(E);
E.remove_edges_from(E.selfloop_edges())
weight_sequence_temp=weight_sequence;
rn.shuffle(weight_sequence_temp);
print('Setting new weights.');
for e in E.edges_iter():
E.edge[e[0]][e[1]]['weight']=weight_sequence_temp[0];
weight_sequence_temp=weight_sequence_temp[1:];
print('Weights setup completed.');
return E
def min_degree_sbm(num_nodes: int,
num_blocks: int,
p_in: float,
p_out: float,
min_degree: int,
seed: int = 0) -> nx.Graph:
"""
This function creates a minimum degree SBM approximating the input parameters. This
requries that num_nodes / num_blocks is an integer division result.
Note that when min_degree was 2, this failed on the assert for actual_degrees. I
don't know why, so we may need to remove that assert.
"""
# First make the random graph with minimum-degree:
degree_list = [min_degree for i in range(num_nodes)]
rnd_G = nx.configuration_model(degree_list, seed=seed)
# The returned graph is a multigraph, which may have parallel edges. To remove any
# parallel edges from the returned graph...
rnd_G = nx.Graph(rnd_G)
# check
actual_degrees = [d for v, d in rnd_G.degree()]
for i in range(len(actual_degrees)):
if actual_degrees[i] != degree_list[i]:
print('At %d, %d != %d' % (i, actual_degrees[i], degree_list[i]))
assert actual_degrees == degree_list, 'Random graph generator failed'
# Make the SBM
num_nodes_per_block = int(num_nodes / num_blocks)
assert num_nodes_per_block * num_blocks == num_nodes, 'Input number of nodes not '\
'divisible by number of blocks'
sizes = [num_nodes_per_block for b in range(num_blocks)]
probs = p_out * np.ones((num_blocks, num_blocks))
for i in range(num_blocks):
probs[i][i] = p_in
SBM_G = nx.stochastic_block_model(sizes, probs, seed=seed)
# Now merge them and return
return merge_graphs(SBM_G, rnd_G)
def configuration_model(G, verbose=True):
"""
Creates a random graph with the same degree sequence as G.
Arguments:
G (networkx.Graph): Graph for which the degree sequence is from
Returns:
A random graph with the same degree sequence as G (configuration model)
"""
deg_sequence = []
for nid in G.nodes():
deg_sequence.append(G.degree(nid))
config = nx.configuration_model(deg_sequence)
if verbose:
print("Number of nodes: {}".format(nx.number_of_nodes(config)))
print("Number of edges: {}".format(nx.number_of_edges(config)))
return config
def test_havel_hakimi_construction():
G = nx.havel_hakimi_graph([])
assert len(G) == 0
z = [1000, 3, 3, 3, 3, 2, 2, 2, 1, 1, 1]
pytest.raises(nx.NetworkXError, nx.havel_hakimi_graph, z)
z = ["A", 3, 3, 3, 3, 2, 2, 2, 1, 1, 1]
pytest.raises(nx.NetworkXError, nx.havel_hakimi_graph, z)
z = [5, 4, 3, 3, 3, 2, 2, 2]
G = nx.havel_hakimi_graph(z)
G = nx.configuration_model(z)
z = [6, 5, 4, 4, 2, 1, 1, 1]
pytest.raises(nx.NetworkXError, nx.havel_hakimi_graph, z)
z = [10, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2]
G = nx.havel_hakimi_graph(z)
pytest.raises(nx.NetworkXError, nx.havel_hakimi_graph, z, create_using=nx.DiGraph())
def sf_net(n, gamma, k_min):
deg = powerlaw_degree_sequence(n, gamma, k_min)
# ================================================================================
# "sum of all degrees" must be even. Why is that?
if sum(deg) % 2 == 1: # if sum of "deg" is odd
deg[0] += 1 # make it "even"
# ================================================================================
# configure the model with "power-law distributed deg"
G = nx.configuration_model(deg)
# ================================================================================
H = nx.Graph(G)
# ================================================================================
H.remove_edges_from(H.selfloop_edges())
# ================================================================================
return H
def get_C_rand_CM(degSeq, samples=10, package='nx', verbose=False):
C_values = np.zeros(samples)
Cws_values = np.zeros(samples)
for i in range(samples):
if verbose:
print('rand CM, it', i)
if package == 'nx':
g = nx.configuration_model(degSeq, seed=i)
g = nx.Graph(g)
C = nx.transitivity(g)
Cws = nx.average_clustering(g)
elif package == 'ig':
g = ig.Graph().Degree_Sequence(degSeq, method='vl')
C = g.transitivity_undirected(mode='zero')
Cws = g.transitivity_avglocal_undirected(mode='zero')
else:
print('ERROR: Package "{}" not supported'.format(package))
C_values[i] = C
Cws_values[i] = Cws
return C_values, Cws_values
def test_havel_hakimi_construction():
G = nx.havel_hakimi_graph([])
assert_equal(len(G), 0)
z = [1000, 3, 3, 3, 3, 2, 2, 2, 1, 1, 1]
assert_raises(nx.NetworkXError, nx.havel_hakimi_graph, z)
z = ["A", 3, 3, 3, 3, 2, 2, 2, 1, 1, 1]
assert_raises(nx.NetworkXError, nx.havel_hakimi_graph, z)
z = [5, 4, 3, 3, 3, 2, 2, 2]
G = nx.havel_hakimi_graph(z)
G = nx.configuration_model(z)
z = [6, 5, 4, 4, 2, 1, 1, 1]
assert_raises(nx.NetworkXError, nx.havel_hakimi_graph, z)
z = [10, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2]
G = nx.havel_hakimi_graph(z)
assert_raises(nx.NetworkXError, nx.havel_hakimi_graph, z,
create_using=nx.DiGraph())
def random_net(G=None):
'''
Random the network but keep the original node degree roughly
@parameter G - graph
@return GG - random graph that only contains genes
'''
sequence = [d for (_, d) in G.degree]
GG = nx.configuration_model(sequence)
GG = nx.Graph(GG)
GG.remove_edges_from(GG.selfloop_edges())
# re-label
mapping = {i: j for i, j in enumerate(G.nodes)}
GG = nx.relabel_nodes(GG, mapping, copy=False)
for node in GG.nodes:
GG.nodes[node]['type'] = 'gene'
return GG
def __graphlet_configuration_model(self, G_in):
""" Converts network input network into graph sequence and
generates new configuration graph.
Number of edges is not conserved!
"""
if G_in.is_directed():
inseq = G_in.in_degree().values()
outseq = G_in.out_degree().values()
H = nx.directed_configuration_model(inseq, outseq)
H = nx.DiGraph(H)
H.remove_edges_from(H.selfloop_edges())
else:
seq = G_in.degree().values()
H = nx.configuration_model(seq)
H = nx.Graph(H)
H.remove_edges_from(H.selfloop_edges())
return H.edges()
def __graphlet_configuration_model(self, G_in):
""" Converts network input network into graph sequence and
generates new configuration graph.
Number of edges is not conserved!
"""
if G_in.is_directed():
inseq = G_in.in_degree().values()
outseq = G_in.out_degree().values()
H = nx.directed_configuration_model(inseq, outseq)
H = nx.DiGraph(H)
H.remove_edges_from(H.selfloop_edges())
else:
seq = G_in.degree().values()
H = nx.configuration_model(seq)
H = nx.Graph(H)
H.remove_edges_from(H.selfloop_edges())
return H.edges()
def build_random_network(model_path, name="random-network.txt"):
"""
Generates a random network with degree sequence matching the network
at model_path.
Args:
model_path (string)
"""
model_networkx, _, protein_to_node = load_network(model_path)
node_to_protein = {
node: protein
for protein, node in protein_to_node.items()
}
deg_sequence = np.array(model_networkx.degree())[:, 1]
random_network = nx.configuration_model(deg_sequence,
create_using=nx.Graph)
with open(os.path.join("data/networks/", name), 'w') as file:
for edge in random_network.edges():
node_1, node_2 = edge[0], edge[1]
protein_1, protein_2 = node_to_protein[node_1], node_to_protein[
node_2]
file.write(str(protein_1) + " " + str(protein_2) + '\n')
def generate_graph(type='PL', n=100, seed=1.0, parameter=2.1):
if type == 'ER':
G = nx.erdos_renyi_graph(n, p=parameter, seed=seed, directed=True)
G = nx.DiGraph(G)
G.remove_edges_from(G.selfloop_edges())
elif type == 'PL':
z = nx.utils.create_degree_sequence(n,
nx.utils.powerlaw_sequence,
exponent=parameter)
while not nx.is_valid_degree_sequence(z):
z = nx.utils.create_degree_sequence(n,
nx.utils.powerlaw_sequence,
exponent=parameter)
G = nx.configuration_model(z)
G = nx.DiGraph(G)
G.remove_edges_from(G.selfloop_edges())
elif type == 'BA':
G = nx.barabasi_albert_graph(n, 3, seed=None)
G = nx.DiGraph(G)
elif type == 'grid':
G = nx.grid_2d_graph(int(np.ceil(np.sqrt(n))),
int(np.ceil(np.sqrt(n))))
G = nx.DiGraph(G)
elif type in [
'facebook', 'enron', 'twitter', 'students', 'tumblr', 'facebookBig'
]:
#print 'start reading'
#_, G, _, _ = readRealGraph(os.path.join("..","..","Data", type+".txt"))
_, G, _, _ = readRealGraph(os.path.join("..", "Data", type + ".txt"))
print 'size of graph', G.number_of_nodes()
#Gcc = sorted(nx.connected_component_subgraphs(G.to_undirected()), key = len, reverse=True)
#print Gcc[0].number_of_nodes()
#print 'num of connected components', len(sorted(nx.connected_component_subgraphs(G.to_undirected()), key = len, reverse=True))
#exit()
if G.number_of_nodes() > n:
G = getSubgraph(G, n)
#G = getSubgraphSimulation(G, n, infP = 0.3)
#nx.draw(G)
#plt.show()
return G
def job(degree_sequence):
try:
G = nx.configuration_model(degree_sequence)
G = nx.Graph(G) # to remove patallel edges
G.remove_edges_from(G.selfloop_edges())
distinct_prop = distinct(G)
only_best_list = [i for x in zip(*distinct_prop)[1] if len(x)==1 for i in x]
if len(set(only_best_list)) >= 2:
len_best = [len(x) for x in zip(*distinct_prop)[1]]
num_uniq = len(set([i for x in zip(*distinct_prop)[1] for i in x]))
if sum(len_best) < 7 and len_best.count(0) == 0 and num_uniq >= 3:
with open("result.txt", "a") as f:
print ""
print num_uniq, zip(*distinct_prop)
print G.nodes(), G.edges()
print ""
print>>f, num_uniq, zip(*distinct_prop)
print>>f, G.nodes(), G.edges()
except nx.exception.NetworkXError, e:
#print e, degree_sequence
pass
def test_SIR_final_sizes(self):
print("test_SIR_final_sizes")
plt.clf()
G = nx.configuration_model([3, 6, 3, 6, 20] * 10000)
N = G.order()
tau = 0.2
gamma = 1
t, S, I, R = EoN.fast_SIR(G, tau, gamma, initial_infecteds=range(5000))
plt.plot(t, S, color=colors[0], label='simulation', alpha=0.3)
plt.plot(t, I, color=colors[0], alpha=0.3)
plt.plot(t, R, color=colors[0], alpha=0.3)
infected_nodes = EoN.get_infected_nodes(G,
tau,
gamma,
initial_infecteds=range(5000))
A = len(infected_nodes)
print(A)
plt.plot([0, 10], [A, A], label=r'percolation based', alpha=0.3)
A = EoN.Attack_rate_cts_time_from_graph(G, tau, gamma, rho=0.1)
plt.plot([0, 10], [A * N, A * N], '-.', label='analytic', alpha=0.3)
plt.legend(loc='upper right')
plt.savefig('test_SIR_final_sizes')
def weight_preserving_configuration_model(G,filename=' '):
import random as rn
import time
weight_dictionary=nx.get_edge_attributes(G,'weight');
weight_sequence=weight_dictionary.values();
degree_sequence=list(nx.degree(G).values());
rn.seed(rn.randint(0,1000000)+time.time());
E=nx.configuration_model(degree_sequence);
E=nx.Graph(E);
E.remove_edges_from(E.selfloop_edges());
weight_sequence_temp=weight_sequence;
for t in range(100):
rn.shuffle(weight_sequence_temp);
for e in E.edges_iter():
E.edge[e[0]][e[1]]['weight']=weight_sequence_temp[0];
weight_sequence_temp=weight_sequence_temp[1:];
if filename!=' ':
nx.write_weighted_edgelist(E, filename , delimiter=' ', encoding='utf-8')
print('Randomized edgelist dumped to '+ filename);
return E;
