def _communicability_to_anchors(graph, anchors, normalize=False):
comm = {}
for node, comm_dict in nx.communicability_exp(graph).items():
d = np.array([comm_dict[a] for a in anchors])
if normalize:
d = normalized(d)
comm[node] = d
return comm
def visualize_communicability():
if len(sys.argv) < 2:
print(f'Usage {sys.argv[1]} <network>')
return
net = fio.read_network(sys.argv[1])
name = fio.get_network_name(sys.argv[1])
communicability = nx.communicability_exp(net.G)
scores = np.array(
[sum(communicability[u].values()) for u in communicability.keys()])
plt.title(f'{name}\nCommunicability')
plt.hist(scores) # type: ignore
plt.show(block=False)
print(f'Network score: {np.sum(scores)}')
scores = (scores - np.min(scores)) / (np.max(scores) - np.min(scores))
node_size = 300 * scores
visualize_network(net.G, net.layout, name, node_size=node_size)
def getHugeStats(g):
if nx.is_directed(g) == True:
P1 = pd.DataFrame({'load_centrality': nx.load_centrality(g, weight='weight'),
'betweenness_centrality': nx.betweenness_centrality(g, weight='weight'),
'pagerank': pd.Series(nx.pagerank(g, alpha=0.85, personalization=None, max_iter=100, tol=1e-08, nstart=None, weight='weight')),
'eigenvector_centrality': nx.eigenvector_centrality_numpy(g),
'degree_centrality': pd.Series(nx.degree_centrality(g)),
'in_degree_centrality': pd.Series(nx.in_degree_centrality(g)),
'out_degree_centrality': pd.Series(nx.out_degree_centrality(g))})
else:
P1 = pd.Panel({'spl': pd.DataFrame(nx.shortest_path_length(g)),
'apdp': pd.DataFrame(nx.all_pairs_dijkstra_path(g)),
'apdl': pd.DataFrame(nx.all_pairs_dijkstra_path_length(g)),
'c_exp': pd.DataFrame(nx.communicability_exp(g))})
return P1
def save_communicabilities():
network_classes = (
'BarabasiAlbert(N=500,m=2)', 'BarabasiAlbert(N=500,m=3)',
'BarabasiAlbert(N=500,m=4)',
'ConnComm(N_comm=10,ib=(5, 10),num_comms=50,ob=(3, 6))',
'ConnComm(N_comm=20,ib=(15, 20),num_comms=25,ob=(3, 6))',
'ErdosRenyi(N=500,p=0.01)', 'ErdosRenyi(N=500,p=0.02)',
'ErdosRenyi(N=500,p=0.03)', 'WattsStrogatz(N=500,k=4,p=0.01)',
'WattsStrogatz(N=500,k=4,p=0.02)', 'WattsStrogatz(N=500,k=5,p=0.01)')
rows = []
for class_name in tqdm(network_classes):
nets = fio.read_network_class(class_name)
communicabilties = (sum(
c for inner_values in nx.communicability_exp(net.G).values()
for c in inner_values.values()) for net in tqdm(nets))
rows.append([class_name])
rows.append(list(map(str, communicabilties)))
with open('communicabilities.csv', 'w', newline='') as csv_file:
writer = csv.writer(csv_file)
writer.writerows(rows)
def infection_entropy_vs_communicability():
classes = ('BarabasiAlbert(N=500,m=2)', 'BarabasiAlbert(N=500,m=3)',
'BarabasiAlbert(N=500,m=4)',
'ConnComm(N_comm=10,ib=(5, 10),num_comms=50,ob=(3, 6))',
'ConnComm(N_comm=20,ib=(15, 20),num_comms=25,ob=(3, 6))',
'ErdosRenyi(N=500,p=0.01)', 'ErdosRenyi(N=500,p=0.02)',
'ErdosRenyi(N=500,p=0.03)', 'WattsStrogatz(N=500,k=4,p=0.01)',
'WattsStrogatz(N=500,k=4,p=0.02)',
'WattsStrogatz(N=500,k=5,p=0.01)')
n_bins = 100 # 1000 should be 1 decimal point of precision for percentages
csv_rows: List[Union[List[str], List[int], List[float]]] = []
for class_ in classes:
rng = np.random.default_rng(777)
nets = fio.read_network_class(class_)
communicabilities: List[int] = [
sum(cell for row in nx.communicability_exp(net.G).values()
for cell in row.values())
for net in tqdm(nets, desc='Communicability')
]
entropies = [
calc_entropy(
run_sim_batch(net, 500, sd.Disease(4, .3),
sd.SimplePressureBehavior(net, rng, 2, .25),
rng), n_bins)
for net in tqdm(nets, 'Simulations & Entropy')
]
csv_rows.append(['Network Class', class_])
csv_rows.append(['Communicability'])
csv_rows.append(communicabilities)
csv_rows.append(['Entropy'])
csv_rows.append(entropies)
with open(
f'results/communicability-vs-infection-entropy-bins-{n_bins}.csv',
'w',
newline='') as csv_file:
writer = csv.writer(csv_file)
writer.writerows(csv_rows)
def dist(self, G1, G2):
r"""Compares the communicability matrix of two graphs.
This distance is based on the communicability matrix, :math:`C`, of
a graph consisting of elements :math:`c_{ij}` which are values
corresponding to the numbers of shortest paths of length :math:`k`
between nodes :math:`i` and :math:`j`.
The commmunicability matrix is symmetric, which means the
communicability sequence is formed by flattening the upper
triangular of :math:`C`, which is then normalized to create the
communicability sequence, :math:`P`.
The communicability sequence entropy distance between two graphs,
`G1` and `G2`, is the Jensen-Shannon divergence between these
communicability sequence distributions, :math:`P1` and :math:`P2`
of the two graphs.
Parameters
----------
G1, G2 (nx.Graph)
two graphs
Returns
-------
dist (float)
between zero and one, this is the communicability sequence
distance bewtween `G1` and `G2`.
Notes
-----
This function uses the networkx approximation of the
communicability of a graph, `nx.communicability_exp`, which
requires `G1` and `G2` to be simple undirected networks. In
addition to the final distance scalar, `self.results` stores the
two vectors :math:`P1` and :math:`P2`, their mixed vector,
:math:`P0`, and their associated entropies.
References
----------
.. [1] Estrada, E., & Hatano, N. (2008). Communicability in complex
networks. Physical Review E, 77(3), 036111.
https://journals.aps.org/pre/abstract/10.1103/PhysRevE.77.036111
.. [2] Chen, D., Shi, D. D., Qin, M., Xu, S. M., & Pan,
G. J. (2018). Complex network comparison based on
communicability sequence entropy. Physical Review E, 98(1),
012319.
"""
N1 = G1.number_of_nodes()
N2 = G2.number_of_nodes()
C1 = nx.communicability_exp(G1)
C2 = nx.communicability_exp(G2)
Ca1 = np.zeros((N1, N1))
Ca2 = np.zeros((N2, N2))
for i in range(Ca1.shape[0]):
Ca1[i] = np.array(list(C1[i].values()))
for i in range(Ca2.shape[0]):
Ca2[i] = np.array(list(C2[i].values()))
lil_sigma1 = np.triu(Ca1).flatten()
lil_sigma2 = np.triu(Ca2).flatten()
big_sigma1 = sum(lil_sigma1[np.nonzero(lil_sigma1)[0]])
big_sigma2 = sum(lil_sigma2[np.nonzero(lil_sigma2)[0]])
P1 = lil_sigma1 / big_sigma1
P2 = lil_sigma2 / big_sigma2
P1 = np.array(sorted(P1))
P2 = np.array(sorted(P2))
dist = entropy.js_divergence(P1, P2)
self.results['P1'] = P1
self.results['P2'] = P2
self.results['dist'] = dist
return dist
def centrality(self):
result = {}
result['degree_centrality'] = nx.degree_centrality(self.graph)
if self.directed == 'directed':
result['in_degree_centrality'] = nx.in_degree_centrality(
self.graph)
result['out_degree_centrality'] = nx.out_degree_centrality(
self.graph)
result['closeness_centrality'] = nx.closeness_centrality(self.graph)
result['betweenness_centrality'] = nx.betweenness_centrality(
self.graph)
# fix the tuple cant decode into json problem
stringify_temp = {}
temp = nx.edge_betweenness_centrality(self.graph)
for key in temp.keys():
stringify_temp[str(key)] = temp[key]
result['edge_betweenness_centrality'] = stringify_temp
if self.directed == 'undirected':
result[
'current_flow_closeness_centrality'] = nx.current_flow_closeness_centrality(
self.graph)
result[
'current_flow_betweenness_centrality'] = nx.current_flow_betweenness_centrality(
self.graph)
stringify_temp = {}
temp = nx.edge_current_flow_betweenness_centrality(self.graph)
for key in temp.keys():
stringify_temp[str(key)] = temp[key]
result['edge_current_flow_betweenness_centrality'] = stringify_temp
result[
'approximate_current_flow_betweenness_centrality'] = nx.approximate_current_flow_betweenness_centrality(
self.graph)
result['eigenvector_centrality'] = nx.eigenvector_centrality(
self.graph)
result[
'eigenvector_centrality_numpy'] = nx.eigenvector_centrality_numpy(
self.graph)
result['katz_centrality'] = nx.katz_centrality(self.graph)
result['katz_centrality_numpy'] = nx.katz_centrality_numpy(
self.graph)
result['communicability'] = nx.communicability(self.graph)
result['communicability_exp'] = nx.communicability_exp(self.graph)
result[
'communicability_centrality'] = nx.communicability_centrality(
self.graph)
result[
'communicability_centrality_exp'] = nx.communicability_centrality_exp(
self.graph)
result[
'communicability_betweenness_centrality'] = nx.communicability_betweenness_centrality(
self.graph)
result['estrada_index'] = nx.estrada_index(self.graph)
result['load_centrality'] = nx.load_centrality(self.graph)
stringify_temp = {}
temp = nx.edge_load(self.graph)
for key in temp.keys():
stringify_temp[str(key)] = temp[key]
result['edge_load'] = stringify_temp
result['dispersion'] = nx.dispersion(self.graph)
fname_centra = self.DIR + '/centrality.json'
with open(fname_centra, "w") as f:
json.dump(result, f, cls=SetEncoder, indent=2)
print(fname_centra)
def low_communicability_objective(edges_present: np.ndarray) -> float:
"""Accept a bitset of edges and return the sum of the communicability values."""
net = lib.edge_set_to_network(edges_present)
communicability = nx.communicability_exp(net.G)
return sum(c for inner_values in communicability.values() for c in inner_values.values())
def dist(self, G1, G2):
"""
This distance is based on the communicability matrix, $C$, of a graph
consisting of elements $c_{ij}$ which are values corresponding to the
numbers of shortest paths of length $k$ between nodes $i$ and $j$.
See: Estrada, E., & Hatano, N. (2008). Communicability in complex
networks. Physical Review E, 77(3), 036111.
https://journals.aps.org/pre/abstract/10.1103/PhysRevE.77.036111
for a full introduction.
The commmunicability matrix is symmetric, which means the
communicability sequence is formed by flattening the upper
triangular of $C$, which is then normalized to create the
communicability sequence, $P$.
The communicability sequence entropy distance between two graphs, $G1$
and $G2$, is the Jensen-Shannon divergence between these communicability
sequence distributions, $P1$ and $P2$ of the two graphs.
Note: this function uses the networkx approximation of the
communicability of a graph, `nx.communicability_exp`, which requires
G1 and G2 to be simple undirected networks. In addition to the final
distance scalar, `self.results` stores the two vectors $P1$ and $P2$,
their mixed vector, $P0$, and their associated entropies.
Params
------
G1 (nx.Graph): the first graph
G2 (nx.Graph): the second graph
Returns
-------
dist (float): between zero and one, this is the communicability
sequence distance bewtween G1 and G2.
"""
N1 = G1.number_of_nodes()
N2 = G2.number_of_nodes()
C1 = nx.communicability_exp(G1)
C2 = nx.communicability_exp(G2)
Ca1 = np.zeros((N1, N1))
Ca2 = np.zeros((N2, N2))
for i in range(Ca1.shape[0]):
Ca1[i] = np.array(list(C1[i].values()))
for i in range(Ca2.shape[0]):
Ca2[i] = np.array(list(C2[i].values()))
lil_sigma1 = np.triu(Ca1).flatten()
lil_sigma2 = np.triu(Ca2).flatten()
big_sigma1 = sum(lil_sigma1[np.nonzero(lil_sigma1)[0]])
big_sigma2 = sum(lil_sigma2[np.nonzero(lil_sigma2)[0]])
P1 = lil_sigma1 / big_sigma1
P2 = lil_sigma2 / big_sigma2
P0 = (P1 + P2) / 2
H1 = sp.stats.entropy(P1)
H2 = sp.stats.entropy(P2)
H0 = sp.stats.entropy(P0)
dist = np.sqrt(H0 - 0.5 * (H1 + H2))
self.results['P1'] = P1
self.results['P2'] = P2
self.results['P0'] = P0
self.results['entropy_1'] = H1
self.results['entropy_2'] = H2
self.results['entropy_mixture'] = H0
self.results['dist'] = dist
return dist
def communicability_exp(uG, ni, nj, rand_node):
c = nx.communicability_exp(uG)
return c[ni][nj], c[ni][rand_node]
