def test_distance_matrix_equal_across_objects(random_paths):
"""test that the distance matrix is the same if constructed from to path objects with
the same paths but different instances"""
p1 = random_paths(40, 20, num_nodes=9)
p2 = random_paths(40, 20, num_nodes=9)
hon1 = pp.HigherOrderNetwork(paths=p1, k=1)
hon2 = pp.HigherOrderNetwork(paths=p2, k=1)
d_matrix1 = shortest_paths.distance_matrix(hon1)
d_matrix2 = shortest_paths.distance_matrix(hon2)
assert d_matrix1 == d_matrix2
def test_distance_matrix_first_order_eq_dist_matrix(random_paths, paths,
num_nodes):
"""test that the distance matrix of k=1 is equal to
distance_matrix_first_order"""
p = random_paths(paths, 10, num_nodes)
hon = pp.HigherOrderNetwork(p, k=1)
dist = shortest_paths.distance_matrix(hon)
dist_alt = shortest_paths.distance_matrix(hon)
m = dict_of_dicts_to_matrix(dist)
m_alt = dict_of_dicts_to_matrix(dist_alt)
assert np.allclose(m, m_alt)
def test_distance_matrix_first_order(random_paths, n_nodes, k, paths, e_sum):
p = random_paths(paths, 10, n_nodes)
hon_k, hon_1 = pp.HigherOrderNetwork(p, k=k), pp.HigherOrderNetwork(p, k=1)
dist_k = shortest_paths.distance_matrix(hon_k)
dist_1 = shortest_paths.distance_matrix(hon_1)
total_distance = 0
for source, target in itertools.product(hon_1.nodes, hon_1.nodes):
dist_st = dist_k[source][target]
assert dist_1[source][target] <= dist_k[source][target], \
"not all distances at order k are at least as long as at order 1"
if dist_st < np.inf:
total_distance += dist_st
assert total_distance == e_sum
def closeness_centrality(network: Network, normalized: bool = False) -> Dict:
"""Calculates the closeness centrality of all nodes.
.. note::
If `normalized=False` (Default) for each node v the closeness centrality
is given as 1/sum_w(dist(v,w)) where dist(v,w) is the shortest path
distance between v and w. For `normalized=True` the counter is
multiplied by n-1 where n is the number of nodes in the
network. Shortest path distances are calculated using the function
`shortest_paths.distance_matrix`.
Parameters
----------
network : Network
The :py:class:`Network` object that contains the network
normalized : bool
If True the resulting centralities will be normalized based on the
average shortest path length.
Examples
--------
Compute closeness centrality in a simple network
>>> import pathpy as pp
>>> net = pp.Network(directed=False)
>>> net.add_edge('a', 'x')
>>> net.add_edge('x', 'b')
>>> c = pp.algorithms.centralities.closeness_centrality(net)
>>> c['a']
0.3333333333333333
"""
distances = shortest_paths.distance_matrix(network)
cl: defaultdict = defaultdict(float)
mapping = {v: k for k, v in network.nodes.index.items()}
n = network.number_of_nodes()
# calculate closeness values
for d in range(n):
for x in range(n):
if d != x and distances[d, x] < np.inf:
cl[mapping[x]] += distances[d, x]
# assign centrality zero to nodes not occurring
# on higher-order shortest paths
for v in network.nodes.uids:
cl[v] += 0.0
if cl[v] > 0.0:
cl[v] = 1.0 / cl[v]
if normalized:
cl[v] *= n-1
return cl
def test_distance_matrix(random_paths, paths, n_nodes, k, e_var, e_sum):
p = random_paths(paths, 20, num_nodes=n_nodes)
hon = pp.HigherOrderNetwork(paths=p, k=k)
d_matrix = shortest_paths.distance_matrix(hon)
np_matrix = dict_of_dicts_to_matrix(d_matrix)
assert np.var(np_matrix) == pytest.approx(e_var)
assert np.sum(np_matrix) == e_sum
def test_distance_matrix_from_file(path_from_edge_file):
p = path_from_edge_file
hon = pp.HigherOrderNetwork(paths=p, k=1)
d_matrix = shortest_paths.distance_matrix(hon)
np_matrix = dict_of_dicts_to_matrix(d_matrix)
assert np.sum(np_matrix) == 8
assert np.min(np_matrix) == 0
assert np.max(np_matrix) == 2
def _cl_paths(paths: PathCollection,
normalized: bool = False,
disconnected=False,
weight: Optional[str] = None,
count: bool = False) -> Dict:
"""Betweenness Centrality for Paths."""
if disconnected and normalized:
raise ParameterError(
'No meaningful definition for normalized closeness centrality in disconnected networks'
)
node_centralities = defaultdict(lambda: 0)
distances = shortest_paths.distance_matrix(paths,
weight=weight,
count=count)
n = len(paths.nodes)
for v in paths.nodes:
for w in paths.nodes:
if v != w:
if w in distances[v]:
dist = distances[v][w]
else:
dist = np.inf
if disconnected:
node_centralities[v] += 1.0 / dist
else:
node_centralities[v] += dist
for v in paths.nodes:
# assign zero value to nodes not occurring
node_centralities[v] += 0
if not disconnected:
if node_centralities[v] > 0:
node_centralities[v] = 1.0 / node_centralities[v]
else:
node_centralities[v] = np.inf
# normalize
if normalized:
node_centralities[v] *= n - 1
return node_centralities
def _cl_network(network: BaseNetwork,
normalized: bool = False,
disconnected=False,
weight: Optional[str] = None,
count: bool = False) -> Dict:
"""Calculates the closeness centrality of all nodes.
.. note::
If `normalized=False` (Default) for each node v the closeness centrality
is given as 1/sum_w(dist(v,w)) where dist(v,w) is the shortest path
distance between v and w. For `normalized=True` the counter is
multiplied by n-1 where n is the number of nodes in the
network. Shortest path distances are calculated using the function
`shortest_paths.distance_matrix`.
Parameters
----------
network : Network
The :py:class:`Network` object that contains the network
normalized : bool
If True the resulting centralities will be normalized based on the
average shortest path length.
Examples
--------
Compute closeness centrality in a simple network
>>> import pathpy as pp
>>> net = pp.Network(directed=False)
>>> net.add_edge('a', 'x')
>>> net.add_edge('x', 'b')
>>> c = pp.algorithms.centralities.closeness_centrality(net)
>>> c['a']
0.3333333333333333
"""
distances = shortest_paths.distance_matrix(network,
weight=weight,
count=count)
cl: defaultdict = defaultdict(float)
if disconnected and normalized:
raise ParameterError(
'No meaningful definition for normalized closeness centrality in disconnected networks'
)
mapping = {v: k for k, v in network.nodes.index.items()}
n = network.number_of_nodes()
for v in range(n):
for w in range(n):
if v != w:
if disconnected:
cl[mapping[v]] += 1.0 / distances[v, w]
else:
cl[mapping[v]] += distances[v, w]
for v in network.nodes.uids:
# assign centrality zero to nodes not occurring on shortest path
cl[v] += 0.0
if not disconnected:
cl[v] = 1.0 / cl[v]
# normalize
if normalized:
cl[v] *= n - 1
return cl