def star(n_branches: int = 3,
metadata: bool = False) -> Union[sparse.csr_matrix, Bunch]:
"""Star (undirected).
Parameters
----------
n_branches : int
Number of branches.
metadata : bool
If ``True``, return a `Bunch` object with metadata (positions).
Returns
-------
adjacency or graph : Union[sparse.csr_matrix, Bunch]
Adjacency matrix or graph with metadata (positions).
Example
-------
>>> from sknetwork.data import star
>>> adjacency = star()
>>> adjacency.shape
(4, 4)
"""
edges = [(0, i + 1) for i in range(n_branches)]
adjacency = edgelist2adjacency(edges, undirected=True)
if metadata:
graph = Bunch()
graph.adjacency = adjacency
angles = 2 * np.pi * np.arange(n_branches) / n_branches
graph.position = np.vstack([np.cos(angles), np.sin(angles)]).T
return graph
else:
return adjacency
def albert_barabasi(n: int = 100, degree: int = 3, undirected: bool = True, seed: Optional[int] = None) \
-> sparse.csr_matrix:
"""Albert-Barabasi model.
Parameters
----------
n : int
Number of nodes.
degree : int
Degree of incoming nodes (less than **n**).
undirected : bool
If ``True``, return an undirected graph.
seed :
Seed of the random generator (optional).
Returns
-------
adjacency : sparse.csr_matrix
Adjacency matrix.
Example
-------
>>> from sknetwork.data import albert_barabasi
>>> adjacency = albert_barabasi(30, 3)
>>> adjacency.shape
(30, 30)
References
----------
Albert, R., Barabási, L. (2002). `Statistical mechanics of complex networks
<https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.74.47>`_
Reviews of Modern Physics.
"""
np.random.seed(seed)
degrees = np.zeros(n, int)
degrees[:degree] = degree - 1
edges = [(i, j) for i in range(degree) for j in range(i)]
for i in range(degree, n):
neighbors = np.random.choice(i,
p=degrees[:i] / degrees.sum(),
size=degree,
replace=False)
degrees[neighbors] += 1
degrees[i] = degree
edges += [(i, j) for j in neighbors]
return edgelist2adjacency(edges, undirected)
def test_adjacency(self):
edge_list = [(1, 2), (3, 4), (1, 0), (1, 2)]
adjacency = edgelist2adjacency(edge_list)
self.assertEqual(adjacency.nnz, 3)
adjacency = edgelist2adjacency(edge_list, undirected=True)
self.assertEqual(adjacency.nnz, 6)
adjacency = edgelist2adjacency(edge_list, weighted=False)
self.assertEqual(np.max(adjacency.data), 1)
edge_list = [(1, 2, 1), (3, 4, 3), (1, 0, 1), (1, 2, 2)]
adjacency = edgelist2adjacency(edge_list)
self.assertEqual(adjacency.nnz, 3)
self.assertEqual(adjacency[1, 2], 3)
adjacency = edgelist2adjacency(edge_list, undirected=True)
self.assertEqual(adjacency.nnz, 6)
adjacency = edgelist2adjacency(edge_list, weighted=False)
self.assertEqual(np.max(adjacency.data), 1)
def grid(n1: int = 10,
n2: int = 10,
metadata: bool = False) -> Union[sparse.csr_matrix, Bunch]:
"""Grid (undirected).
Parameters
----------
n1, n2 : int
Grid dimension.
metadata : bool
If ``True``, return a `Bunch` object with metadata.
Returns
-------
adjacency or graph : Union[sparse.csr_matrix, Bunch]
Adjacency matrix or graph with metadata (positions).
Example
-------
>>> from sknetwork.data import grid
>>> adjacency = grid(10, 5)
>>> adjacency.shape
(50, 50)
"""
nodes = [(i1, i2) for i1 in range(n1) for i2 in range(n2)]
edges = [((i1, i2), (i1 + 1, i2)) for i1 in range(n1 - 1)
for i2 in range(n2)]
edges += [((i1, i2), (i1, i2 + 1)) for i1 in range(n1)
for i2 in range(n2 - 1)]
node_id = {u: i for i, u in enumerate(nodes)}
edges = list(map(lambda edge: (node_id[edge[0]], node_id[edge[1]]), edges))
adjacency = edgelist2adjacency(edges, undirected=True)
if metadata:
graph = Bunch()
graph.adjacency = adjacency
graph.position = np.array(nodes)
return graph
else:
return adjacency