probinet.synthetic.dynamic

Class definition of the reciprocity generative models with the member functions required.

Functions

eq_c(c, M, N, E, rho_a, mu)	Compute the value of a function used to find the value of the sparsity parameter 'c'.
membership_vectors(rng[, L1, eta, alpha, ...])	Compute the NxK membership vectors u, v using a Dirichlet or a Gamma distribution.

Classes

SyntheticDynCRep(N, K[, T, eta, L, ...])

A class to generate a synthetic network using the DynCRep models.

class probinet.synthetic.dynamic.SyntheticDynCRep(N: int, K: int, T: int = 1, eta: float = 0.0, L: int = 1, avg_degree: float = 5.0, verbose: int = 0, beta: float = 0.2, ag: float = 1.0, bg: float = 0.5, eta_dir: float = 0.5, L1: bool = True, corr: float = 1.0, over: float = 0.0, label: str | None = None, end_file: str = '.dat', folder: Path = PosixPath('outputs'), structure: str = 'assortative', output_parameters: bool = False, output_adj: bool = False, outfile_adj: str | None = None, figsize: Tuple[int, int] = (7, 7), fontsize: int = 15, ExpM: ndarray | None = None, rng: Generator | None = None)

A class to generate a synthetic network using the DynCRep models.

Exp_ija_matrix(u, v, w)

Compute the expected adjacency matrix for the DynCRep models.

Parameters:

• u (np.ndarray) – Outgoing membership matrix.

• v (np.ndarray) – Incoming membership matrix.

• w (np.ndarray) – Affinity tensor.

Returns:

Exp_ija – Expected adjacency matrix.

Return type:

np.ndarray

check_reciprocity_tm1(A: List[coo_matrix]) → None

Check the reciprocity of the adjacency matrices at time t and t-1.

Parameters:

A (List[scipy.sparse.coo_matrix]) – List of adjacency matrices for each time step.

generate_net(parameters=None)

Generate a directed, possibly weighted network by using DynCRep.

Steps:

1. Generate a network A[0].

2. Extract A[t] entries (network edges) using transition probabilities.

Parameters:

parameters (dict) – Latent variables eta, beta, u, v and w.

Returns:

G – NetworkX DiGraph object. Self-loops allowed.

Return type:

networkx.classes.digraph.DiGraph

probinet.synthetic.dynamic.eq_c(c: float, M: ndarray, N: int, E: int, rho_a: float, mu: float) → float

Compute the value of a function used to find the value of the sparsity parameter ‘c’.

Parameters:

• c (float) – The sparsity parameter.

• M (np.ndarray) – The matrix representing the expected number of edges between each pair of nodes.

• N (int) – The number of nodes in the network.

• E (int) – The expected total number of edges in the network.

• rho_a (float) – The expected proportion of reciprocal edges in the network.

• mu (float) – The proportion of reciprocal edges in the Erdos-Renyi network.

Returns:

The value of the function for the given parameters.

Return type:

float

probinet.synthetic.dynamic.membership_vectors(rng: Generator, L1: bool = False, eta: float = 0.5, alpha: float = 0.6, beta: float = 1, K: int = 2, N: int = 100, corr: float = 0.0, over: float = 0.0) → Tuple[ndarray, ndarray]

Compute the NxK membership vectors u, v using a Dirichlet or a Gamma distribution.

Parameters:

• rng (np.random.Generator) – Random number generator container.

• L1 (bool) – Flag for parameter generation method. True for Dirichlet, False for Gamma.

• eta (float) – Parameter for Dirichlet.

• alpha (float) – Parameter (alpha) for Gamma.

• beta (float) – Parameter (beta) for Gamma.

• K (int) – Number of communities.

• N (int) – Number of nodes.

• corr (float) – Correlation between u and v synthetically generated.

• over (float) – Fraction of nodes with mixed membership.

Returns:

uNumpy array

Matrix NxK of out-going membership vectors, positive element-wise. Possibly None if in pure SpringRank or pure Multitensor. With unitary L1 norm computed row-wise.

vNumpy array

Matrix NxK of in-coming membership vectors, positive element-wise. Possibly None if in pure SpringRank or pure Multitensor. With unitary L1 norm computed row-wise.

Return type:

Tuple[np.ndarray, np.ndarray]