# Source code for graspy.models.er

from .sbm import SBMEstimator, DCSBMEstimator
from ..utils import import_graph
import numpy as np

[docs]class EREstimator(SBMEstimator): """ Erdos-Reyni Model The Erdos-Reyni (ER) model is a simple random graph model in which the probability of any potential edge in the graph existing is the same for any two nodes :math:i and :math:j. :math:P_{ij} = p for all i, j Read more in the :ref:tutorials <models_tutorials> Parameters ---------- directed : boolean, optional (default=True) Whether to treat the input graph as directed. Even if a directed graph is inupt, this determines whether to force symmetry upon the block probability matrix fit for the SBM. It will also determine whether graphs sampled from the model are directed. loops : boolean, optional (default=False) Whether to allow entries on the diagonal of the adjacency matrix, i.e. loops in the graph where a node connects to itself. Attributes ---------- p_ : float Value between 0 and 1 (inclusive) representing the probability of any edge in the ER graph model p_mat_ : np.ndarray, shape (n_verts, n_verts) Probability matrix :math:P for the fit model, from which graphs could be sampled. See also -------- graspy.models.DCEREstimator graspy.models.SBMEstimator graspy.simulations.er_np References ---------- .. [1] https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_model """ def __init__(self, directed=True, loops=False): super().__init__(directed=directed, loops=loops)
[docs] def fit(self, graph, y=None): graph = import_graph(graph) er = super().fit(graph, y=np.ones(graph.shape[0])) self.p_ = er.block_p_[0, 0] delattr(self, "block_p_") return self
def _n_parameters(self): n_parameters = 1 # p return n_parameters
[docs]class DCEREstimator(DCSBMEstimator): r""" Degree-corrected Erdos-Reyni Model The Degree-corrected Erdos-Reyni (DCER) model is an extension of the ER model in which each node has an additional "promiscuity" parameter :math:\theta_i that determines its expected degree in the graph. :math:P_{ij} = \theta_i \theta_j p Read more in the :ref:tutorials <models_tutorials> Parameters ---------- directed : boolean, optional (default=True) Whether to treat the input graph as directed. Even if a directed graph is inupt, this determines whether to force symmetry upon the block probability matrix fit for the SBM. It will also determine whether graphs sampled from the model are directed. loops : boolean, optional (default=False) Whether to allow entries on the diagonal of the adjacency matrix, i.e. loops in the graph where a node connects to itself. degree_directed : boolean Whether to allow seperate degree correction parameters for the in and out degree of each node. Ignored if directed is False. Attributes ---------- p_ : float The :math:p parameter as described in the above model, which weights the overall probability of connections between any two nodes. p_mat_ : np.ndarray, shape (n_verts, n_verts) Probability matrix :math:P for the fit model, from which graphs could be sampled. degree_corrections_ : np.ndarray, shape (n_verts, 1) or (n_verts, 2) Degree correction vector(s) :math:\theta. If degree_directed parameter was False, then will be of shape (n_verts, 1) and element i represents the degree correction for node :math:i. Otherwise, the first column contains out degree corrections and the second column contains in degree corrections. Notes ----- The DCER model is rarely mentioned in literature, though it is simply a special case of the DCSBM where there is only one community. See also -------- graspy.models.DCSBMEstimator graspy.models.EREstimator graspy.simulations.er_np References ---------- .. [1] https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_model .. [2] Karrer, B., & Newman, M. E. (2011). Stochastic blockmodels and community structure in networks. Physical review E, 83(1), 016107. """ def __init__(self, directed=True, loops=False, degree_directed=False): super().__init__( directed=directed, loops=loops, degree_directed=degree_directed )
[docs] def fit(self, graph, y=None): dcer = super().fit(graph, y=np.ones(graph.shape[0])) self.p_ = dcer.block_p_[0, 0] delattr(self, "block_p_") return self
def _n_parameters(self): n_parameters = 1 # p n_parameters += self.degree_corrections_.size return n_parameters