o h@spdZddlZddlmZddlmZddgZedejddd d d dZ ed ejddd d d dZ dS)zFunctions for generating graphs based on the "duplication" method. These graph generators start with a small initial graph then duplicate nodes and (partially) duplicate their edges. These functions are generally inspired by biological networks. N) NetworkXError)py_random_statepartial_duplication_graphduplication_divergence_graphT)graphs returns_graphc Cs|dks|dks|dks|dkrd}t|||krtdt|}t||D]2}|d|d}||tt||D]} ||krM| || q?||krZ| ||q(|S)aReturns a random graph using the partial duplication model. Parameters ---------- N : int The total number of nodes in the final graph. n : int The number of nodes in the initial clique. p : float The probability of joining each neighbor of a node to the duplicate node. Must be a number in the between zero and one, inclusive. q : float The probability of joining the source node to the duplicate node. Must be a number in the between zero and one, inclusive. seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. Notes ----- A graph of nodes is grown by creating a fully connected graph of size `n`. The following procedure is then repeated until a total of `N` nodes have been reached. 1. A random node, *u*, is picked and a new node, *v*, is created. 2. For each neighbor of *u* an edge from the neighbor to *v* is created with probability `p`. 3. An edge from *u* to *v* is created with probability `q`. This algorithm appears in [1]. This implementation allows the possibility of generating disconnected graphs. References ---------- .. [1] Knudsen Michael, and Carsten Wiuf. "A Markov chain approach to randomly grown graphs." Journal of Applied Mathematics 2008. rz3partial duplication graph must have 0 <= p, q <= 1.z+partial duplication graph must have n <= N.) rnxcomplete_graphrangerandintadd_nodelist all_neighborsrandomadd_edge) NnpqseedmsgGnew_nodesrc_nodenbr_noderZ/var/www/html/env_mimamsha/lib/python3.10/site-packages/networkx/generators/duplication.pyrs" 1      c Cs|dks|dkrd|d}t||dkrd}t|t}|ddd}||krb|t|}||d}||D]}||krQ|||d}qA|sZ| |n|d7}||ks.|S) aReturns an undirected graph using the duplication-divergence model. A graph of `n` nodes is created by duplicating the initial nodes and retaining edges incident to the original nodes with a retention probability `p`. Parameters ---------- n : int The desired number of nodes in the graph. p : float The probability for retaining the edge of the replicated node. seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. Returns ------- G : Graph Raises ------ NetworkXError If `p` is not a valid probability. If `n` is less than 2. Notes ----- This algorithm appears in [1]. This implementation disallows the possibility of generating disconnected graphs. References ---------- .. [1] I. Ispolatov, P. L. Krapivsky, A. Yuryev, "Duplication-divergence model of protein interaction network", Phys. Rev. E, 71, 061911, 2005. r rzNetworkXError p=z is not in [0,1].rz$n must be greater than or equal to 2FT) r rGraphrchoicerr neighborsr remove_node) rrrrri random_nodeflagnbrrrrrZs.+        )N) __doc__networkxr networkx.exceptionrnetworkx.utilsr__all__ _dispatchablerrrrrrs   I