o ]ZŽhÇã@sˆdZddlZddlmZddlmZddlmZddgZ edƒej dd d ddd œd d„ƒƒZ ed ƒej dd d ddd œdd„ƒƒZ dS)zøFunctions 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. éN)Ú NetworkXError)Úpy_random_state)Úcheck_create_usingÚpartial_duplication_graphÚduplication_divergence_graphéT)ZgraphsZ returns_graph©Ú create_usingc CsÊt|ddd}|dks|dks|dks|dkrd}t|ƒ‚||kr%tdƒ‚t ||¡}t||ƒD]2}| d|d¡} | |¡tt || ¡ƒD]} |  ¡|krU|  || ¡qG|  ¡|krb|  || ¡q0|S)aµReturns 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`. create_using : Graph constructor, optional (default=nx.Graph) Graph type to create. If graph instance, then cleared before populated. Multigraph and directed types are not supported and raise a ``NetworkXError``. 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. F©ZdirectedZ multigraphréz3partial duplication graph must have 0 <= p, q <= 1.z+partial duplication graph must have n <= N.) rrÚnxZcomplete_graphÚrangeÚrandintÚadd_nodeÚlistZ all_neighborsÚrandomÚadd_edge) ÚNÚnÚpÚqÚseedr ÚmsgÚGÚnew_nodeZsrc_nodeZnbr_node©rúN/var/www/auris/lib/python3.10/site-packages/networkx/generators/duplication.pyrs$5     €  €éc CsÚ|dks|dkrd|›d}t |¡‚|dkrd}t |¡‚t|ddd}tj|d }| dd¡d}||krk| t|ƒ¡}| |¡d}| |¡D]} |  ¡|krZ| || ¡d }qJ|sc|  |¡n|d7}||ks7|S) aReturns an undirected graph using the duplication-divergence model. A graph of `n` nodes is created by duplicating the initial nodes and retaining edges incident to the original nodes with a retention probability `p`. Parameters ---------- n : int The desired number of nodes in the graph. p : float The probability for retaining the edge of the replicated node. seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. create_using : Graph constructor, optional (default=nx.Graph) Graph type to create. If graph instance, then cleared before populated. Multigraph and directed types are not supported and raise a ``NetworkXError``. Returns ------- G : Graph Raises ------ NetworkXError If `p` is not a valid probability. If `n` is less than 2. Notes ----- This algorithm appears in [1]. This implementation disallows the possibility of generating disconnected graphs. References ---------- .. [1] I. Ispolatov, P. L. Krapivsky, A. Yuryev, "Duplication-divergence model of protein interaction network", Phys. Rev. E, 71, 061911, 2005. r rzNetworkXError p=z is not in [0,1].rz$n must be greater than or equal to 2Fr rT) r rrZ empty_graphrÚchoicerrZ neighborsrÚ remove_node) rrrr rrÚiZ random_nodeÚflagZnbrrrrras0.        € ï)N) Ú__doc__Znetworkxr Znetworkx.exceptionrZnetworkx.utilsrZnetworkx.utils.miscrÚ__all__Z _dispatchablerrrrrrÚs    N