ó ,µ[c@srdZddlZddlmZddlmZddgZedƒdd„ƒZ ed ƒdd „ƒZ dS( søFunctions 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. iÿÿÿÿN(tpy_random_state(t NetworkXErrortpartial_duplication_graphtduplication_divergence_graphic Cs|dks0|dks0|dks0|dkrEd}t|ƒ‚n||kr`tdƒ‚ntj|ƒ}x£t||ƒD]’}|j|ƒ|jd|ƒ}|jƒ|krÉ|j||ƒnxEttj ||ƒƒD]+} |jƒ|krâ|j|| ƒqâqâWqW|S(sÊReturn 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. iis3partial duplication graph must have 0 <= p, q <= 1.s+partial duplication graph must have n <= N.( Rtnxtcomplete_graphtrangetadd_nodetrandinttrandomtadd_edgetlistt all_neighbors( tNtntptqtseedtmsgtGtnew_nodetsrc_nodet neighbor_node((s>lib/python2.7/site-packages/networkx/generators/duplication.pyRs00  ic Cs#|dks|dkr9dj|ƒ}tj|ƒ‚n|dkr]d}tj|ƒ‚ntjƒ}|jddƒd}x||kr|jt|ƒƒ}|j|ƒt}xB|j |ƒD]1}|j ƒ|krÆ|j||ƒt }qÆqÆW|s|j |ƒq‚|d7}q‚W|S(sReturns 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. iis$NetworkXError p={0} is not in [0,1].is$n must be greater than or equal to 2( tformatRRtGraphR tchoiceR RtFalset neighborsR tTruet remove_node( RRRRRtit random_nodetflagtnbr((s>lib/python2.7/site-packages/networkx/generators/duplication.pyRes**    ( t__doc__tnetworkxRtnetworkx.utilsRtnetworkx.exceptionRt__all__tNoneRR(((s>lib/python2.7/site-packages/networkx/generators/duplication.pyts   I