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Diffstat (limited to '.venv/lib/python3.12/site-packages/networkx/generators/duplication.py')
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diff --git a/.venv/lib/python3.12/site-packages/networkx/generators/duplication.py b/.venv/lib/python3.12/site-packages/networkx/generators/duplication.py new file mode 100644 index 00000000..3c3ade63 --- /dev/null +++ b/.venv/lib/python3.12/site-packages/networkx/generators/duplication.py @@ -0,0 +1,174 @@ +"""Functions 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. + +""" + +import networkx as nx +from networkx.exception import NetworkXError +from networkx.utils import py_random_state +from networkx.utils.misc import check_create_using + +__all__ = ["partial_duplication_graph", "duplication_divergence_graph"] + + +@py_random_state(4) +@nx._dispatchable(graphs=None, returns_graph=True) +def partial_duplication_graph(N, n, p, q, seed=None, *, create_using=None): + """Returns 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<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. + <https://doi.org/10.1155/2008/190836> + + """ + create_using = check_create_using(create_using, directed=False, multigraph=False) + if p < 0 or p > 1 or q < 0 or q > 1: + msg = "partial duplication graph must have 0 <= p, q <= 1." + raise NetworkXError(msg) + if n > N: + raise NetworkXError("partial duplication graph must have n <= N.") + + G = nx.complete_graph(n, create_using) + for new_node in range(n, N): + # Pick a random vertex, u, already in the graph. + src_node = seed.randint(0, new_node - 1) + + # Add a new vertex, v, to the graph. + G.add_node(new_node) + + # For each neighbor of u... + for nbr_node in list(nx.all_neighbors(G, src_node)): + # Add the neighbor to v with probability p. + if seed.random() < p: + G.add_edge(new_node, nbr_node) + + # Join v and u with probability q. + if seed.random() < q: + G.add_edge(new_node, src_node) + return G + + +@py_random_state(2) +@nx._dispatchable(graphs=None, returns_graph=True) +def duplication_divergence_graph(n, p, seed=None, *, create_using=None): + """Returns 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<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. + + """ + if p > 1 or p < 0: + msg = f"NetworkXError p={p} is not in [0,1]." + raise nx.NetworkXError(msg) + if n < 2: + msg = "n must be greater than or equal to 2" + raise nx.NetworkXError(msg) + + create_using = check_create_using(create_using, directed=False, multigraph=False) + G = nx.empty_graph(create_using=create_using) + + # Initialize the graph with two connected nodes. + G.add_edge(0, 1) + i = 2 + while i < n: + # Choose a random node from current graph to duplicate. + random_node = seed.choice(list(G)) + # Make the replica. + G.add_node(i) + # flag indicates whether at least one edge is connected on the replica. + flag = False + for nbr in G.neighbors(random_node): + if seed.random() < p: + # Link retention step. + G.add_edge(i, nbr) + flag = True + if not flag: + # Delete replica if no edges retained. + G.remove_node(i) + else: + # Successful duplication. + i += 1 + return G |