117 lines
4.0 KiB
Python
117 lines
4.0 KiB
Python
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"""Generate graphs with given degree and triangle sequence.
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"""
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import networkx as nx
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from networkx.utils import py_random_state
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__all__ = ["random_clustered_graph"]
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@py_random_state(2)
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def random_clustered_graph(joint_degree_sequence, create_using=None, seed=None):
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r"""Generate a random graph with the given joint independent edge degree and
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triangle degree sequence.
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This uses a configuration model-like approach to generate a random graph
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(with parallel edges and self-loops) by randomly assigning edges to match
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the given joint degree sequence.
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The joint degree sequence is a list of pairs of integers of the form
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$[(d_{1,i}, d_{1,t}), \dotsc, (d_{n,i}, d_{n,t})]$. According to this list,
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vertex $u$ is a member of $d_{u,t}$ triangles and has $d_{u, i}$ other
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edges. The number $d_{u,t}$ is the *triangle degree* of $u$ and the number
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$d_{u,i}$ is the *independent edge degree*.
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Parameters
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----------
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joint_degree_sequence : list of integer pairs
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Each list entry corresponds to the independent edge degree and
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triangle degree of a node.
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create_using : NetworkX graph constructor, optional (default MultiGraph)
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Graph type to create. If graph instance, then cleared before populated.
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seed : integer, random_state, or None (default)
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Indicator of random number generation state.
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See :ref:`Randomness<randomness>`.
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Returns
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-------
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G : MultiGraph
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A graph with the specified degree sequence. Nodes are labeled
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starting at 0 with an index corresponding to the position in
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deg_sequence.
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Raises
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------
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NetworkXError
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If the independent edge degree sequence sum is not even
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or the triangle degree sequence sum is not divisible by 3.
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Notes
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-----
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As described by Miller [1]_ (see also Newman [2]_ for an equivalent
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description).
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A non-graphical degree sequence (not realizable by some simple
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graph) is allowed since this function returns graphs with self
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loops and parallel edges. An exception is raised if the
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independent degree sequence does not have an even sum or the
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triangle degree sequence sum is not divisible by 3.
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This configuration model-like construction process can lead to
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duplicate edges and loops. You can remove the self-loops and
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parallel edges (see below) which will likely result in a graph
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that doesn't have the exact degree sequence specified. This
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"finite-size effect" decreases as the size of the graph increases.
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References
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----------
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.. [1] Joel C. Miller. "Percolation and epidemics in random clustered
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networks". In: Physical review. E, Statistical, nonlinear, and soft
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matter physics 80 (2 Part 1 August 2009).
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.. [2] M. E. J. Newman. "Random Graphs with Clustering".
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In: Physical Review Letters 103 (5 July 2009)
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Examples
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--------
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>>> deg = [(1, 0), (1, 0), (1, 0), (2, 0), (1, 0), (2, 1), (0, 1), (0, 1)]
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>>> G = nx.random_clustered_graph(deg)
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To remove parallel edges:
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>>> G = nx.Graph(G)
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To remove self loops:
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>>> G.remove_edges_from(nx.selfloop_edges(G))
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"""
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# In Python 3, zip() returns an iterator. Make this into a list.
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joint_degree_sequence = list(joint_degree_sequence)
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N = len(joint_degree_sequence)
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G = nx.empty_graph(N, create_using, default=nx.MultiGraph)
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if G.is_directed():
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raise nx.NetworkXError("Directed Graph not supported")
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ilist = []
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tlist = []
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for n in G:
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degrees = joint_degree_sequence[n]
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for icount in range(degrees[0]):
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ilist.append(n)
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for tcount in range(degrees[1]):
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tlist.append(n)
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if len(ilist) % 2 != 0 or len(tlist) % 3 != 0:
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raise nx.NetworkXError("Invalid degree sequence")
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seed.shuffle(ilist)
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seed.shuffle(tlist)
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while ilist:
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G.add_edge(ilist.pop(), ilist.pop())
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while tlist:
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n1 = tlist.pop()
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n2 = tlist.pop()
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n3 = tlist.pop()
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G.add_edges_from([(n1, n2), (n1, n3), (n2, n3)])
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return G
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