193 lines
6 KiB
Python
193 lines
6 KiB
Python
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"""
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Provides functions for finding and testing for locally `(k, l)`-connected
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graphs.
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"""
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import copy
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import networkx as nx
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__all__ = ["kl_connected_subgraph", "is_kl_connected"]
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def kl_connected_subgraph(G, k, l, low_memory=False, same_as_graph=False):
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"""Returns the maximum locally `(k, l)`-connected subgraph of `G`.
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A graph is locally `(k, l)`-connected if for each edge `(u, v)` in the
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graph there are at least `l` edge-disjoint paths of length at most `k`
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joining `u` to `v`.
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Parameters
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----------
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G : NetworkX graph
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The graph in which to find a maximum locally `(k, l)`-connected
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subgraph.
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k : integer
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The maximum length of paths to consider. A higher number means a looser
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connectivity requirement.
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l : integer
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The number of edge-disjoint paths. A higher number means a stricter
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connectivity requirement.
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low_memory : bool
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If this is True, this function uses an algorithm that uses slightly
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more time but less memory.
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same_as_graph : bool
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If True then return a tuple of the form `(H, is_same)`,
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where `H` is the maximum locally `(k, l)`-connected subgraph and
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`is_same` is a Boolean representing whether `G` is locally `(k,
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l)`-connected (and hence, whether `H` is simply a copy of the input
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graph `G`).
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Returns
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-------
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NetworkX graph or two-tuple
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If `same_as_graph` is True, then this function returns a
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two-tuple as described above. Otherwise, it returns only the maximum
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locally `(k, l)`-connected subgraph.
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See also
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--------
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is_kl_connected
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References
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----------
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.. [1]: Chung, Fan and Linyuan Lu. "The Small World Phenomenon in Hybrid
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Power Law Graphs." *Complex Networks*. Springer Berlin Heidelberg,
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2004. 89--104.
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"""
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H = copy.deepcopy(G) # subgraph we construct by removing from G
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graphOK = True
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deleted_some = True # hack to start off the while loop
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while deleted_some:
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deleted_some = False
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# We use `for edge in list(H.edges()):` instead of
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# `for edge in H.edges():` because we edit the graph `H` in
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# the loop. Hence using an iterator will result in
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# `RuntimeError: dictionary changed size during iteration`
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for edge in list(H.edges()):
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(u, v) = edge
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# Get copy of graph needed for this search
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if low_memory:
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verts = {u, v}
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for i in range(k):
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for w in verts.copy():
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verts.update(G[w])
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G2 = G.subgraph(verts).copy()
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else:
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G2 = copy.deepcopy(G)
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###
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path = [u, v]
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cnt = 0
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accept = 0
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while path:
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cnt += 1 # Found a path
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if cnt >= l:
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accept = 1
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break
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# record edges along this graph
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prev = u
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for w in path:
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if prev != w:
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G2.remove_edge(prev, w)
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prev = w
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# path = shortest_path(G2, u, v, k) # ??? should "Cutoff" be k+1?
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try:
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path = nx.shortest_path(G2, u, v) # ??? should "Cutoff" be k+1?
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except nx.NetworkXNoPath:
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path = False
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# No Other Paths
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if accept == 0:
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H.remove_edge(u, v)
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deleted_some = True
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if graphOK:
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graphOK = False
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# We looked through all edges and removed none of them.
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# So, H is the maximal (k,l)-connected subgraph of G
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if same_as_graph:
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return (H, graphOK)
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return H
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def is_kl_connected(G, k, l, low_memory=False):
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"""Returns True if and only if `G` is locally `(k, l)`-connected.
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A graph is locally `(k, l)`-connected if for each edge `(u, v)` in the
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graph there are at least `l` edge-disjoint paths of length at most `k`
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joining `u` to `v`.
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Parameters
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----------
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G : NetworkX graph
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The graph to test for local `(k, l)`-connectedness.
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k : integer
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The maximum length of paths to consider. A higher number means a looser
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connectivity requirement.
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l : integer
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The number of edge-disjoint paths. A higher number means a stricter
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connectivity requirement.
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low_memory : bool
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If this is True, this function uses an algorithm that uses slightly
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more time but less memory.
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Returns
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-------
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bool
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Whether the graph is locally `(k, l)`-connected subgraph.
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See also
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--------
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kl_connected_subgraph
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References
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----------
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.. [1]: Chung, Fan and Linyuan Lu. "The Small World Phenomenon in Hybrid
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Power Law Graphs." *Complex Networks*. Springer Berlin Heidelberg,
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2004. 89--104.
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"""
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graphOK = True
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for edge in G.edges():
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(u, v) = edge
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# Get copy of graph needed for this search
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if low_memory:
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verts = {u, v}
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for i in range(k):
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[verts.update(G.neighbors(w)) for w in verts.copy()]
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G2 = G.subgraph(verts)
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else:
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G2 = copy.deepcopy(G)
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###
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path = [u, v]
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cnt = 0
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accept = 0
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while path:
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cnt += 1 # Found a path
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if cnt >= l:
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accept = 1
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break
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# record edges along this graph
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prev = u
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for w in path:
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if w != prev:
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G2.remove_edge(prev, w)
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prev = w
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# path = shortest_path(G2, u, v, k) # ??? should "Cutoff" be k+1?
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try:
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path = nx.shortest_path(G2, u, v) # ??? should "Cutoff" be k+1?
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except nx.NetworkXNoPath:
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path = False
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# No Other Paths
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if accept == 0:
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graphOK = False
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break
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# return status
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return graphOK
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