wehub-resource-sync
245 lines
6.8 KiB
Python
245 lines
6.8 KiB
Python
import easygraph as eg
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from easygraph.utils.decorators import *
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__all__ = [
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"number_strongly_connected_components",
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"strongly_connected_components",
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"is_strongly_connected",
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"condensation",
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]
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@not_implemented_for("undirected")
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@hybrid("cpp_strongly_connected_components")
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def strongly_connected_components(G):
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"""Generate nodes in strongly connected components of graph.
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Parameters
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----------
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G : EasyGraph Graph
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A directed graph.
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Returns
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-------
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comp : generator of sets
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A generator of sets of nodes, one for each strongly connected
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component of G.
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Raises
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------
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EasyGraphNotImplemented
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If G is undirected.
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Examples
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--------
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Generate a sorted list of strongly connected components, largest first.
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If you only want the largest component, it's more efficient to
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use max instead of sort.
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>>> largest = max(eg.strongly_connected_components(G), key=len)
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See Also
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--------
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connected_components
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Notes
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-----
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Uses Tarjan's algorithm[1]_ with Nuutila's modifications[2]_.
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Nonrecursive version of algorithm.
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References
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----------
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.. [1] Depth-first search and linear graph algorithms, R. Tarjan
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SIAM Journal of Computing 1(2):146-160, (1972).
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.. [2] On finding the strongly connected components in a directed graph.
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E. Nuutila and E. Soisalon-Soinen
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Information Processing Letters 49(1): 9-14, (1994)..
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"""
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preorder = {}
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lowlink = {}
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scc_found = set()
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scc_queue = []
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i = 0 # Preorder counter
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neighbors = {v: iter(G[v]) for v in G}
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for source in G:
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if source not in scc_found:
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queue = [source]
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while queue:
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v = queue[-1]
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if v not in preorder:
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i = i + 1
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preorder[v] = i
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done = True
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for w in neighbors[v]:
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if w not in preorder:
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queue.append(w)
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done = False
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break
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if done:
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lowlink[v] = preorder[v]
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for w in G[v]:
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if w not in scc_found:
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if preorder[w] > preorder[v]:
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lowlink[v] = min([lowlink[v], lowlink[w]])
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else:
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lowlink[v] = min([lowlink[v], preorder[w]])
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queue.pop()
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if lowlink[v] == preorder[v]:
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scc = {v}
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while scc_queue and preorder[scc_queue[-1]] > preorder[v]:
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k = scc_queue.pop()
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scc.add(k)
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scc_found.update(scc)
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yield scc
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else:
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scc_queue.append(v)
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def number_strongly_connected_components(G):
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"""Returns number of strongly connected components in graph.
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Parameters
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----------
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G : Easygraph graph
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A directed graph.
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Returns
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-------
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n : integer
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Number of strongly connected components
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Raises
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------
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EasygraphNotImplemented
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If G is undirected.
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Examples
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--------
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>>> G = eg.DiGraph([(0, 1), (1, 2), (2, 0), (2, 3), (4, 5), (3, 4), (5, 6), (6, 3), (6, 7)])
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>>> eg.number_strongly_connected_components(G)
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3
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See Also
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--------
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strongly_connected_components
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number_connected_components
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Notes
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-----
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For directed graphs only.
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"""
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return sum(1 for scc in strongly_connected_components(G))
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@not_implemented_for("undirected")
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def is_strongly_connected(G):
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"""Test directed graph for strong connectivity.
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A directed graph is strongly connected if and only if every vertex in
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the graph is reachable from every other vertex.
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Parameters
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----------
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G : EasyGraph Graph
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A directed graph.
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Returns
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-------
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connected : bool
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True if the graph is strongly connected, False otherwise.
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Examples
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--------
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>>> G = eg.DiGraph([(0, 1), (1, 2), (2, 3), (3, 0), (2, 4), (4, 2)])
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>>> eg.is_strongly_connected(G)
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True
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>>> G.remove_edge(2, 3)
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>>> eg.is_strongly_connected(G)
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False
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Raises
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------
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EasyGraphNotImplemented
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If G is undirected.
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See Also
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--------
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is_connected
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is_biconnected
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strongly_connected_components
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Notes
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-----
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For directed graphs only.
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"""
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if len(G) == 0:
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raise eg.EasyGraphPointlessConcept(
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"""Connectivity is undefined for the null graph."""
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)
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return len(next(strongly_connected_components(G))) == len(G)
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@not_implemented_for("multigraph")
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@only_implemented_for_Directed_graph
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def condensation(G, scc=None):
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"""Returns the condensation of G.
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The condensation of G is the graph with each of the strongly connected
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components contracted into a single node.
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Parameters
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----------
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G : easygraph.DiGraph
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A directed graph.
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scc: list or generator (optional, default=None)
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Strongly connected components. If provided, the elements in
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`scc` must partition the nodes in `G`. If not provided, it will be
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calculated as scc=strongly_connected_components(G).
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Returns
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-------
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C : easygraph.DiGraph
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The condensation graph C of G. The node labels are integers
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corresponding to the index of the component in the list of
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strongly connected components of G. C has a graph attribute named
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'mapping' with a dictionary mapping the original nodes to the
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nodes in C to which they belong. Each node in C also has a node
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attribute 'members' with the set of original nodes in G that
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form the SCC that the node in C represents.
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Examples
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--------
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# >>> condensation(G)
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Notes
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-----
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After contracting all strongly connected components to a single node,
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the resulting graph is a directed acyclic graph.
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"""
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if scc is None:
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scc = strongly_connected_components(G)
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mapping = {}
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incoming_info = {}
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members = {}
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C = eg.DiGraph()
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# Add mapping dict as graph attribute
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C.graph["mapping"] = mapping
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if len(G) == 0:
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return C
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for i, component in enumerate(scc):
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members[i] = component
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mapping.update((n, i) for n in component)
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number_of_components = i + 1
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for i in range(number_of_components):
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C.add_node(i, member=members[i], incoming=set())
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C.add_nodes(range(number_of_components))
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for edge in G.edges:
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if mapping[edge[0]] != mapping[edge[1]]:
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C.add_edge(mapping[edge[0]], mapping[edge[1]])
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if edge[1] not in incoming_info.keys():
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incoming_info[edge[1]] = set()
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incoming_info[edge[1]].add(edge[0])
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C.graph["incoming_info"] = incoming_info
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return C
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