U td,@szdZddlmZddlmZGdddeZGdddeZdd Zdd d ZdddZ dddZ dddZ dddZ d S)z.Classes representing cuts and flows on graphs.) GraphBase)VertexClusteringcsbeZdZdZdfdd ZddZddZed d Zed d Z ed dZ eddZ Z S)CutaA cut of a given graph. This is a simple class used to represent cuts returned by L{Graph.mincut()}, L{Graph.all_st_cuts()} and other functions that calculate cuts. A cut is a special vertex clustering with only two clusters. Besides the usual L{VertexClustering} methods, it also has the following attributes: - C{value} - the value (capacity) of the cut. It is equal to the number of edges if there are no capacities on the edges. - C{partition} - vertex IDs in the parts created after removing edges in the cut - C{cut} - edge IDs in the cut - C{es} - an edge selector restricted to the edges in the cut. You can use indexing on this object to obtain lists of vertex IDs for both sides of the partition. This class is usually not instantiated directly, everything is taken care of by the functions that return cuts. Examples: >>> from igraph import Graph >>> g = Graph.Ring(20) >>> mc = g.mincut() >>> print(mc.value) 2.0 >>> print(min(len(x) for x in mc)) 1 >>> mc.es["color"] = "red" Ncst|dks|dkrtddg|}|D] }d||<q*t|||dkrVt|}t||_t||_||_ dS)zInitializes the cut. This should not be called directly, everything is taken care of by the functions that return cuts. Nzpartition and cut must be givenr) ValueErrorvcountsuper__init__lenfloat_valuesorted _partition_cut)selfgraphvaluecut partitionZ partition2Z membershipZvid __class__C/home/sam/Atlas/atlas_env/lib/python3.8/site-packages/igraph/cut.pyr 4s   z Cut.__init__cCsd|jj|j|j|j|jfS)Nz%s(%r, %r, %r, %r))r__name___graphr rrrrrr__repr__Lsz Cut.__repr__cCs.dt|jt|j|jt|j|jfS)Nz3Graph cut (%d edges, %d vs %d vertices, value=%.4f)r rrrrr rrrr__str__Us z Cut.__str__cCs|jj|jS)z.Returns an edge selector restricted to the cut)resselectrrrrrr]szCut.escCst|S)z7Returns the vertex IDs partitioned according to the cut)listrrrrrbsz Cut.partitioncCs|jS)zReturns the edge IDs in the cut)rrrrrrgszCut.cutcCs|jS)z-Returns the sum of edge capacities in the cut)r rrrrrlsz Cut.value)NNNN) r __module__ __qualname____doc__r rrpropertyrrrr __classcell__rrrrr s(    rcs<eZdZdZfddZddZddZedd ZZ S) FlowaA flow of a given graph. This is a simple class used to represent flows returned by L{Graph.maxflow}. It has the following attributes: - C{graph} - the graph on which this flow is defined - C{value} - the value (capacity) of the flow - C{flow} - the flow values on each edge. For directed graphs, this is simply a list where element M{i} corresponds to the flow on edge M{i}. For undirected graphs, the direction of the flow is not constrained (since the edges are undirected), hence positive flow always means a flow from the smaller vertex ID to the larger, while negative flow means a flow from the larger vertex ID to the smaller. - C{cut} - edge IDs in the minimal cut corresponding to the flow. - C{partition} - vertex IDs in the parts created after removing edges in the cut - C{es} - an edge selector restricted to the edges in the cut. This class is usually not instantiated directly, everything is taken care of by L{Graph.maxflow}. Examples: >>> from igraph import Graph >>> g = Graph.Ring(20) >>> mf = g.maxflow(0, 10) >>> print(mf.value) 2.0 >>> mf.es["color"] = "red" cst||||||_dS)zInitializes the flow. This should not be called directly, everything is taken care of by L{Graph.maxflow}. N)rr _flow)rrrflowrrrrrr sz Flow.__init__cCs"d|jj|j|j|j|j|jfS)Nz%s(%r, %r, %r, %r, %r))rrrr r(rrrrrrrsz Flow.__repr__cCs.dt|jt|j|jt|j|jfS)Nz4Graph flow (%d edges, %d vs %d vertices, value=%.4f)rrrrrrs z Flow.__str__cCs|jS)aReturns the flow values for each edge. For directed graphs, this is simply a list where element M{i} corresponds to the flow on edge M{i}. For undirected graphs, the direction of the flow is not constrained (since the edges are undirected), hence positive flow always means a flow from the smaller vertex ID to the larger, while negative flow means a flow from the larger vertex ID to the smaller. )r(rrrrr)s z Flow.flow) rr"r#r$r rrr%r)r&rrrrr'rs '  r'cs fddtt||DS)a Returns all the cuts between the source and target vertices in a directed graph. This function lists all edge-cuts between a source and a target vertex. Every cut is listed exactly once. @param source: the source vertex ID @param target: the target vertex ID @return: a list of L{Cut} objects. @newfield ref: Reference @ref: JS Provan and DR Shier: A paradigm for listing (s,t)-cuts in graphs. Algorithmica 15, 351--372, 1996. csg|]\}}t||dqS)rrr.0rpartrrr sz _all_st_cuts..)ziprZ all_st_cuts)rsourcetargetrr/r _all_st_cutss r4Ncs0t|||\}}fddt||DS)aG Returns all the mincuts between the source and target vertices in a directed graph. This function lists all minimum edge-cuts between a source and a target vertex. @param source: the source vertex ID @param target: the target vertex ID @param capacity: the edge capacities (weights). If C{None}, all edges have equal weight. May also be an attribute name. @return: a list of L{Cut} objects. @newfield ref: Reference @ref: JS Provan and DR Shier: A paradigm for listing (s,t)-cuts in graphs. Algorithmica 15, 351--372, 1996. cs g|]\}}t||dqSr*r+r,rrrrr0sz#_all_st_mincuts..)rZall_st_mincutsr1)rr2r3capacitycutspartsrr5r_all_st_mincutss r9r)cCst||\}}||j|<|S)aCalculates the Gomory-Hu tree of an undirected graph with optional edge capacities. The Gomory-Hu tree is a concise representation of the value of all the maximum flows (or minimum cuts) in a graph. The vertices of the tree correspond exactly to the vertices of the original graph in the same order. Edges of the Gomory-Hu tree are annotated by flow values. The value of the maximum flow (or minimum cut) between an arbitrary (u,v) vertex pair in the original graph is then given by the minimum flow value (i.e. edge annotation) along the shortest path between u and v in the Gomory-Hu tree. @param capacity: the edge capacities (weights). If C{None}, all edges have equal weight. May also be an attribute name. @param flow: the name of the edge attribute in the returned graph in which the flow values will be stored. @return: the Gomory-Hu tree as a L{Graph} object. )rZgomory_hu_treer)rr6r)Z flow_valuesrrr_gomory_hu_trees r:cCst|ft||||S)a~Returns a maximum flow between the given source and target vertices in a graph. A maximum flow from I{source} to I{target} is an assignment of non-negative real numbers to the edges of the graph, satisfying two properties: 1. For each edge, the flow (i.e. the assigned number) is not more than the capacity of the edge (see the I{capacity} argument) 2. For every vertex except the source and the target, the incoming flow is the same as the outgoing flow. The value of the flow is the incoming flow of the target or the outgoing flow of the source (which are equal). The maximum flow is the maximum possible such value. @param capacity: the edge capacities (weights). If C{None}, all edges have equal weight. May also be an attribute name. @return: a L{Flow} object describing the maximum flow )r'rZmaxflowrr2r3r6rrr_maxflow sr<cCst|ft||||S)aCalculates the minimum cut between the given source and target vertices or within the whole graph. The minimum cut is the minimum set of edges that needs to be removed to separate the source and the target (if they are given) or to disconnect the graph (if neither the source nor the target are given). The minimum is calculated using the weights (capacities) of the edges, so the cut with the minimum total capacity is calculated. For undirected graphs and no source and target, the method uses the Stoer-Wagner algorithm. For a given source and target, the method uses the push-relabel algorithm; see the references below. @param source: the source vertex ID. If C{None}, the target must also be C{None} and the calculation will be done for the entire graph (i.e. all possible vertex pairs). @param target: the target vertex ID. If C{None}, the source must also be C{None} and the calculation will be done for the entire graph (i.e. all possible vertex pairs). @param capacity: the edge capacities (weights). If C{None}, all edges have equal weight. May also be an attribute name. @return: a L{Cut} object describing the minimum cut )rrZmincutr;rrr_mincut#sr=cCst|ft||||S)aCalculates the minimum cut between the source and target vertices in a graph. @param source: the source vertex ID @param target: the target vertex ID @param capacity: the capacity of the edges. It must be a list or a valid attribute name or C{None}. In the latter case, every edge will have the same capacity. @return: the value of the minimum cut, the IDs of vertices in the first and second partition, and the IDs of edges in the cut, packed in a 4-tuple )rrZ st_mincutr;rrr _st_mincut>s r>)N)Nr))N)NNN)N) r$Zigraph._igraphrZigraph.clusteringrrr'r4r9r:r<r=r>rrrrs  gQ