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altgraph.Graph - Base Graph class
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=================================
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..
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#--Version 2.1
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#--Bob Ippolito October, 2004
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#--Version 2.0
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#--Istvan Albert June, 2004
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#--Version 1.0
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#--Nathan Denny, May 27, 1999
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é )Údeque)Ú
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GraphErrorc ón e Zd ZdZd9dZd Zd9dZd:dZd Zd Z d Z
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d
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Z d Z d Z d Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Z d Z d Z d Z d Z d Z!d! Z"d" Z#d# Z$d$ Z%d% Z&d& Z'd' Z(d( Z)d;d)Z*d* Z+d+ Z,d;d,Z-d- Z.d. Z/d<d/Z0d=d0Z1d<d1Z2d9d2Z3d9d3Z4d9d4Z5d9d5Z6d6 Z7d7 Z8d<d8Z9y)>ÚGrapha¼
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The Graph class represents a directed graph with *N* nodes and *E* edges.
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Naming conventions:
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- the prefixes such as *out*, *inc* and *all* will refer to methods
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that operate on the outgoing, incoming or all edges of that node.
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For example: :py:meth:`inc_degree` will refer to the degree of the node
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computed over the incoming edges (the number of neighbours linking to
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the node).
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- the prefixes such as *forw* and *back* will refer to the
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orientation of the edges used in the method with respect to the node.
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For example: :py:meth:`forw_bfs` will start at the node then use the
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outgoing edges to traverse the graph (goes forward).
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Nc ó d| _ i i c| _ | _ i i c| _ | _ |c|D ]] }t |« dk( r|\ }}| j ||« )t |« dk( r|\ }}}| j |||« Qt d|« yy)z
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Initialization
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r Né é zCannot create edge from )Ú next_edgeÚnodesÚedgesÚ hidden_edgesÚ hidden_nodesÚlenÚadd_edger )Úselfr ÚitemÚheadÚtailÚdatas úAH:\Change_password\venv_build\Lib\site-packages\altgraph/Graph.pyÚ__init__zGraph.__init__) s ð
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Ø!# RÐ
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DJØ/1°2Ð,Ô4Ô,à Ð Ø ò MÜt9 >Ø!%JD$ØMM $¨Õ-ÜY !^Ø'+Ñ$D$ ØMM $¨¨dÕ3å$ÁTÐ%KÓLÐLñ Mð ó c óH d| j « | j « fz S )Nz<Graph: %d nodes, %d edges>)Únumber_of_nodesÚnumber_of_edges©r s r Ú__repr__zGraph.__repr__= s, Ø,Ø × Ñ Ó "Ø × Ñ Ó "ð0
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ñ
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ð
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r c ód || j v ry|| j vrg g |f| j |< yy)zê
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Adds a new node to the graph. Arbitrary data can be attached to the
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node via the node_data parameter. Adding the same node twice will be
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silently ignored.
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The node must be a hashable value.
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N)r r )r ÚnodeÚ node_datas r Úadd_nodezGraph.add_nodeC s; ð 4×$Ñ$Ñ $à à tzzÑ !Ø " B¨ Ð 2DJJtÒ ð "r c ót | j }|r"| j |« | j |« | j | d j |« | j | d j |« |||f| j |< | xj dz c_ y# t $ r t d|d|« w xY w)aÈ
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Adds a directed edge going from head_id to tail_id.
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Arbitrary data can be attached to the edge via edge_data.
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It may create the nodes if adding edges between nonexisting ones.
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:param head_id: head node
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:param tail_id: tail node
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:param edge_data: (optional) data attached to the edge
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:param create_nodes: (optional) creates the head_id or tail_id
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node in case they did not exist
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r é zInvalid nodes z -> N)r
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r! r ÚappendÚKeyErrorr r )r Úhead_idÚtail_idÚ edge_dataÚ create_nodesÚedges r r zGraph.add_edgeY s° ð ~~ñ Ø MM'Ô "Ø MM'Ô "ð LØ JJwÑ Ñ "× )Ñ )¨$Ô /Ø JJwÑ Ñ "× )Ñ )¨$Ô /ð
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$ W¨iÐ8
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4Ñà !Ñøô ò LÝ ºÁ'Ð JÓKÐ Kð Lús ²AB  B7c ó | j | x\ }}}| j |< | j | d j |« | j | d j |« | j |= y# t $ r t d|z « w xY w)zd
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Hides an edge from the graph. The edge may be unhidden at some later
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time.
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r r# úInvalid edge %sN)r r r Úremover% r )r r* r& r' r( s r Ú hide_edgezGraph.hide_edge| s ð
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7ØDHÇJÁJÈtÑDTÐ TÑ 'GWi¨$×*;Ñ*;¸DÑ*AØ JJwÑ Ñ "× )Ñ )¨$Ô /Ø JJwÑ Ñ "× )Ñ )¨$Ô /Ø
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4Ñ øÜò 7Ü Ð .°Ñ 5Ó6Ð 6ð 7ús A1A4 Á4B c óä | j |« }| j | |f| j |< |D ] }| j |« | j |= y# t $ r t d|z « w xY w)z¦
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Hides a node from the graph. The incoming and outgoing edges of the
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node will also be hidden. The node may be unhidden at some later time.
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úInvalid node %sN)Ú all_edgesr r r. r% r ©r r r1 r* s r Ú hide_nodezGraph.hide_node sz ð
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7Ø tÓ,IØ'+§z¡z°$Ñ'7¸Ð&CD× Ñ dÑ #Ø!ò %ØtÕ$ð %à
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4Ñ øÜò 7Ü Ð .°Ñ 5Ó6Ð 6ð 7ús AA ÁA/c óÄ | j | \ | j |< }|D ] }| j |« | j |= y# t $ r t d|z « w xY w)z
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Restores a previously hidden node back into the graph and restores
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all of its incoming and outgoing edges.
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r0 N)r r Ú restore_edger% r r2 s r Ú restore_nodezGraph.restore_node sp ð
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7Ø*.×*;Ñ*;¸DÑ*AÑ 'DJJtÑ iØ!ò (Ø×!Ñ! $Õ'ð (à×!Ñ! $Ñ'øÜò 7Ü Ð .°Ñ 5Ó6Ð 6ð 7ús AA ÁA c ó$ | j | \ }}}| j | d j |« | j | d j |« |||f| j |< | j |= y# t $ r t d|z « w xY w)zH
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Restores a previously hidden edge back into the graph.
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r r# r, N)r r r$ r r% r )r r* r& r' r s r r5 zGraph.restore_edge¤ s ð 7Ø%)×%6Ñ%6°tÑ%<Ñ "GWdØ JJwÑ Ñ "× )Ñ )¨$Ô /Ø JJwÑ Ñ "× )Ñ )¨$Ô /Ø &¨°Ð 5DJJtÑ Ø×!Ñ! $Ñ'øÜò 7Ü Ð .°Ñ 5Ó6Ð 6ð 7ús A4A7 Á7Bc ó t | j j « « D ] } | j |« y# t $ r Y #w xY w)z,
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Restores all hidden edges.
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N)Úlistr Úkeysr5 r ©r r* s r Úrestore_all_edgeszGraph.restore_all_edges± sN ô ×*Ñ*×/Ñ/Ó1Ó2ò Dð Ø×!Ñ! $Õ'ñ øô ò Ùð ús ¨<¼ AÁAc óv t | j j « « D ] }| j |« y)z,
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Restores all hidden nodes.
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N)r9 r r: r6 ©r r s r Úrestore_all_nodeszGraph.restore_all_nodes» s5 ô ×*Ñ*×/Ñ/Ó1Ó2ò $DØ × Ñ dÕ #ñ $r c ó || j v S )z5
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Test whether a node is in the graph
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©r r> s r Ú __contains__zGraph.__contains__Â s ð tzzÐ!Ð!r c ór | j | \ }}}||fS # t $ r d\ }}t d|z « w xY w)úN
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Returns the edge that connects the head_id and tail_id nodes
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)NNr, )r r% r ©r r* r r r s r Ú
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edge_by_idzGraph.edge_by_idÈ sS ð 7Ø #zz¨$Ñ /Ñ D$ð
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d|Ðøô ò 7Ø#JD$Ü Ð .°Ñ 5Ó6Ð 6ð 7ús 6c ó` | j |« D ] }| j |« |k( s|c S y)rD N©Ú out_edgesr )r r r r* s r Ú edge_by_nodezGraph.edge_by_nodeÔ s6 ð NN 4Ó(ò DØyy $Ó&Ø ð ð r c ó, t | j « S )z-
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Returns the number of nodes
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)r r r s r r zGraph.number_of_nodesÝ ó ô 4::Ð r c ó, t | j « S )z-
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Returns the number of edges
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)r r r s r r zGraph.number_of_edgesã rL r c ó, t | j « S )z6
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Iterates over all nodes in the graph
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)Úiterr r s r Ú__iter__zGraph.__iter__é s ô DJJÓ Ð r c óH t | j j « « S )zS
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Return a list of the node ids for all visible nodes in the graph.
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)r9 r r: r s r Ú node_listzGraph.node_listï ó ô DJJOOÓ%Ó&Ð&r c óH t | j j « « S )zI
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Returns an iterator for all visible nodes in the graph.
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)r9 r r: r s r Ú edge_listzGraph.edge_listõ rS r c ó, t | j « S )z4
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Returns the number of hidden edges
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)r r r s r Únumber_of_hidden_edgesz Graph.number_of_hidden_edgesû ó ô 4×$Ñ$Ó%Ð%r c ó, t | j « S )z4
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Returns the number of hidden nodes
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)r r r s r Únumber_of_hidden_nodesz Graph.number_of_hidden_nodes rX r c óH t | j j « « S )z8
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Returns the list with the hidden nodes
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)r9 r r: r s r Úhidden_node_listzGraph.hidden_node_list ó ô D×%Ñ%×*Ñ*Ó,Ó-Ð-r c óH t | j j « « S )z6
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Returns a list with the hidden edges
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)r9 r r: r s r Úhidden_edge_listzGraph.hidden_edge_list r] r c ó4 | j | \ }}}||||fS )zQ
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return node, node data, outgoing edges, incoming edges for node
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rA )r r ÚincomingÚoutgoingr s r Ú describe_nodezGraph.describe_node s( ð $(§:¡:¨dÑ#3Ñ (DØT8 XÐ-Ð-r c ó4 | j | \ }}}||||fS )z=
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return edge, edge data, head, tail for edge
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©r rE s r Ú describe_edgezGraph.describe_edge s( ð :: dÑ+ÑdDØT4 Ð%Ð%r c ó& | j | d S )z9
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Returns the data associated with a node
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r rA r> s r r zGraph.node_data! ó ð zz$Ñ Ñ"Ð"r c ó& | j | d S )z:
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Returns the data associated with an edge
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r re r; s r r( zGraph.edge_data' rh r c óJ | j | dd |fz | j |< y)z;
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Replace the edge data for a specific edge
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r r Nre )r r* r( s r Úupdate_edge_datazGraph.update_edge_data- s) ð :: dÑ+¨A¨aÐ0°I°<Ñ?
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4Òr c ó& | j | d S )z;
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Returns the node of the head of the edge.
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r re r; s r r z
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Graph.head3 rh r c ó& | j | d S )z7
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Returns node of the tail of the edge.
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r# re r; s r r z
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Graph.tail9 rh r c óh | j |« D cg c] }| j |« c}S c c}w )z;
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List of nodes connected by outgoing edges
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rH ©r r Úns r Úout_nbrszGraph.out_nbrs? ó) ð '+§n¡n°TÓ&:Ö; ! Ò;Ð;ùÒ;ó /c óh | j |« D cg c] }| j |« c}S c c}w )z;
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List of nodes connected by incoming edges
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)Ú inc_edgesr ro s r Úinc_nbrszGraph.inc_nbrsE rr rs c ó t t j | j |« | j |« z « « S )zH
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List of nodes connected by incoming and outgoing edges
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)r9 ÚdictÚfromkeysrv rq r> s r Úall_nbrszGraph.all_nbrsK s/ ô DMM $§-¡-°Ó"5¸¿ ¹ ÀdÓ8KÑ"KÓLÓMÐMr c óp t | j | d « S # t $ r t d|z « w xY w)z6
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Returns a list of the outgoing edges
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r# r0 ©r9 r r% r r> s r rI zGraph.out_edgesQ ó@ ð 7Ü
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4Ñ(¨Ñ+Ó,Ð ,øÜò 7Ü Ð .°Ñ 5Ó6Ð 6ð 7úó 5c óp t | j | d « S # t $ r t d|z « w xY w)z6
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Returns a list of the incoming edges
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r r0 r| r> s r ru zGraph.inc_edgesZ r} r~ c óZ t | j |« | j |« z « S )z?
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Returns a list of incoming and outging edges.
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)Úsetru rI r> s r r1 zGraph.all_edgesc s& ô 4>> $Ó'¨$¯.©.¸Ó*>Ñ>Ó?Ð?r c ó6 t | j |« « S )z6
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Returns the number of outgoing edges
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)r rI r> s r Ú
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out_degreezGraph.out_degreei ó ô 4>> $Ó'Ó(Ð(r c ó6 t | j |« « S )z6
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Returns the number of incoming edges
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)r ru r> s r Ú
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inc_degreezGraph.inc_degreeo r r c óH | j |« | j |« z S )z,
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The total degree of a node
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)r r r> s r Ú
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all_degreezGraph.all_degreeu s! ð tÓ$ t§¡°tÓ'<Ñ<Ð<r c óP g }t « }i }|r%| j }| j }| j }n$| j }| j
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}| j }| j « D ]# } ||« } | r| ||< |j |« % |re|j « }
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|j |
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« ||
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« D ]6 } || « } | |v s|| xx dz cc< || dk( s&|j | « 8 |ret |« t | j « « k( rd} | |fS d} | |fS )zì
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Topological sort.
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Returns a list of nodes where the successors (based on outgoing and
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incoming edges selected by the forward parameter) of any given node
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appear in the sequence after that node.
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r# r TF) r rI r r ru r r rR r$ Úpopleftr )r ÚforwardÚ topo_listÚqueueÚindegÚ get_edgesÚ
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get_degreeÚget_nextr ÚdegreeÚ curr_noder* r' Úvalids r Ú
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_topo_sortzGraph._topo_sort{ s4 ð ÜØñ Ø IØ JØyyHà IØ JØyyHàNNÓ$ò #DÙ Ó%FÙØ $d à TÕ"ð #ñ Ø IØ × Ñ YÔ 'Ù! )Ó,ò .Ù" 4.ØeÒ#Ø'N aÑ'NØ W~¨Ó*Ø WÕ-ð .ò ô y>S § ¡ Ó!1Ó 2Ò 2ØEð
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yÐ!Ð!ð EàyÐ!Ð!r c ó& | j d¬« S )zµ
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Topological sort.
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Returns a list of nodes where the successors (based on outgoing edges)
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of any given node appear in the sequence after that node.
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T©r ©r r s r Úforw_topo_sortzGraph.forw_topo_sortª s ð tÓ,Ð,r c ó& | j d¬« S )z½
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Reverse topological sort.
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Returns a list of nodes where the successors (based on incoming edges)
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of any given node appear in the sequence after that node.
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Fr r r s r Úback_topo_sortzGraph.back_topo_sort³ s ð uÓ-Ð-r c ó6 |r| j }| j }n| j }| j }t « } ||« }|D ] }|j |« |D ]6 } ||« D ]) }|r|j ||« |j ||« + 8 |S )z£
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Private method creates a subgraph in a bfs order.
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The forward parameter specifies whether it is a forward or backward
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traversal.
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)Úforw_bfsrq Úback_bfsrv r r! r ) r Ústart_idr Úget_bfsÚget_nbrsÚgÚbfs_listr Únbr_ids r Ú _bfs_subgraphzGraph._bfs_subgraph¼ s¡ ñ ØmmGØ}}HàmmGØ}}Hä GÙ8Ó$Ø ò DØ JJtÕ ð ð ò -DÙ" 4.ò -ÙØJJt VÕ,àJJv tÕ,ñ -ð -ð r c ó( | j |d¬« S )z
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Creates and returns a subgraph consisting of the breadth first
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reachable nodes based on their outgoing edges.
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Tr ©r¥ ©r r s r Úforw_bfs_subgraphzGraph.forw_bfs_subgraphØ s ð
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×!Ñ! (°DÐ!Ó9Ð9r c ó( | j |d¬« S )z
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Creates and returns a subgraph consisting of the breadth first
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reachable nodes based on the incoming edges.
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Fr r§ r¨ s r Úback_bfs_subgraphzGraph.back_bfs_subgraphß s ð
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×!Ñ! (°EÐ!Ó:Ð:r c # óZ K |ht |g« }}|r| j }| j }n| j }| j }|rc|j « }| ||k( ryt ||« « D ]1 } || « }
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|vs|j |
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« |j |
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« 3 |rbyyw)z¡
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Collecting nodes in some depth first traversal.
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The forward parameter specifies whether it is a forward or backward
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traversal.
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N) r rI r ru r ÚpopÚsortedÚaddr$ ) r ÚstartÚendr ÚvisitedÚstackr r r r* r s r Úiterdfsz Graph.iterdfsæ s¥ è ø ð ¤%¨¨£.á Ø IØyyHà IØyyHáØ IØOØCÒ ØÜ y¨Ó 3Ó4ò 'Ù ~ØwÒ&ØKK Ô%ØLL Õ&ð 'ô ùs A?B+Â&B+Â)B+c # ó K |ht |g« }}|r| j }| j }n| j }| j }| j
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} |ro|j « }
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| |
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« } | | || « s'| |
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|k( ry ||
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« D ]1 } || « } | |vs|j | « |j | « 3 |rnyyw)zÛ
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Perform a depth-first walk of the graph (as ``iterdfs``)
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and yield the item data of every node where condition matches. The
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condition callback is only called when node_data is not None.
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N) r rI r ru r r r r¯ r$ )r r° r± r Ú conditionr² r³ r r Úget_datar Ú curr_datar* r s r ÚiterdatazGraph.iterdata sÉ è ø ð ¤%¨¨£.á Ø IØyyHà IØyyHà>>áØ IÙ Ó+IØÐ$Ø Ð(±¸9Ô1EØ Ø ØCÒ ØÙ! )Ó,ò 'Ù ~ØwÒ&ØKK Ô%ØLL Õ&ð 'ô ùs BCÂ&CÃCc # ó` K t |dfg« |h}}|r| j }| j }n| j }| j }|rd|j « \ }} || f ||k( ry ||« D ]6 }
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||
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« } | |vs|j | « |j | | dz f« 8 |rcyyw)zÒ
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The forward parameter specifies whether it is a forward or backward
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traversal. Returns a list of tuples where the first value is the hop
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value the second value is the node id.
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r r# N)r rI r ru r r r¯ r$ ) r r° r± r r r² r r r Ú curr_stepr* r s r Ú_iterbfszGraph._iterbfs" s» è ø ô ¨
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|Ó,¨u¨gwñ Ø IØyyHà IØyyHáØ#(§=¡=£?Ñ IyØ iÐ(Ò (ØCÒ ØÙ! )Ó,ò 8Ù ~ØwÒ&ØKK Ô%ØLL $¨ °A© Ð!6Õ7ð 8ô ùs A=B. +B.Â,B.c ó\ | j ||d¬« D cg c] \ }}| c}}S c c}}w )zª
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Returns a list of nodes in some forward BFS order.
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Starting from the start node the breadth first search proceeds along
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outgoing edges.
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Tr ©r¼ )r r° r± r Ústeps r r zGraph.forw_bfs= s+ ð (,§}¡}°U¸CÈ }Ó'N×OtÓOÐOùÓOó (c ó\ | j ||d¬« D cg c] \ }}| c}}S c c}}w )z«
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Returns a list of nodes in some backward BFS order.
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Starting from the start node the breadth first search proceeds along
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incoming edges.
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Fr r¾ )r r° r± r Ú_s r r zGraph.back_bfsF s+ ð %)§M¡M°%¸Àe MÓ$L×MqÓMÐMùÓMrÀ c ó< t | j ||d¬« « S )z¨
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Returns a list of nodes in some forward DFS order.
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Starting with the start node the depth first search proceeds along
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outgoing edges.
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Tr ©r9 r´ ©r r° r± s r Úforw_dfszGraph.forw_dfsO s ô DLL ¨°TLÓ:Ó;Ð;r c ó< t | j ||d¬« « S )z©
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Returns a list of nodes in some backward DFS order.
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Starting from the start node the depth first search proceeds along
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incoming edges.
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Fr rÄ rÅ s r Úback_dfszGraph.back_dfsX s ô DLL ¨°ULÓ;Ó<Ð<r c ó | j « }|D ], }| j |« }t |« t |« k7 s, y y)zq
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Returns :py:data:`True` if the graph's every node can be reached from
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every other node.
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FT)rR r r )r rR r r£ s r Ú connectedzGraph.connecteda sE ð
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NNÓ$ Ø ò DØ}} TÓ*HÜ8}¤ I£Ó.Ù ð ð r c ó@ d}t | j |« « }||v r|j |« |D ]B }t | j |« « }||v r|j |« |t ||z « z }D t |« }|rt |« ||dz
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z z }|S d}|S )a
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Computes and returns the local clustering coefficient of node.
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The local cluster coefficient is proportion of the actual number of
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edges between neighbours of node and the maximum number of edges
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between those neighbours.
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See "Local Clustering Coefficient" on
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<http://en.wikipedia.org/wiki/Clustering_coefficient>
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for a formal definition.
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r r# g )r rq r- r Úfloat)r r ÚnumÚnbr_setÚnbrÚsec_setÚnbr_numÚ
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clust_coefs r rÒ zGraph.clust_coefm s² ð Üdmm DÓ)Ó*à 7?Ø NN4Ô àò *CÜ$--¨Ó,Ó-GØg~ØsÔ#Ø 3w Ñ(Ó)Ñ )Cð *ô g,Ù Ü s w°'¸A±+Ñ'>Ñ?Jð Ðð JØÐr c óz |r t | j ||d¬« « S t | j ||d¬« « S )a$
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Computes the hop distance to all nodes centered around a node.
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First order neighbours are at hop 1, their neigbours are at hop 2 etc.
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Uses :py:meth:`forw_bfs` or :py:meth:`back_bfs` depending on the value
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of the forward parameter. If the distance between all neighbouring
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nodes is 1 the hop number corresponds to the shortest distance between
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the nodes.
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:param start: the starting node
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:param end: ending node (optional). When not specified will search the
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whole graph.
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:param forward: directionality parameter (optional).
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If C{True} (default) it uses L{forw_bfs} otherwise L{back_bfs}.
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:return: returns a list of tuples where each tuple contains the
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node and the hop.
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Typical usage::
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>>> print (graph.get_hops(1, 8))
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>>> [(1, 0), (2, 1), (3, 1), (4, 2), (5, 3), (7, 4), (8, 5)]
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# node 1 is at 0 hops
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# node 2 is at 1 hop
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# ...
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# node 8 is at 5 hops
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T)r° r± r F)r9 r¼ )r r° r± r s r Úget_hopszGraph.get_hops s; ñ6 Ü ¨E°sÀD ÓIÓJÐ Jä ¨E°sÀE ÓJÓKÐ Kr )N)r# T)T)NT)NTN):Ú__name__Ú
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__module__Ú __qualname__Ú__doc__r r r! r r. r3 r6 r5 r< r? rB rF rJ r r rP rR rU rW rZ r\ r_ rc rf r r( rk r r rq rv rz rI ru r1 r r r r r r r¥ r© r« r´ r¹ r¼ r r rÆ rÈ rÊ rÒ rÔ © r r r r s ñó&Mò(
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ó 3ó,! òF 7ò 7ò 7ò 7òò$ò"ò
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òò ò ò ò 'ò 'ò &ò &ò .ò .ò .ò&ò#ò #ò @ò #ò #ò <ò <ò Nò 7ò7ò@ò )ò )ò =ó -"ò^-ò.óò8:ò;ó'ó6 'óB8ó6PóNó<ó=ò
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ò ô> Lr r N)rØ Ú collectionsr Úaltgraphr Úobjectr rÙ r r ú<module>rÝ s" ðñ õ å ôU
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LFõ U
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Lr
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