o 3ήc*@sHdZddlZddlmZmZddgZGdddeZGdddeZdS) u ***************************** Time-respecting VF2 Algorithm ***************************** An extension of the VF2 algorithm for time-respecting graph isomorphism testing in temporal graphs. A temporal graph is one in which edges contain a datetime attribute, denoting when interaction occurred between the incident nodes. A time-respecting subgraph of a temporal graph is a subgraph such that all interactions incident to a node occurred within a time threshold, delta, of each other. A directed time-respecting subgraph has the added constraint that incoming interactions to a node must precede outgoing interactions from the same node - this enforces a sense of directed flow. Introduction ------------ The TimeRespectingGraphMatcher and TimeRespectingDiGraphMatcher extend the GraphMatcher and DiGraphMatcher classes, respectively, to include temporal constraints on matches. This is achieved through a semantic check, via the semantic_feasibility() function. As well as including G1 (the graph in which to seek embeddings) and G2 (the subgraph structure of interest), the name of the temporal attribute on the edges and the time threshold, delta, must be supplied as arguments to the matching constructors. A delta of zero is the strictest temporal constraint on the match - only embeddings in which all interactions occur at the same time will be returned. A delta of one day will allow embeddings in which adjacent interactions occur up to a day apart. Examples -------- Examples will be provided when the datetime type has been incorporated. Temporal Subgraph Isomorphism ----------------------------- A brief discussion of the somewhat diverse current literature will be included here. References ---------- [1] Redmond, U. and Cunningham, P. Temporal subgraph isomorphism. In: The 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM). Niagara Falls, Canada; 2013: pages 1451 - 1452. [65] For a discussion of the literature on temporal networks: [3] P. Holme and J. Saramaki. Temporal networks. Physics Reports, 519(3):97–125, 2012. Notes ----- Handles directed and undirected graphs and graphs with parallel edges. N)DiGraphMatcher GraphMatcherTimeRespectingGraphMatcherTimeRespectingDiGraphMatchercs4eZdZfddZddZddZddZZS) rc||_||_t||dS)aiInitialize TimeRespectingGraphMatcher. G1 and G2 should be nx.Graph or nx.MultiGraph instances. Examples -------- To create a TimeRespectingGraphMatcher which checks for syntactic and semantic feasibility: >>> from networkx.algorithms import isomorphism >>> from datetime import timedelta >>> G1 = nx.Graph(nx.path_graph(4, create_using=nx.Graph())) >>> G2 = nx.Graph(nx.path_graph(4, create_using=nx.Graph())) >>> GM = isomorphism.TimeRespectingGraphMatcher( ... G1, G2, "date", timedelta(days=1) ... ) Ntemporal_attribute_namedeltasuper__init__selfG1G2r r  __class__Z/tmp/pip-target-vg8gfxp4/lib/python/networkx/algorithms/isomorphism/temporalisomorphvf2.pyr Lz#TimeRespectingGraphMatcher.__init__cCsg}|D](}t|tjr|||||jq|||D] }|||jq!qtdd|Dr:td| pGt|t ||j kS)z| Edges one hop out from a node in the mapping should be time-respecting with respect to each other. cs|]}|duVqdSNr.0xrrr rz5TimeRespectingGraphMatcher.one_hop..z,Datetime not supplied for at least one edge.) isinstancenxGraphappendr valuesany ValueErrormaxminr )rGxGx_node neighborsdatesnedgerrrone_hopds z"TimeRespectingGraphMatcher.one_hopctfdd|DS)zK Paths of length 2 from Gx_node should be time-respecting. c3s6|]}|fdd|DgVqdS)cg|]}|vr|qSrrrr*core_xrr {z@TimeRespectingGraphMatcher.two_hop...N)r,)rvr&r'r1rrrrzs $ z5TimeRespectingGraphMatcher.two_hop..all)rr&r1r'r(rr5rtwo_hopvsz"TimeRespectingGraphMatcher.two_hopcsHfddj|D}j||sdSjj||s"dSdS)Returns True if adding (G1_node, G2_node) is semantically feasible. Any subclass which redefines semantic_feasibility() must maintain the self.tests if needed, to keep the match() method functional. Implementations should consider multigraphs. cg|] }|jvr|qSrcore_1r/rrrr2zCTimeRespectingGraphMatcher.semantic_feasibility..FT)rr,r8r<)rG1_nodeG2_noder(rr=rsemantic_feasibilitys z/TimeRespectingGraphMatcher.semantic_feasibility)__name__ __module__ __qualname__r r,r8rA __classcell__rrrrrKs   cspeZdZfddZddZddZddZd d Zd d ZdddZ dddZ ddZ ddZ ddZ ZS)rcr)a{Initialize TimeRespectingDiGraphMatcher. G1 and G2 should be nx.DiGraph or nx.MultiDiGraph instances. Examples -------- To create a TimeRespectingDiGraphMatcher which checks for syntactic and semantic feasibility: >>> from networkx.algorithms import isomorphism >>> from datetime import timedelta >>> G1 = nx.DiGraph(nx.path_graph(4, create_using=nx.DiGraph())) >>> G2 = nx.DiGraph(nx.path_graph(4, create_using=nx.DiGraph())) >>> GM = isomorphism.TimeRespectingDiGraphMatcher( ... G1, G2, "date", timedelta(days=1) ... ) Nrr rrrr rz%TimeRespectingDiGraphMatcher.__init__cCsjg}t|tjr|D]}|||||jq |S|D]}|||D] }|||jq'q|S)z; Get the dates of edges from predecessors. rrDiGraphr r r!)rr&r'r1pred pred_datesr*r+rrrget_pred_dates z+TimeRespectingDiGraphMatcher.get_pred_datescCsjg}t|tjr|D]}|||||jq |S|D]}|||D] }|||jq'q|S)z7 Get the dates of edges to successors. rF)rr&r'r1succ succ_datesr*r+rrrget_succ_datesrKz+TimeRespectingDiGraphMatcher.get_succ_datescCs8|||||}|||||}|||o|||S)z The ego node. )rJrNtest_onetest_two)rr&r'r1rHrLrIrMrrrr,s z$TimeRespectingDiGraphMatcher.one_hopcr-)z4 The predeccessors of the ego node. c 3s8|]}|||VqdSrr,predssuccs)rpr5rrrs  z.r6)rr&r'r1rHrr5r two_hop_predz)TimeRespectingDiGraphMatcher.two_hop_predcr-)z1 The successors of the ego node. c 3s8|]}|||VqdSrrQ)rsr5rrrs  z.r6)rr&r'r1rLrr5r two_hop_succrVz)TimeRespectingDiGraphMatcher.two_hop_succNc*fdd||D}|r|||S)Ncr.rrr/r0rrr2r3z6TimeRespectingDiGraphMatcher.preds..) predecessorsr )rr&r1r4r'rHrr0rrR z"TimeRespectingDiGraphMatcher.predscrY)Ncr.rrr/r0rrr2r3z6TimeRespectingDiGraphMatcher.succs..) successorsr )rr&r1r4r'rLrr0rrSr[z"TimeRespectingDiGraphMatcher.succscCsXd}||}tdd|Drtd|dt|kr*|d|d|jks*d}|S)z Edges one hop out from Gx_node in the mapping should be time-respecting with respect to each other, regardless of direction. Tcsrrrrrrrrrz8TimeRespectingDiGraphMatcher.test_one..z4Date or datetime not supplied for at least one edge.rF)r"r#sortlenr )rrIrMtime_respectingr)rrrrOs"z%TimeRespectingDiGraphMatcher.test_onecCsDd}||dt|kr dt|kr |d|dkr d}|S)zq Edges from a dual Gx_node in the mapping should be ordered in a time-respecting manner. Trr]F)r^r_)rrIrMr`rrrrPs  z%TimeRespectingDiGraphMatcher.test_twocsfddj|Dfddj|D}}j|j||s(dSj|j|s4dSj|j|s@dSdS)r9cr:rr;r/r=rrr2(r>zETimeRespectingDiGraphMatcher.semantic_feasibility..cr:rr;r/r=rrr2)r>FT)rrZr\r,r<rUrX)rr?r@rHrLrr=rrAs z1TimeRespectingDiGraphMatcher.semantic_feasibilityr)rBrCrDr rJrNr,rUrXrRrSrOrPrArErrrrrs    ) __doc__networkxr isomorphvf2rr__all__rrrrrrs CE