o ˷eY@sdZddlZddlmZgdZdddZddd Zdd d Zdd dZ dddZ dddZ dddZ dddZ ddZedd ddZdS)!z:Graph diameter, radius, eccentricity and other properties.N)not_implemented_for)extrema_bounding eccentricitydiameterradius peripherycenter barycenterresistance_distancercCsPddl}d}|dvr|d|d7}|dkr|d7}|j|td d t||d S) aCompute requested extreme distance metric of undirected graph G .. deprecated:: 2.8 extrema_bounding is deprecated and will be removed in NetworkX 3.0. Use the corresponding distance measure with the `usebounds=True` option instead. Computation is based on smart lower and upper bounds, and in practice linear in the number of nodes, rather than quadratic (except for some border cases such as complete graphs or circle shaped graphs). Parameters ---------- G : NetworkX graph An undirected graph compute : string denoting the requesting metric "diameter" for the maximal eccentricity value, "radius" for the minimal eccentricity value, "periphery" for the set of nodes with eccentricity equal to the diameter, "center" for the set of nodes with eccentricity equal to the radius, "eccentricities" for the maximum distance from each node to all other nodes in G Returns ------- value : value of the requested metric int for "diameter" and "radius" or list of nodes for "center" and "periphery" or dictionary of eccentricity values keyed by node for "eccentricities" Raises ------ NetworkXError If the graph consists of multiple components ValueError If `compute` is not one of "diameter", "radius", "periphery", "center", or "eccentricities". Notes ----- This algorithm was proposed in the following papers: F.W. Takes and W.A. Kosters, Determining the Diameter of Small World Networks, in Proceedings of the 20th ACM International Conference on Information and Knowledge Management (CIKM 2011), pp. 1191-1196, 2011. doi: https://doi.org/10.1145/2063576.2063748 F.W. Takes and W.A. Kosters, Computing the Eccentricity Distribution of Large Graphs, Algorithms 6(1): 100-118, 2013. doi: https://doi.org/10.3390/a6010100 M. Borassi, P. Crescenzi, M. Habib, W.A. Kosters, A. Marino and F.W. Takes, Fast Graph Diameter and Radius BFS-Based Computation in (Weakly Connected) Real-World Graphs, Theoretical Computer Science 586: 59-80, 2015. doi: https://doi.org/10.1016/j.tcs.2015.02.033 rNzCextrema_bounding is deprecated and will be removed in networkx 3.0 >rrrrzUse nx.z(G, usebounds=True) instead.eccentricitieszUse nx.eccentricity(G) instead.) stacklevelcompute)warningswarnDeprecationWarning_extrema_bounding)Grrmsgr\/var/www/ideatree/venv/lib/python3.10/site-packages/networkx/algorithms/distance_measures.pyrs: rcst|}t||jd}t|}d}t|dt||t|}|d|d|rG|r3|}n|}| }tt||} t| |krMd} t | t| } d}d}|D]?} | | } t| t| | | | <}t | | | | <}t | t| t | t| qY|dkrfdd|D}nA|d krfd d|D}n0|d kṙfd d|D}n|d kr݇fdd|D}n|dkrt}nd} t | | fdd|D||8}|D]F} |dus | |kr|| ||ks | |kr"| }|dusB| |kr9|| ||ksB| |krD| }q|s.|dkrNS|d krUS|d krffdd|D}|S|d krwfdd|D}|S|dkr~SdS)aCompute requested extreme distance metric of undirected graph G Computation is based on smart lower and upper bounds, and in practice linear in the number of nodes, rather than quadratic (except for some border cases such as complete graphs or circle shaped graphs). Parameters ---------- G : NetworkX graph An undirected graph compute : string denoting the requesting metric "diameter" for the maximal eccentricity value, "radius" for the minimal eccentricity value, "periphery" for the set of nodes with eccentricity equal to the diameter, "center" for the set of nodes with eccentricity equal to the radius, "eccentricities" for the maximum distance from each node to all other nodes in G Returns ------- value : value of the requested metric int for "diameter" and "radius" or list of nodes for "center" and "periphery" or dictionary of eccentricity values keyed by node for "eccentricities" Raises ------ NetworkXError If the graph consists of multiple components ValueError If `compute` is not one of "diameter", "radius", "periphery", "center", or "eccentricities". Notes ----- This algorithm was proposed in the following papers: F.W. Takes and W.A. Kosters, Determining the Diameter of Small World Networks, in Proceedings of the 20th ACM International Conference on Information and Knowledge Management (CIKM 2011), pp. 1191-1196, 2011. doi: https://doi.org/10.1145/2063576.2063748 F.W. Takes and W.A. Kosters, Computing the Eccentricity Distribution of Large Graphs, Algorithms 6(1): 100-118, 2013. doi: https://doi.org/10.3390/a6010100 M. Borassi, P. Crescenzi, M. Habib, W.A. Kosters, A. Marino and F.W. Takes, Fast Graph Diameter and Radius BFS-Based Computation in (Weakly Connected) Real-World Graphs, Theoretical Computer Science 586: 59-80, 2015. doi: https://doi.org/10.1016/j.tcs.2015.02.033 )keyFrz5Cannot compute metric because graph is not connected.Nrcs,h|]}|krd|kr|qS)r r.0i ecc_lower ecc_uppermaxlowermaxupperrr s z$_extrema_bounding..rcs0h|]}|kr|ddkr|qSr rrrrminlowerminupperrrr!s  rcs0h|]}|krks|kr|qSrrrrrrr!s  rcs8h|]}|krks|ddkr|qSr"rrr$rrr!s  r zTcompute must be one of 'diameter', 'radius', 'periphery', 'center', 'eccentricities'c3s$|] }||kr|VqdS)Nrr)rrrr s"z$_extrema_bounding..cg|] }|kr|qSrrrv)rrrr z%_extrema_bounding..cr(rrr))rr&rrr+r,)dictdegreemaxgetlenfromkeyssetnx"single_source_shortest_path_length NetworkXErrorvaluesmin ValueErrorupdate)rrdegrees minlowernodeNhigh candidates maxuppernodecurrentdistr current_eccrdlowupp ruled_outpcr)rrrr r%r&rrYs 4          s    rc Cs|}i}||D]H}|durt||}t|}nz ||}t|}Wnty8}ztd|d}~ww||krK|rDd} nd} t| t| ||<q ||vr\||S|S)aReturns the eccentricity of nodes in G. The eccentricity of a node v is the maximum distance from v to all other nodes in G. Parameters ---------- G : NetworkX graph A graph v : node, optional Return value of specified node sp : dict of dicts, optional All pairs shortest path lengths as a dictionary of dictionaries Returns ------- ecc : dictionary A dictionary of eccentricity values keyed by node. Examples -------- >>> G = nx.Graph([(1, 2), (1, 3), (1, 4), (3, 4), (3, 5), (4, 5)]) >>> dict(nx.eccentricity(G)) {1: 2, 2: 3, 3: 2, 4: 2, 5: 3} >>> dict(nx.eccentricity(G, v=[1, 5])) # This returns the eccentrity of node 1 & 5 {1: 2, 5: 3} NzFormat of "sp" is invalid.zHFound infinite path length because the digraph is not strongly connectedz=Found infinite path length because the graph is not connected) order nbunch_iterr4r5r1 TypeErrorr6 is_directedr/r7) rr*sprJenlengthLerrrrrrr s.&     rFcC@|dur|dur|st|ddS|durt|}t|S)aReturns the diameter of the graph G. The diameter is the maximum eccentricity. Parameters ---------- G : NetworkX graph A graph e : eccentricity dictionary, optional A precomputed dictionary of eccentricities. Returns ------- d : integer Diameter of graph Examples -------- >>> G = nx.Graph([(1, 2), (1, 3), (1, 4), (3, 4), (3, 5), (4, 5)]) >>> nx.diameter(G) 3 See Also -------- eccentricity TNrrrMrrr/r7rrO useboundsrrrres   csX|durdur|st|ddSdurt|tfddD}|S)aReturns the periphery of the graph G. The periphery is the set of nodes with eccentricity equal to the diameter. Parameters ---------- G : NetworkX graph A graph e : eccentricity dictionary, optional A precomputed dictionary of eccentricities. Returns ------- p : list List of nodes in periphery Examples -------- >>> G = nx.Graph([(1, 2), (1, 3), (1, 4), (3, 4), (3, 5), (4, 5)]) >>> nx.periphery(G) [2, 5] See Also -------- barycenter center TNrrcsg|] }|kr|qSrrr)rrOrrr+r,zperiphery..rUrrOrWrHrrXrr  rcCrT)aReturns the radius of the graph G. The radius is the minimum eccentricity. Parameters ---------- G : NetworkX graph A graph e : eccentricity dictionary, optional A precomputed dictionary of eccentricities. Returns ------- r : integer Radius of graph Examples -------- >>> G = nx.Graph([(1, 2), (1, 3), (1, 4), (3, 4), (3, 5), (4, 5)]) >>> nx.radius(G) 2 TNrrrMrrr8r7rVrrrrs   rcsX|durdur|st|ddSdurt|tfddD}|S)aReturns the center of the graph G. The center is the set of nodes with eccentricity equal to radius. Parameters ---------- G : NetworkX graph A graph e : eccentricity dictionary, optional A precomputed dictionary of eccentricities. Returns ------- c : list List of nodes in center Examples -------- >>> G = nx.Graph([(1, 2), (1, 3), (1, 4), (3, 4), (3, 5), (4, 5)]) >>> list(nx.center(G)) [1, 3, 4] See Also -------- barycenter periphery TNrrcr(rrr)rOrrrr+r,zcenter..r[rYrr\rrrZrc Cs|dur tj||d}n |}|durtdtdgt|}}}|D]7\}}t||kr9td|dt|} |durJ| |j ||<| |krT| }|g}q&| |kr]| |q&|S)aZCalculate barycenter of a connected graph, optionally with edge weights. The :dfn:`barycenter` a :func:`connected ` graph :math:`G` is the subgraph induced by the set of its nodes :math:`v` minimizing the objective function .. math:: \sum_{u \in V(G)} d_G(u, v), where :math:`d_G` is the (possibly weighted) :func:`path length `. The barycenter is also called the :dfn:`median`. See [West01]_, p. 78. Parameters ---------- G : :class:`networkx.Graph` The connected graph :math:`G`. weight : :class:`str`, optional Passed through to :func:`~networkx.algorithms.shortest_paths.generic.shortest_path_length`. attr : :class:`str`, optional If given, write the value of the objective function to each node's `attr` attribute. Otherwise do not store the value. sp : dict of dicts, optional All pairs shortest path lengths as a dictionary of dictionaries Returns ------- list Nodes of `G` that induce the barycenter of `G`. Raises ------ NetworkXNoPath If `G` is disconnected. `G` may appear disconnected to :func:`barycenter` if `sp` is given but is missing shortest path lengths for any pairs. ValueError If `sp` and `weight` are both given. Examples -------- >>> G = nx.Graph([(1, 2), (1, 3), (1, 4), (3, 4), (3, 5), (4, 5)]) >>> nx.barycenter(G) [1, 3, 4] See Also -------- center periphery Nweightz-Cannot use both sp, weight arguments togetherinfz Input graph zH is disconnected, so every induced subgraph has infinite barycentricity.) r4shortest_path_lengthitemsr9floatr1NetworkXNoPathsumr7nodesappend) rr^attrrNsmallestbarycenter_verticesrPr*distsbarycentricityrrrr s*6     r cCsTd}|}tt|D]}|||kr'|d7}||}||||<|||<q |S)z=Counts the number of permutations in SuperLU perm_c or perm_rrr#)tolistranger1index) perm_arrayperm_cntarrrrPrrr_count_lu_permutationsBs   rrdirectedTcCsddl}ddl}ddl}t|sd}t|||vr#d}t|||vr.d}t|||kr9d}t||}t|} |rv|durv|rb|j dddD]\} } } } d | || |<qRn|j dd D] \} } } d | || |<qhtj || |d  d }tt |j d}|| |||ddfdd|f}|| |||ddfdd|f}|jjj|tdd d}|j}|||||j}|dt|j9}|dt|j9}||}||}|jjj|tdd d}|j}|||||j}|dt|j9}|dt|j9}||}||}||||d g|}|||}|S)unReturns the resistance distance between node A and node B on graph G. The resistance distance between two nodes of a graph is akin to treating the graph as a grid of resistorses with a resistance equal to the provided weight. If weight is not provided, then a weight of 1 is used for all edges. Parameters ---------- G : NetworkX graph A graph nodeA : node A node within graph G. nodeB : node A node within graph G, exclusive of Node A. weight : string or None, optional (default=None) The edge data key used to compute the resistance distance. If None, then each edge has weight 1. invert_weight : boolean (default=True) Proper calculation of resistance distance requires building the Laplacian matrix with the reciprocal of the weight. Not required if the weight is already inverted. Weight cannot be zero. Returns ------- rd : float Value of effective resistance distance Examples -------- >>> G = nx.Graph([(1, 2), (1, 3), (1, 4), (3, 4), (3, 5), (4, 5)]) >>> nx.resistance_distance(G, 1, 3) 0.625 Notes ----- Overview discussion: * https://en.wikipedia.org/wiki/Resistance_distance * http://mathworld.wolfram.com/ResistanceDistance.html Additional details: Vaya Sapobi Samui Vos, “Methods for determining the effective resistance,” M.S., Mathematisch Instituut, Universiteit Leiden, Leiden, Netherlands, 2016 Available: `Link to thesis `_ rNz#Graph G must be strongly connected.zNode A is not in graph G.zNode B is not in graph G.z%Node A and Node B cannot be the same.T)keysdatar#)rur]csc) SymmetricMode)options) numpyscipyscipy.sparse.linalgr4 is_connectedr6copylist is_multigraphedgeslaplacian_matrixasformatrmshaperemovernsparselinalgsplur-UdiagonalproductsignrRrrperm_rperm_cabsolutesortdividerf)rnodeAnodeBr^ invert_weightnprNr{r node_listur*krDrRindicesL_aL_ablu_aLdiagALdiagA_slu_abLdiagAB LdiagAB_sLdetrdrrrr Ps^4               r )r)NN)NF)NNN)NT)__doc__networkxr4networkx.utilsr__all__rrrrrrrr rrr rrrrs   G H E # & &N