h<SrSSKrSS/rSrSr\R "SS0SS 9S S j5r\R "SS0SS 9S S j5rg)zG Functions for constructing matrix-like objects from graph attributes. N attr_matrixattr_sparse_matrixcP^^TcSnU$[T5(d UU4SjnU$TnU$)aReturns a function that returns a value from G.nodes[u]. We return a function expecting a node as its sole argument. Then, in the simplest scenario, the returned function will return G.nodes[u][node_attr]. However, we also handle the case when `node_attr` is None or when it is a function itself. Parameters ---------- G : graph A NetworkX graph node_attr : {None, str, callable} Specification of how the value of the node attribute should be obtained from the node attribute dictionary. Returns ------- value : function A function expecting a node as its sole argument. The function will returns a value from G.nodes[u] that depends on `edge_attr`. cU$N)us L/var/www/html/env/lib/python3.13/site-packages/networkx/linalg/attrmatrix.pyvalue_node_value..value$sHc(>TRUT$r)nodes)r G node_attrs r r r )s771:i( (r )callable)rrr s`` r _node_valuer s<0  Li  ) L Lr c&^^Tc#TR5(aU4SjnU$SnU$[T5(dVTS:Xa(TR5(a UU4SjnU$UU4SjnU$TR5(a UU4SjnU$UU4SjnU$TnU$)arReturns a function that returns a value from G[u][v]. Suppose there exists an edge between u and v. Then we return a function expecting u and v as arguments. For Graph and DiGraph, G[u][v] is the edge attribute dictionary, and the function (essentially) returns G[u][v][edge_attr]. However, we also handle cases when `edge_attr` is None and when it is a function itself. For MultiGraph and MultiDiGraph, G[u][v] is a dictionary of all edges between u and v. In this case, the returned function sums the value of `edge_attr` for every edge between u and v. Parameters ---------- G : graph A NetworkX graph edge_attr : {None, str, callable} Specification of how the value of the edge attribute should be obtained from the edge attribute dictionary, G[u][v]. For multigraphs, G[u][v] is a dictionary of all the edges between u and v. This allows for special treatment of multiedges. Returns ------- value : function A function expecting two nodes as parameters. The nodes should represent the from- and to- node of an edge. The function will return a value from G[u][v] that depends on `edge_attr`. c&>[TUU5$r)len)r vrs r r _edge_value..value[s1Q47|#r cgNr)r rs r r r`sr weightcV>[U4SjTUUR555$)Nc3F># UHoRTS5v M g7f)rNget.0d edge_attrs r -_edge_value..value..ksMTUURTS5$rrr*s r r rosQ47;;y!44r cV>[U4SjTUUR555$)Nc3,># UH oTv M g7frrr!s r r%r&wsF5E|5Esr'r*s r r rvs#FQqT!W^^5EFFFr c>TUUT$rrr*s r r r{sQ479--r ) is_multigraphr)rr$r s`` r _edge_valuer07s> ??   $h L_ ^ LYi     NJ LA5@ L7  G2 L).( L Lr r$r) edge_attrs node_attrsc SSKn[X5n[X5n Uc"[UV s1sH o"U 5iM sn 5n OUn [ U 5n UR 5(+n [ [U [U 555nURX4XVS9n[5nUR5HpunnUHJnX"U5X"U5nnUU;dMUUU4==U"UU5- ss'U (dM>UUU4UUU4'ML U (dM_URU5 Mr U(a"XRSS9RU S45-nUcX4$U$s sn f)aqReturns the attribute matrix using attributes from `G` as a numpy array. If only `G` is passed in, then the adjacency matrix is constructed. Let A be a discrete set of values for the node attribute `node_attr`. Then the elements of A represent the rows and columns of the constructed matrix. Now, iterate through every edge e=(u,v) in `G` and consider the value of the edge attribute `edge_attr`. If ua and va are the values of the node attribute `node_attr` for u and v, respectively, then the value of the edge attribute is added to the matrix element at (ua, va). Parameters ---------- G : graph The NetworkX graph used to construct the attribute matrix. edge_attr : str, optional Each element of the matrix represents a running total of the specified edge attribute for edges whose node attributes correspond to the rows/cols of the matrix. The attribute must be present for all edges in the graph. If no attribute is specified, then we just count the number of edges whose node attributes correspond to the matrix element. node_attr : str, optional Each row and column in the matrix represents a particular value of the node attribute. The attribute must be present for all nodes in the graph. Note, the values of this attribute should be reliably hashable. So, float values are not recommended. If no attribute is specified, then the rows and columns will be the nodes of the graph. normalized : bool, optional If True, then each row is normalized by the summation of its values. rc_order : list, optional A list of the node attribute values. This list specifies the ordering of rows and columns of the array. If no ordering is provided, then the ordering will be random (and also, a return value). Other Parameters ---------------- dtype : NumPy data-type, optional A valid NumPy dtype used to initialize the array. Keep in mind certain dtypes can yield unexpected results if the array is to be normalized. The parameter is passed to numpy.zeros(). If unspecified, the NumPy default is used. order : {'C', 'F'}, optional Whether to store multidimensional data in C- or Fortran-contiguous (row- or column-wise) order in memory. This parameter is passed to numpy.zeros(). If unspecified, the NumPy default is used. Returns ------- M : 2D NumPy ndarray The attribute matrix. ordering : list If `rc_order` was specified, then only the attribute matrix is returned. However, if `rc_order` was None, then the ordering used to construct the matrix is returned as well. Examples -------- Construct an adjacency matrix: >>> G = nx.Graph() >>> G.add_edge(0, 1, thickness=1, weight=3) >>> G.add_edge(0, 2, thickness=2) >>> G.add_edge(1, 2, thickness=3) >>> nx.attr_matrix(G, rc_order=[0, 1, 2]) array([[0., 1., 1.], [1., 0., 1.], [1., 1., 0.]]) Alternatively, we can obtain the matrix describing edge thickness. >>> nx.attr_matrix(G, edge_attr="thickness", rc_order=[0, 1, 2]) array([[0., 1., 2.], [1., 0., 3.], [2., 3., 0.]]) We can also color the nodes and ask for the probability distribution over all edges (u,v) describing: Pr(v has color Y | u has color X) >>> G.nodes[0]["color"] = "red" >>> G.nodes[1]["color"] = "red" >>> G.nodes[2]["color"] = "blue" >>> rc = ["red", "blue"] >>> nx.attr_matrix(G, node_attr="color", normalized=True, rc_order=rc) array([[0.33333333, 0.66666667], [1. , 0. ]]) For example, the above tells us that for all edges (u,v): Pr( v is red | u is red) = 1/3 Pr( v is blue | u is red) = 2/3 Pr( v is red | u is blue) = 1 Pr( v is blue | u is blue) = 0 Finally, we can obtain the total weights listed by the node colors. >>> nx.attr_matrix(G, edge_attr="weight", node_attr="color", rc_order=rc) array([[3., 2.], [2., 0.]]) Thus, the total weight over all edges (u,v) with u and v having colors: (red, red) is 3 # the sole contribution is from edge (0,1) (red, blue) is 2 # contributions from edges (0,2) and (1,2) (blue, red) is 2 # same as (red, blue) since graph is undirected (blue, blue) is 0 # there are no edges with blue endpoints rN)dtypeorderraxis)numpyr0rlistr is_directeddictziprangezerosset adjacencyaddr(reshape)rr$r normalizedrc_orderr4r5np edge_value node_valuenorderingN undirectedindexMseenr nbrdictrijs r rrsN~Q*JQ*J21A23 H A]]_$J XuQx( )E !u2A 5Dkkm 7AA'z!})=qA}!Q$:a++:1gAadG  : HHQK$ UUU] " "Aq6 **{93sEc SSKnSSKn[X5n[X5n Uc"[ UV s1sH o"U 5iM sn 5n OUn [ U 5n UR 5(+n [[U [U 555nURRX4US9n[5nUR5HpunnUHJnX"U5X"U5nnUU;dMUUU4==U"UU5- ss'U (dM>UUU4UUU4'ML U (dM_URU5 Mr U(a&USURSS9SS2UR 4- -nUcX4$U$s sn f)aReturns a SciPy sparse array using attributes from G. If only `G` is passed in, then the adjacency matrix is constructed. Let A be a discrete set of values for the node attribute `node_attr`. Then the elements of A represent the rows and columns of the constructed matrix. Now, iterate through every edge e=(u,v) in `G` and consider the value of the edge attribute `edge_attr`. If ua and va are the values of the node attribute `node_attr` for u and v, respectively, then the value of the edge attribute is added to the matrix element at (ua, va). Parameters ---------- G : graph The NetworkX graph used to construct the NumPy matrix. edge_attr : str, optional Each element of the matrix represents a running total of the specified edge attribute for edges whose node attributes correspond to the rows/cols of the matrix. The attribute must be present for all edges in the graph. If no attribute is specified, then we just count the number of edges whose node attributes correspond to the matrix element. node_attr : str, optional Each row and column in the matrix represents a particular value of the node attribute. The attribute must be present for all nodes in the graph. Note, the values of this attribute should be reliably hashable. So, float values are not recommended. If no attribute is specified, then the rows and columns will be the nodes of the graph. normalized : bool, optional If True, then each row is normalized by the summation of its values. rc_order : list, optional A list of the node attribute values. This list specifies the ordering of rows and columns of the array. If no ordering is provided, then the ordering will be random (and also, a return value). Other Parameters ---------------- dtype : NumPy data-type, optional A valid NumPy dtype used to initialize the array. Keep in mind certain dtypes can yield unexpected results if the array is to be normalized. The parameter is passed to numpy.zeros(). If unspecified, the NumPy default is used. Returns ------- M : SciPy sparse array The attribute matrix. ordering : list If `rc_order` was specified, then only the matrix is returned. However, if `rc_order` was None, then the ordering used to construct the matrix is returned as well. Examples -------- Construct an adjacency matrix: >>> G = nx.Graph() >>> G.add_edge(0, 1, thickness=1, weight=3) >>> G.add_edge(0, 2, thickness=2) >>> G.add_edge(1, 2, thickness=3) >>> M = nx.attr_sparse_matrix(G, rc_order=[0, 1, 2]) >>> M.toarray() array([[0., 1., 1.], [1., 0., 1.], [1., 1., 0.]]) Alternatively, we can obtain the matrix describing edge thickness. >>> M = nx.attr_sparse_matrix(G, edge_attr="thickness", rc_order=[0, 1, 2]) >>> M.toarray() array([[0., 1., 2.], [1., 0., 3.], [2., 3., 0.]]) We can also color the nodes and ask for the probability distribution over all edges (u,v) describing: Pr(v has color Y | u has color X) >>> G.nodes[0]["color"] = "red" >>> G.nodes[1]["color"] = "red" >>> G.nodes[2]["color"] = "blue" >>> rc = ["red", "blue"] >>> M = nx.attr_sparse_matrix(G, node_attr="color", normalized=True, rc_order=rc) >>> M.toarray() array([[0.33333333, 0.66666667], [1. , 0. ]]) For example, the above tells us that for all edges (u,v): Pr( v is red | u is red) = 1/3 Pr( v is blue | u is red) = 2/3 Pr( v is red | u is blue) = 1 Pr( v is blue | u is blue) = 0 Finally, we can obtain the total weights listed by the node colors. >>> M = nx.attr_sparse_matrix(G, edge_attr="weight", node_attr="color", rc_order=rc) >>> M.toarray() array([[3., 2.], [2., 0.]]) Thus, the total weight over all edges (u,v) with u and v having colors: (red, red) is 3 # the sole contribution is from edge (0,1) (red, blue) is 2 # contributions from edges (0,2) and (1,2) (blue, red) is 2 # same as (red, blue) since graph is undirected (blue, blue) is 0 # there are no edges with blue endpoints rN)r4rr6)r8scipyr0rr9rr:r;r<r=sparse lil_arrayr?r@rAr(newaxis)rr$rrCrDr4rEsprFrGrHrIrJrKrLrMrNr rOrrPrQs r rr6s]pQ*JQ*J21A23 H A]]_$J XuQx( )E QF%0A 5Dkkm 7AA'z!})=qA}!Q$:a++:1gAadG  : HHQK$ QAq"**}- --{93sE")NNFNNN)NNFNN) __doc__networkxnx__all__rr0 _dispatchablerrrr r r]s . /*ZXvk40[I   `J`Fk40[INRZJZr