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465 lines
15 KiB
465 lines
15 KiB
5 months ago
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"""
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Functions for constructing matrix-like objects from graph attributes.
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"""
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import networkx as nx
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__all__ = ["attr_matrix", "attr_sparse_matrix"]
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def _node_value(G, node_attr):
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"""Returns a function that returns a value from G.nodes[u].
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We return a function expecting a node as its sole argument. Then, in the
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simplest scenario, the returned function will return G.nodes[u][node_attr].
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However, we also handle the case when `node_attr` is None or when it is a
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function itself.
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Parameters
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----------
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G : graph
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A NetworkX graph
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node_attr : {None, str, callable}
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Specification of how the value of the node attribute should be obtained
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from the node attribute dictionary.
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Returns
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-------
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value : function
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A function expecting a node as its sole argument. The function will
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returns a value from G.nodes[u] that depends on `edge_attr`.
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"""
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if node_attr is None:
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def value(u):
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return u
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elif not callable(node_attr):
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# assume it is a key for the node attribute dictionary
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def value(u):
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return G.nodes[u][node_attr]
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else:
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# Advanced: Allow users to specify something else.
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#
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# For example,
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# node_attr = lambda u: G.nodes[u].get('size', .5) * 3
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#
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value = node_attr
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return value
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def _edge_value(G, edge_attr):
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"""Returns a function that returns a value from G[u][v].
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Suppose there exists an edge between u and v. Then we return a function
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expecting u and v as arguments. For Graph and DiGraph, G[u][v] is
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the edge attribute dictionary, and the function (essentially) returns
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G[u][v][edge_attr]. However, we also handle cases when `edge_attr` is None
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and when it is a function itself. For MultiGraph and MultiDiGraph, G[u][v]
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is a dictionary of all edges between u and v. In this case, the returned
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function sums the value of `edge_attr` for every edge between u and v.
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Parameters
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----------
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G : graph
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A NetworkX graph
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edge_attr : {None, str, callable}
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Specification of how the value of the edge attribute should be obtained
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from the edge attribute dictionary, G[u][v]. For multigraphs, G[u][v]
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is a dictionary of all the edges between u and v. This allows for
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special treatment of multiedges.
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Returns
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-------
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value : function
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A function expecting two nodes as parameters. The nodes should
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represent the from- and to- node of an edge. The function will
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return a value from G[u][v] that depends on `edge_attr`.
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"""
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if edge_attr is None:
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# topological count of edges
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if G.is_multigraph():
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def value(u, v):
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return len(G[u][v])
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else:
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def value(u, v):
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return 1
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elif not callable(edge_attr):
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# assume it is a key for the edge attribute dictionary
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if edge_attr == "weight":
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# provide a default value
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if G.is_multigraph():
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def value(u, v):
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return sum(d.get(edge_attr, 1) for d in G[u][v].values())
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else:
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def value(u, v):
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return G[u][v].get(edge_attr, 1)
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else:
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# otherwise, the edge attribute MUST exist for each edge
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if G.is_multigraph():
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def value(u, v):
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return sum(d[edge_attr] for d in G[u][v].values())
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else:
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def value(u, v):
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return G[u][v][edge_attr]
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else:
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# Advanced: Allow users to specify something else.
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#
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# Alternative default value:
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# edge_attr = lambda u,v: G[u][v].get('thickness', .5)
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#
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# Function on an attribute:
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# edge_attr = lambda u,v: abs(G[u][v]['weight'])
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#
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# Handle Multi(Di)Graphs differently:
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# edge_attr = lambda u,v: numpy.prod([d['size'] for d in G[u][v].values()])
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#
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# Ignore multiple edges
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# edge_attr = lambda u,v: 1 if len(G[u][v]) else 0
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#
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value = edge_attr
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return value
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@nx._dispatchable(edge_attrs={"edge_attr": None}, node_attrs="node_attr")
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def attr_matrix(
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G,
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edge_attr=None,
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node_attr=None,
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normalized=False,
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rc_order=None,
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dtype=None,
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order=None,
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):
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"""Returns the attribute matrix using attributes from `G` as a numpy array.
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If only `G` is passed in, then the adjacency matrix is constructed.
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Let A be a discrete set of values for the node attribute `node_attr`. Then
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the elements of A represent the rows and columns of the constructed matrix.
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Now, iterate through every edge e=(u,v) in `G` and consider the value
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of the edge attribute `edge_attr`. If ua and va are the values of the
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node attribute `node_attr` for u and v, respectively, then the value of
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the edge attribute is added to the matrix element at (ua, va).
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Parameters
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----------
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G : graph
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The NetworkX graph used to construct the attribute matrix.
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edge_attr : str, optional
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Each element of the matrix represents a running total of the
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specified edge attribute for edges whose node attributes correspond
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to the rows/cols of the matrix. The attribute must be present for
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all edges in the graph. If no attribute is specified, then we
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just count the number of edges whose node attributes correspond
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to the matrix element.
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node_attr : str, optional
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Each row and column in the matrix represents a particular value
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of the node attribute. The attribute must be present for all nodes
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in the graph. Note, the values of this attribute should be reliably
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hashable. So, float values are not recommended. If no attribute is
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specified, then the rows and columns will be the nodes of the graph.
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normalized : bool, optional
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If True, then each row is normalized by the summation of its values.
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rc_order : list, optional
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A list of the node attribute values. This list specifies the ordering
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of rows and columns of the array. If no ordering is provided, then
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the ordering will be random (and also, a return value).
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Other Parameters
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----------------
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dtype : NumPy data-type, optional
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A valid NumPy dtype used to initialize the array. Keep in mind certain
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dtypes can yield unexpected results if the array is to be normalized.
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The parameter is passed to numpy.zeros(). If unspecified, the NumPy
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default is used.
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order : {'C', 'F'}, optional
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Whether to store multidimensional data in C- or Fortran-contiguous
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(row- or column-wise) order in memory. This parameter is passed to
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numpy.zeros(). If unspecified, the NumPy default is used.
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Returns
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-------
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M : 2D NumPy ndarray
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The attribute matrix.
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ordering : list
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If `rc_order` was specified, then only the attribute matrix is returned.
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However, if `rc_order` was None, then the ordering used to construct
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the matrix is returned as well.
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Examples
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--------
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Construct an adjacency matrix:
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>>> G = nx.Graph()
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>>> G.add_edge(0, 1, thickness=1, weight=3)
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>>> G.add_edge(0, 2, thickness=2)
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>>> G.add_edge(1, 2, thickness=3)
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>>> nx.attr_matrix(G, rc_order=[0, 1, 2])
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array([[0., 1., 1.],
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[1., 0., 1.],
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[1., 1., 0.]])
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Alternatively, we can obtain the matrix describing edge thickness.
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>>> nx.attr_matrix(G, edge_attr="thickness", rc_order=[0, 1, 2])
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array([[0., 1., 2.],
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[1., 0., 3.],
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[2., 3., 0.]])
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We can also color the nodes and ask for the probability distribution over
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all edges (u,v) describing:
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Pr(v has color Y | u has color X)
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>>> G.nodes[0]["color"] = "red"
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>>> G.nodes[1]["color"] = "red"
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>>> G.nodes[2]["color"] = "blue"
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>>> rc = ["red", "blue"]
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>>> nx.attr_matrix(G, node_attr="color", normalized=True, rc_order=rc)
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array([[0.33333333, 0.66666667],
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[1. , 0. ]])
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For example, the above tells us that for all edges (u,v):
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Pr( v is red | u is red) = 1/3
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Pr( v is blue | u is red) = 2/3
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Pr( v is red | u is blue) = 1
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Pr( v is blue | u is blue) = 0
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Finally, we can obtain the total weights listed by the node colors.
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>>> nx.attr_matrix(G, edge_attr="weight", node_attr="color", rc_order=rc)
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array([[3., 2.],
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[2., 0.]])
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Thus, the total weight over all edges (u,v) with u and v having colors:
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(red, red) is 3 # the sole contribution is from edge (0,1)
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(red, blue) is 2 # contributions from edges (0,2) and (1,2)
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(blue, red) is 2 # same as (red, blue) since graph is undirected
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(blue, blue) is 0 # there are no edges with blue endpoints
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"""
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import numpy as np
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edge_value = _edge_value(G, edge_attr)
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node_value = _node_value(G, node_attr)
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if rc_order is None:
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ordering = list({node_value(n) for n in G})
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else:
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ordering = rc_order
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N = len(ordering)
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undirected = not G.is_directed()
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index = dict(zip(ordering, range(N)))
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M = np.zeros((N, N), dtype=dtype, order=order)
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seen = set()
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for u, nbrdict in G.adjacency():
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for v in nbrdict:
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# Obtain the node attribute values.
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i, j = index[node_value(u)], index[node_value(v)]
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if v not in seen:
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M[i, j] += edge_value(u, v)
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if undirected:
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M[j, i] = M[i, j]
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if undirected:
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seen.add(u)
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if normalized:
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M /= M.sum(axis=1).reshape((N, 1))
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if rc_order is None:
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return M, ordering
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else:
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return M
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@nx._dispatchable(edge_attrs={"edge_attr": None}, node_attrs="node_attr")
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def attr_sparse_matrix(
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G, edge_attr=None, node_attr=None, normalized=False, rc_order=None, dtype=None
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):
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"""Returns a SciPy sparse array using attributes from G.
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If only `G` is passed in, then the adjacency matrix is constructed.
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Let A be a discrete set of values for the node attribute `node_attr`. Then
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the elements of A represent the rows and columns of the constructed matrix.
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Now, iterate through every edge e=(u,v) in `G` and consider the value
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of the edge attribute `edge_attr`. If ua and va are the values of the
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node attribute `node_attr` for u and v, respectively, then the value of
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the edge attribute is added to the matrix element at (ua, va).
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Parameters
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----------
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G : graph
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The NetworkX graph used to construct the NumPy matrix.
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edge_attr : str, optional
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Each element of the matrix represents a running total of the
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specified edge attribute for edges whose node attributes correspond
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to the rows/cols of the matrix. The attribute must be present for
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all edges in the graph. If no attribute is specified, then we
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just count the number of edges whose node attributes correspond
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to the matrix element.
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node_attr : str, optional
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Each row and column in the matrix represents a particular value
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of the node attribute. The attribute must be present for all nodes
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in the graph. Note, the values of this attribute should be reliably
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hashable. So, float values are not recommended. If no attribute is
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specified, then the rows and columns will be the nodes of the graph.
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normalized : bool, optional
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If True, then each row is normalized by the summation of its values.
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rc_order : list, optional
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A list of the node attribute values. This list specifies the ordering
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of rows and columns of the array. If no ordering is provided, then
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the ordering will be random (and also, a return value).
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Other Parameters
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----------------
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dtype : NumPy data-type, optional
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A valid NumPy dtype used to initialize the array. Keep in mind certain
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dtypes can yield unexpected results if the array is to be normalized.
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The parameter is passed to numpy.zeros(). If unspecified, the NumPy
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default is used.
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Returns
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-------
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M : SciPy sparse array
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The attribute matrix.
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ordering : list
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If `rc_order` was specified, then only the matrix is returned.
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However, if `rc_order` was None, then the ordering used to construct
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the matrix is returned as well.
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Examples
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--------
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Construct an adjacency matrix:
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>>> G = nx.Graph()
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>>> G.add_edge(0, 1, thickness=1, weight=3)
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>>> G.add_edge(0, 2, thickness=2)
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>>> G.add_edge(1, 2, thickness=3)
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>>> M = nx.attr_sparse_matrix(G, rc_order=[0, 1, 2])
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>>> M.toarray()
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array([[0., 1., 1.],
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|
[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
|
||
|
|
|
||
|
|
"""
|
||
|
|
import numpy as np
|
||
|
|
import scipy as sp
|
||
|
|
|
||
|
|
edge_value = _edge_value(G, edge_attr)
|
||
|
|
node_value = _node_value(G, node_attr)
|
||
|
|
|
||
|
|
if rc_order is None:
|
||
|
|
ordering = list({node_value(n) for n in G})
|
||
|
|
else:
|
||
|
|
ordering = rc_order
|
||
|
|
|
||
|
|
N = len(ordering)
|
||
|
|
undirected = not G.is_directed()
|
||
|
|
index = dict(zip(ordering, range(N)))
|
||
|
|
M = sp.sparse.lil_array((N, N), dtype=dtype)
|
||
|
|
|
||
|
|
seen = set()
|
||
|
|
for u, nbrdict in G.adjacency():
|
||
|
|
for v in nbrdict:
|
||
|
|
# Obtain the node attribute values.
|
||
|
|
i, j = index[node_value(u)], index[node_value(v)]
|
||
|
|
if v not in seen:
|
||
|
|
M[i, j] += edge_value(u, v)
|
||
|
|
if undirected:
|
||
|
|
M[j, i] = M[i, j]
|
||
|
|
|
||
|
|
if undirected:
|
||
|
|
seen.add(u)
|
||
|
|
|
||
|
|
if normalized:
|
||
|
|
M *= 1 / M.sum(axis=1)[:, np.newaxis] # in-place mult preserves sparse
|
||
|
|
|
||
|
|
if rc_order is None:
|
||
|
|
return M, ordering
|
||
|
|
else:
|
||
|
|
return M
|