From 4a52a71956a8d46fcb7294ac71734504bb09bcc2 Mon Sep 17 00:00:00 2001
From: S. Solomon Darnell
Date: Fri, 28 Mar 2025 21:52:21 -0500
Subject: two version of R2R are here
---
.../networkx/linalg/modularitymatrix.py | 166 +++++++++++++++++++++
1 file changed, 166 insertions(+)
create mode 100644 .venv/lib/python3.12/site-packages/networkx/linalg/modularitymatrix.py
(limited to '.venv/lib/python3.12/site-packages/networkx/linalg/modularitymatrix.py')
diff --git a/.venv/lib/python3.12/site-packages/networkx/linalg/modularitymatrix.py b/.venv/lib/python3.12/site-packages/networkx/linalg/modularitymatrix.py
new file mode 100644
index 00000000..0287910b
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/networkx/linalg/modularitymatrix.py
@@ -0,0 +1,166 @@
+"""Modularity matrix of graphs."""
+
+import networkx as nx
+from networkx.utils import not_implemented_for
+
+__all__ = ["modularity_matrix", "directed_modularity_matrix"]
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatchable(edge_attrs="weight")
+def modularity_matrix(G, nodelist=None, weight=None):
+ r"""Returns the modularity matrix of G.
+
+ The modularity matrix is the matrix B = A - , where A is the adjacency
+ matrix and is the average adjacency matrix, assuming that the graph
+ is described by the configuration model.
+
+ More specifically, the element B_ij of B is defined as
+
+ .. math::
+ A_{ij} - {k_i k_j \over 2 m}
+
+ where k_i is the degree of node i, and where m is the number of edges
+ in the graph. When weight is set to a name of an attribute edge, Aij, k_i,
+ k_j and m are computed using its value.
+
+ Parameters
+ ----------
+ G : Graph
+ A NetworkX graph
+
+ nodelist : list, optional
+ The rows and columns are ordered according to the nodes in nodelist.
+ If nodelist is None, then the ordering is produced by G.nodes().
+
+ weight : string or None, optional (default=None)
+ The edge attribute that holds the numerical value used for
+ the edge weight. If None then all edge weights are 1.
+
+ Returns
+ -------
+ B : Numpy array
+ The modularity matrix of G.
+
+ Examples
+ --------
+ >>> k = [3, 2, 2, 1, 0]
+ >>> G = nx.havel_hakimi_graph(k)
+ >>> B = nx.modularity_matrix(G)
+
+
+ See Also
+ --------
+ to_numpy_array
+ modularity_spectrum
+ adjacency_matrix
+ directed_modularity_matrix
+
+ References
+ ----------
+ .. [1] M. E. J. Newman, "Modularity and community structure in networks",
+ Proc. Natl. Acad. Sci. USA, vol. 103, pp. 8577-8582, 2006.
+ """
+ import numpy as np
+
+ if nodelist is None:
+ nodelist = list(G)
+ A = nx.to_scipy_sparse_array(G, nodelist=nodelist, weight=weight, format="csr")
+ k = A.sum(axis=1)
+ m = k.sum() * 0.5
+ # Expected adjacency matrix
+ X = np.outer(k, k) / (2 * m)
+
+ return A - X
+
+
+@not_implemented_for("undirected")
+@not_implemented_for("multigraph")
+@nx._dispatchable(edge_attrs="weight")
+def directed_modularity_matrix(G, nodelist=None, weight=None):
+ """Returns the directed modularity matrix of G.
+
+ The modularity matrix is the matrix B = A - , where A is the adjacency
+ matrix and is the expected adjacency matrix, assuming that the graph
+ is described by the configuration model.
+
+ More specifically, the element B_ij of B is defined as
+
+ .. math::
+ B_{ij} = A_{ij} - k_i^{out} k_j^{in} / m
+
+ where :math:`k_i^{in}` is the in degree of node i, and :math:`k_j^{out}` is the out degree
+ of node j, with m the number of edges in the graph. When weight is set
+ to a name of an attribute edge, Aij, k_i, k_j and m are computed using
+ its value.
+
+ Parameters
+ ----------
+ G : DiGraph
+ A NetworkX DiGraph
+
+ nodelist : list, optional
+ The rows and columns are ordered according to the nodes in nodelist.
+ If nodelist is None, then the ordering is produced by G.nodes().
+
+ weight : string or None, optional (default=None)
+ The edge attribute that holds the numerical value used for
+ the edge weight. If None then all edge weights are 1.
+
+ Returns
+ -------
+ B : Numpy array
+ The modularity matrix of G.
+
+ Examples
+ --------
+ >>> G = nx.DiGraph()
+ >>> G.add_edges_from(
+ ... (
+ ... (1, 2),
+ ... (1, 3),
+ ... (3, 1),
+ ... (3, 2),
+ ... (3, 5),
+ ... (4, 5),
+ ... (4, 6),
+ ... (5, 4),
+ ... (5, 6),
+ ... (6, 4),
+ ... )
+ ... )
+ >>> B = nx.directed_modularity_matrix(G)
+
+
+ Notes
+ -----
+ NetworkX defines the element A_ij of the adjacency matrix as 1 if there
+ is a link going from node i to node j. Leicht and Newman use the opposite
+ definition. This explains the different expression for B_ij.
+
+ See Also
+ --------
+ to_numpy_array
+ modularity_spectrum
+ adjacency_matrix
+ modularity_matrix
+
+ References
+ ----------
+ .. [1] E. A. Leicht, M. E. J. Newman,
+ "Community structure in directed networks",
+ Phys. Rev Lett., vol. 100, no. 11, p. 118703, 2008.
+ """
+ import numpy as np
+
+ if nodelist is None:
+ nodelist = list(G)
+ A = nx.to_scipy_sparse_array(G, nodelist=nodelist, weight=weight, format="csr")
+ k_in = A.sum(axis=0)
+ k_out = A.sum(axis=1)
+ m = k_in.sum()
+ # Expected adjacency matrix
+ X = np.outer(k_out, k_in) / m
+
+ return A - X
--
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