From 8e6d6b147523487ca3166a24f4504a9791917c2c Mon Sep 17 00:00:00 2001
From: Matteo Cati <matteo.cati@keble.ox.ac.uk>
Date: Sun, 29 Jan 2023 15:49:26 +0000
Subject: [PATCH 1/2] Add construction of strongly regular digraph

---
 src/doc/en/reference/references/index.rst |  5 +++
 src/sage/graphs/digraph_generators.py     | 47 +++++++++++++++++++++++
 2 files changed, 52 insertions(+)

diff --git a/src/doc/en/reference/references/index.rst b/src/doc/en/reference/references/index.rst
index e747b14139d..2250ec93016 100644
--- a/src/doc/en/reference/references/index.rst
+++ b/src/doc/en/reference/references/index.rst
@@ -2174,6 +2174,11 @@ REFERENCES:
 .. [Duv1983] J.-P. Duval, Factorizing words over an ordered alphabet,
             J. Algorithms 4 (1983) 363--381.
 
+.. [Duv1988] \A. Duval.
+            *A directed graph version of strongly regular graphs*,
+            Journal of Combinatorial Theory, Series A 47(1) (1988): 71-100.
+            :doi:`10.1016/0097-3165(88)90043-X`
+
 .. [DW1995] Andreas W.M. Dress and Walter Wenzel, *A Simple Proof of
             an Identity Concerning Pfaffians of Skew Symmetric
             Matrices*, Advances in Mathematics, volume 112, Issue 1,
diff --git a/src/sage/graphs/digraph_generators.py b/src/sage/graphs/digraph_generators.py
index f1d88178ebb..29fbcf99614 100644
--- a/src/sage/graphs/digraph_generators.py
+++ b/src/sage/graphs/digraph_generators.py
@@ -349,6 +349,53 @@ def Path(self, n):
         g.set_pos({i: (i, 0) for i in range(n)})
         return g
 
+    def StronglyRegular(self, n):
+        r"""
+        Return a Strongly Regular digraph with `n` vertices.
+
+        The adjacency matrix of the graph is constructed from a skew Hadamard
+        matrix of order `n+1`. These graphs were first constructed in [Duv1988]_.
+
+        INPUT:
+
+        - ``n`` -- integer, the number of vertices of the digraph.
+
+        .. SEEALSO::
+
+            - :func:`sage.combinat.matrices.hadamard_matrix.skew_hadamard_matrix`
+            - :meth:`Paley`
+
+        EXAMPLES:
+
+        A Strongly Regular digraph satisfies the condition `AJ = JA = kJ` where
+        `A` is the adjacency matrix::
+
+            sage: g = digraphs.StronglyRegular(7); g
+            Strongly regular digraph: Digraph on 7 vertices
+            sage: A = g.adjacency_matrix()*ones_matrix(7); B = ones_matrix(7)*g.adjacency_matrix()
+            sage: A == B == A[0, 0]*ones_matrix(7)
+            True
+
+        TESTS:
+
+        Wrong parameter::
+
+            sage: digraphs.StronglyRegular(73)
+            Traceback (most recent call last):
+            ...
+            ValueError: strongly regular digraph with 73 vertices not yet implemented
+
+        """
+        from sage.combinat.matrices.hadamard_matrix import skew_hadamard_matrix
+        from sage.matrix.constructor import ones_matrix, identity_matrix
+        if skew_hadamard_matrix(n+1, existence=True) is not True:
+            raise ValueError(f'strongly regular digraph with {n} vertices not yet implemented')
+
+        H = skew_hadamard_matrix(n+1, skew_normalize=True)
+        M = H[1:, 1:]
+        M = (M + ones_matrix(n)) / 2 - identity_matrix(n)
+        return DiGraph(M, format='adjacency_matrix', name=f'Strongly regular digraph')
+
     def Paley(self, q):
         r"""
         Return a Paley digraph on `q` vertices.

From 5bd750c18590a266e95a84f44158f800ab0b2301 Mon Sep 17 00:00:00 2001
From: Matteo Cati <matteo.cati@keble.ox.ac.uk>
Date: Mon, 13 Feb 2023 12:21:12 +0000
Subject: [PATCH 2/2] Fix code style

---
 src/sage/graphs/digraph_generators.py | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/src/sage/graphs/digraph_generators.py b/src/sage/graphs/digraph_generators.py
index 5270d81ed9c..2b864b54284 100644
--- a/src/sage/graphs/digraph_generators.py
+++ b/src/sage/graphs/digraph_generators.py
@@ -388,13 +388,13 @@ def StronglyRegular(self, n):
         """
         from sage.combinat.matrices.hadamard_matrix import skew_hadamard_matrix
         from sage.matrix.constructor import ones_matrix, identity_matrix
-        if skew_hadamard_matrix(n+1, existence=True) is not True:
+        if skew_hadamard_matrix(n + 1, existence=True) is not True:
             raise ValueError(f'strongly regular digraph with {n} vertices not yet implemented')
 
-        H = skew_hadamard_matrix(n+1, skew_normalize=True)
+        H = skew_hadamard_matrix(n + 1, skew_normalize=True)
         M = H[1:, 1:]
         M = (M + ones_matrix(n)) / 2 - identity_matrix(n)
-        return DiGraph(M, format='adjacency_matrix', name=f'Strongly regular digraph')
+        return DiGraph(M, format='adjacency_matrix', name='Strongly regular digraph')
 
     def Paley(self, q):
         r"""