Ticket #8513: trac_8513_graph_theory_documentation-smallfixes.patch

sage/graphs/generic_graph.py

@@ -2916 +2916 @@
         itself has no cut vertices. Two distinct blocks cannot overlap in
         more than a single cut vertex.
         
-        OUTPUT: ( B, C ), where B is a list of blocks- each is a list of
-        vertices and the blocks are the corresponding induced subgraphs-
-        and C is a list of cut vertices.
+        OUTPUT: ``( B, C )``, where ``B`` is a list of blocks- each is 
+        a list of vertices and the blocks are the corresponding induced
+        subgraphs-and ``C`` is a list of cut vertices.
         
         EXAMPLES::
         
@@ -2949 +2949 @@
             ...
             NotImplementedError: ...
 
-        ALGORITHM: 8.3.8 in [1]. Notice that the termination condition on 
-        line (23) of the algorithm uses "p[v] == 0" which in the book 
-        means that the parent is undefined; in this case, v must be the 
-        root s.  Since our vertex names start with 0, we substitute instead
-        the condition "v == s".  This is the terminating condition used 
+        ALGORITHM: 8.3.8 in [Jungnickel05]_. Notice that the termination condition on 
+        line (23) of the algorithm uses ``p[v] == 0`` which in the book 
+        means that the parent is undefined; in this case, `v` must be the 
+        root `s`.  Since our vertex names start with `0`, we substitute instead
+        the condition ``v == s``.  This is the terminating condition used 
         in the general Depth First Search tree in Algorithm 8.2.1.
         
         REFERENCE:
 
-        - [1] D. Jungnickel, Graphs, Networks and Algorithms,
+        .. [Jungnickel05] D. Jungnickel, Graphs, Networks and Algorithms,
           Springer, 2005.
         """
         if not self: # empty graph
@@ -3826 +3826 @@
 
         This function returns a list of such paths.
 
-        NOTE:
-
-        This function is topological : it does not take the eventual
-        weights of the edges into account.
+        .. NOTE::
+
+            This function is topological : it does not take the eventual
+            weights of the edges into account.
 
         EXAMPLE:
 
@@ -6583 +6583 @@
         ordered list.
         
         The clustering coefficient of a graph is the fraction of possible
-        triangles that are triangles, c_i = triangles_i /
-        (k_i\*(k_i-1)/2) where k_i is the degree of vertex i, [1]. A
-        coefficient for the whole graph is the average of the c_i.
+        triangles that are triangles, `c_i = triangles_i /
+        (k_i\*(k_i-1)/2)` where `k_i` is the degree of vertex `i`, [1]. A
+        coefficient for the whole graph is the average of the `c_i`.
         Transitivity is the fraction of all possible triangles which are
         triangles, T = 3\*triangles/triads, [HSSNX]_.
         
@@ -6622 +6622 @@
         Returns the average clustering coefficient.
         
         The clustering coefficient of a graph is the fraction of possible
-        triangles that are triangles, c_i = triangles_i /
-        (k_i\*(k_i-1)/2) where k_i is the degree of vertex i, [1]. A
-        coefficient for the whole graph is the average of the c_i.
+        triangles that are triangles, `c_i = triangles_i /
+        (k_i\*(k_i-1)/2)` where `k_i` is the degree of vertex `i`, [1]. A
+        coefficient for the whole graph is the average of the `c_i`.
         Transitivity is the fraction of all possible triangles which are
         triangles, T = 3\*triangles/triads, [1].
         
@@ -6648 +6648 @@
         ordered list.
         
         The clustering coefficient of a graph is the fraction of possible
-        triangles that are triangles, c_i = triangles_i /
-        (k_i\*(k_i-1)/2) where k_i is the degree of vertex i, [1]. A
-        coefficient for the whole graph is the average of the c_i.
+        triangles that are triangles, `c_i = triangles_i /
+        (k_i\*(k_i-1)/2)` where `k_i` is the degree of vertex `i`, [1]. A
+        coefficient for the whole graph is the average of the `c_i`.
         Transitivity is the fraction of all possible triangles which are
         triangles, T = 3\*triangles/triads, [1].
         
@@ -6697 +6697 @@
         graph.
         
         The clustering coefficient of a graph is the fraction of possible
-        triangles that are triangles, c_i = triangles_i /
-        (k_i\*(k_i-1)/2) where k_i is the degree of vertex i, [1]. A
-        coefficient for the whole graph is the average of the c_i.
+        triangles that are triangles, `c_i = triangles_i /
+        (k_i\*(k_i-1)/2)` where `k_i` is the degree of vertex `i`, [1]. A
+        coefficient for the whole graph is the average of the `c_i`.
         Transitivity is the fraction of all possible triangles which are
         triangles, T = 3\*triangles/triads, [1].
         
         REFERENCE:
 
-        - [1] Aric Hagberg, Dan Schult and Pieter Swart. NetworkX
+        .. [1] Aric Hagberg, Dan Schult and Pieter Swart. NetworkX
           documentation. [Online] Available:
           https://networkx.lanl.gov/reference/networkx/
         
@@ -8526 +8526 @@
         """
         Returns the Cartesian product of self and other.
         
-        The Cartesian product of G and H is the graph L with vertex set
-        V(L) equal to the Cartesian product of the vertices V(G) and V(H),
-        and ((u,v), (w,x)) is an edge iff either - (u, w) is an edge of
-        self and v = x, or - (v, x) is an edge of other and u = w.
+        The Cartesian product of `G` and `H` is the graph `L` with vertex set
+        `V(L)` equal to the Cartesian product of the vertices `V(G)` and `V(H)`,
+        and `((u,v), (w,x))` is an edge iff either - `(u, w)` is an edge of
+        self and `v = x`, or - `(v, x)` is an edge of other and `u = w`.
         
         EXAMPLES::
         
@@ -8573 +8573 @@
         Returns the tensor product, also called the categorical product, of
         self and other.
         
-        The tensor product of G and H is the graph L with vertex set V(L)
-        equal to the Cartesian product of the vertices V(G) and V(H), and
-        ((u,v), (w,x)) is an edge iff - (u, w) is an edge of self, and -
-        (v, x) is an edge of other.
+        The tensor product of `G` and `H` is the graph `L` with vertex set `V(L)`
+        equal to the Cartesian product of the vertices `V(G)` and `V(H)`, and
+        `((u,v), (w,x))` is an edge iff - `(u, w)` is an edge of self, and -
+        `(v, x)` is an edge of other.
         
         EXAMPLES::
         

sage/graphs/graph.py

@@ -1411 +1411 @@
           as a Graph object.
         - When no solution exists, returns ``False``
 
-        NOTES:
+        .. NOTE::
 
-        - This algorithm computes the degree-constrained subgraph of minimum weight.
-        - If the graph's edges are weighted, these are taken into account.
-        - This problem can be solved in polynomial time.
+            - This algorithm computes the degree-constrained subgraph of minimum weight.
+            - If the graph's edges are weighted, these are taken into account.
+            - This problem can be solved in polynomial time.
 
         EXAMPLES:
 
@@ -1491 +1491 @@
 
         A digraph representing an orientation of the current graph.
 
-        NOTES:
+        .. NOTE::
         
-        - This method assumes the graph is connected.
-        - This algorithm works in O(m).
+            - This method assumes the graph is connected.
+            - This algorithm works in O(m).
 
         EXAMPLE:
 
@@ -2163 +2163 @@
         by a list of vertices. A clique is an induced complete subgraph, and a
         maximal clique is one not contained in a larger one.
         
-        NOTES:
+        .. NOTE::
         
-         - Currently only implemented for undirected graphs. Use to_undirected
-           to convert a digraph to an undirected graph.
+            Currently only implemented for undirected graphs. Use to_undirected
+            to convert a digraph to an undirected graph.
         
         ALGORITHM:
         
@@ -2223 +2223 @@
         by a list of vertices. A clique is an induced complete subgraph, and a
         maximum clique is one of maximal order.
         
-        NOTES:
+        .. NOTE::
         
-        - Currently only implemented for undirected graphs. Use to_undirected
-          to convert a digraph to an undirected graph.
+            Currently only implemented for undirected graphs. Use to_undirected
+            to convert a digraph to an undirected graph.
         
         ALGORITHM:
         
@@ -2262 +2262 @@
         """
         Returns the vertex set of a maximal order complete subgraph.
         
-        NOTE:
+        .. NOTE::
         
-         - Currently only implemented for undirected graphs. Use to_undirected
-           to convert a digraph to an undirected graph.
+            Currently only implemented for undirected graphs. Use to_undirected
+            to convert a digraph to an undirected graph.
         
         ALGORITHM:
         
@@ -2289 +2289 @@
         Returns the order of the largest clique of the graph (the clique
         number).
 
-        NOTE:
+        .. NOTE::
         
-         - Currently only implemented for undirected graphs. Use ``to_undirected``
-           to convert a digraph to an undirected graph.
+            Currently only implemented for undirected graphs. Use ``to_undirected``
+            to convert a digraph to an undirected graph.
 
         INPUT:
         
@@ -2334 +2334 @@
         Returns a list of the number of maximal cliques containing each
         vertex. (Returns a single value if only one input vertex).
         
-        NOTES:
+        .. NOTE::
         
-         - Currently only implemented for undirected graphs. Use to_undirected
-           to convert a digraph to an undirected graph.
+            Currently only implemented for undirected graphs. Use to_undirected
+            to convert a digraph to an undirected graph.
         
         INPUT:
         
@@ -2387 +2387 @@
         edges between maximal cliques with common members in the original
         graph.
         
-        NOTES:
+        .. NOTE::
         
-         - Currently only implemented for undirected graphs. Use to_undirected
-           to convert a digraph to an undirected graph.
+            Currently only implemented for undirected graphs. Use to_undirected
+            to convert a digraph to an undirected graph.
         
         INPUT:
         
@@ -2417 +2417 @@
         graph. Right and left vertices are connected if the bottom vertex
         belongs to the clique represented by a top vertex.
         
-        NOTES:
+        .. NOTE::
         
-         - Currently only implemented for undirected graphs. Use to_undirected
-           to convert a digraph to an undirected graph.
+            Currently only implemented for undirected graphs. Use to_undirected
+            to convert a digraph to an undirected graph.
         
         EXAMPLES::
         
@@ -2442 +2442 @@
         Returns a maximal independent set, which is a set of vertices which
         induces an empty subgraph. Uses Cliquer [NisOst2003]_.
         
-        NOTES:
+        .. NOTE::
         
-         - Currently only implemented for undirected graphs. Use to_undirected
-           to convert a digraph to an undirected graph.
+            Currently only implemented for undirected graphs. Use to_undirected
+            to convert a digraph to an undirected graph.
         
         EXAMPLES::
         
@@ -2462 +2462 @@
         Returns a list of sizes of the largest maximal cliques containing
         each vertex. (Returns a single value if only one input vertex).
         
-        NOTES:
+        .. NOTE::
         
-         - Currently only implemented for undirected graphs. Use to_undirected
-           to convert a digraph to an undirected graph.
+            Currently only implemented for undirected graphs. Use to_undirected
+            to convert a digraph to an undirected graph.
         
         INPUT:
         
@@ -2535 +2535 @@
         Returns the cliques containing each vertex, represented as a list
         of lists. (Returns a single list if only one input vertex).
         
-        NOTE:
+        .. NOTE::
         
-         - Currently only implemented for undirected graphs. Use to_undirected
-           to convert a digraph to an undirected graph.
+            Currently only implemented for undirected graphs. Use to_undirected
+            to convert a digraph to an undirected graph.
         
         INPUT: