Change "Topologically Identical" Definition

Avoid mixing UB and exception conditions of topologically
identical. Only specify violating topologically identical
conditions as UB.

sycl/doc/extensions/experimental/sycl_ext_oneapi_graph.asciidoc

@@ -206,7 +206,7 @@ Table {counter: tableNumber}. Values of the `SYCL_EXT_ONEAPI_GRAPH` macro.
 |1     |Initial extension version. Base features are supported.
 |===
 
-=== SYCL Graph Terminology
+=== SYCL Graph Terminology [[terminology]]
 
 Table {counter: tableNumber}. Terminology.
 [%header,cols="1,3"]
@@ -776,34 +776,37 @@ conditions:
 
 * Both graphs must have been created with the same device and context.
 * Both graphs must be topologically identical. The graphs are considered
-topologically identical when:
-
-** Both graphs have the same number of nodes and edges.
-** Where edges are specified through the `depends_on` property or through event
-dependencies in recorded queue submisions, these must be specified in the same
-order. 
-** Nodes with dependencies on events outside of the graph must have the same
-number of these dependencies.
-** A kernel node's command function must have the same type in both graphs,
-whether that be a lambda function, function object or otherwise.
-** When creating both graphs all graph-related API calls or operations which
-modify the structure of the graph must have been done in the same order, these
-are:
-
-*** Explicit API calls to add nodes to the graph or calls to `make_edge()`.
-*** Nodes added to a graph via recorded queue submissions.
+  topologically identical when:
+
+** Both graphs must have the same number of nodes and edges.
+** Internal edges must be between corresponding nodes in each graph.
+** Nodes must be added in the same order in the two graphs. Nodes may be added
+   via `command_graph::add`, or for a recorded queue via `queue::submit` or
+   queue shortcut functions.
+** Corresponding nodes in each graph must be kernels that have the same type:
+
+*** When the kernel is defined as a lambda, the lambda must be the same.
+*** When the kernel is defined as a named function object, the kernel class
+    must be the same.
+*** When the kernel is defined as a plain function, the function must be the
+    same.
+
+** Edge dependencies for each node in the two graphs must be created in the
+   same order and using the same API mechanism to create each edge. See
+   the <<terminology, terminology section>> for an exhaustive definition of
+   how edges are defined in a graph for each of the two graph construction
+   APIs.
 
 Attempting to use whole-graph update with source or target graphs which do not
-satisfy these conditions results in undefined behaviour as it may prevent the
-runtime from pairing nodes in the source and target graphs.
+satisfy the conditions of topological identity results in undefined behaviour,
+as it may prevent the runtime from pairing nodes in the source and target
+graphs.
 
 It is valid to use nodes that contain dynamic parameters in whole graph updates.
 If a node containing a dynamic parameter is updated through the whole graph
 update API, then any previous updates to the dynamic parameter will be reflected
 in the new graph.
 
-:sycl-kernel-function: https://registry.khronos.org/SYCL/specs/sycl-2020/html/sycl-2020.html#sycl-kernel-function
-
 ==== Graph Properties [[graph-properties]]
 
 ===== No-Cycle-Check Property
@@ -1228,7 +1231,7 @@ The characteristics in the executable graph which will be updated are detailed
 in the section on <<executable-graph-update, Executable Graph Update>>.
 
 It is not an error to update an executable graph such that all parameters of
-nodes in `graph` are identical to the arguments of the executable graph prior to
+nodes in `source` are identical to the arguments of the executable graph prior to
 the update.
 
 The implementation may perform a blocking wait during this call on
@@ -1248,22 +1251,13 @@ Parameters:
 
 Exceptions:
 
-* Throws synchronously with error code `invalid` if the topology of
-  `source` is not the same as the target graph topology in the following ways:
-
-** The number of nodes in the graph does not match.
-** The number of edges between nodes does not match.
-** Any node in `source` has a dependency which does not matched the paired node
-   in the target graph.
-
 * Throws synchronously with error code `invalid` if `source` contains any node
-  which is not of the following `node_type`s:
+  which is not one of the following types:
 
-** `node_type::empty`  
+** `node_type::empty`
 ** `node_type::ext_oneapi_barrier`
 ** `node_type::kernel`
 
-
 * Throws synchronously with error code `invalid` if the context or device
   associated with `source` does not match that of the `command_graph` being
   updated.