diff --git a/lemon/network_simplex.h b/lemon/network_simplex.h
--- a/lemon/network_simplex.h
+++ b/lemon/network_simplex.h
@@ -43,13 +43,13 @@
   /// for finding a \ref min_cost_flow "minimum cost flow"
   /// \ref amo93networkflows, \ref dantzig63linearprog,
   /// \ref kellyoneill91netsimplex.
-  /// This algorithm is a specialized version of the linear programming
-  /// simplex method directly for the minimum cost flow problem.
-  /// It is one of the most efficient solution methods.
+  /// This algorithm is a highly efficient specialized version of the
+  /// linear programming simplex method directly for the minimum cost
+  /// flow problem.
   ///
-  /// In general this class is the fastest implementation available
-  /// in LEMON for the minimum cost flow problem.
-  /// Moreover it supports both directions of the supply/demand inequality
+  /// In general, %NetworkSimplex is the fastest implementation available
+  /// in LEMON for this problem.
+  /// Moreover, it supports both directions of the supply/demand inequality
   /// constraints. For more information, see \ref SupplyType.
   ///
   /// Most of the parameters of the problem (except for the digraph)
@@ -58,12 +58,12 @@
   /// specified, then default values will be used.
   ///
   /// \tparam GR The digraph type the algorithm runs on.
-  /// \tparam V The value type used for flow amounts, capacity bounds
+  /// \tparam V The number type used for flow amounts, capacity bounds
   /// and supply values in the algorithm. By default, it is \c int.
-  /// \tparam C The value type used for costs and potentials in the
+  /// \tparam C The number type used for costs and potentials in the
   /// algorithm. By default, it is the same as \c V.
   ///
-  /// \warning Both value types must be signed and all input data must
+  /// \warning Both number types must be signed and all input data must
   /// be integer.
   ///
   /// \note %NetworkSimplex provides five different pivot rule
@@ -126,7 +126,7 @@
     /// of the algorithm.
     /// By default, \ref BLOCK_SEARCH "Block Search" is used, which
     /// proved to be the most efficient and the most robust on various
-    /// test inputs according to our benchmark tests.
+    /// test inputs.
     /// However, another pivot rule can be selected using the \ref run()
     /// function with the proper parameter.
     enum PivotRule {
@@ -637,7 +637,7 @@
       INF(std::numeric_limits<Value>::has_infinity ?
           std::numeric_limits<Value>::infinity() : MAX)
     {
-      // Check the value types
+      // Check the number types
       LEMON_ASSERT(std::numeric_limits<Value>::is_signed,
         "The flow type of NetworkSimplex must be signed");
       LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,
@@ -729,7 +729,7 @@
     /// This function sets the upper bounds (capacities) on the arcs.
     /// If it is not used before calling \ref run(), the upper bounds
     /// will be set to \ref INF on all arcs (i.e. the flow value will be
-    /// unbounded from above on each arc).
+    /// unbounded from above).
     ///
     /// \param map An arc map storing the upper bounds.
     /// Its \c Value type must be convertible to the \c Value type