03_example_graphs.ipynb: Minor fixes and corrections

Author: jnareb

03_example_graphs.ipynb

@@ -35,7 +35,7 @@
     "# Example directed graphs\n",
     "\n",
     "> Various functions to generate examples of directed graphs (DAGs),\n",
-    "> mainly graphs from various [related works](01_related.ipynb)"
+    "> mainly graphs from various [related works](02_related.ipynb)"
    ]
   },
   {
@@ -187,7 +187,7 @@
    "source": [
     "Draw the 6-nodes crown DAG, known as the $S_3^0$ graph, using automatic bipartite layout.\n",
     "\n",
-    "This is similar layout to the one used in left side of Figure 4 in the FELINE paper, just with changed order of nodes in each of sets of vertices (each partition)."
+    "This is a similar layout to the one used in left side of Figure 4 in the FELINE paper, just with changed order of nodes in each of sets of vertices (each partition)."
    ]
   },
   {
@@ -271,7 +271,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Create small DAG (example in Figure 2 in FELINE paper)"
+    "## Create the small DAG (example in Figure 2 in FELINE paper)"
    ]
   },
   {
@@ -689,7 +689,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "**NOTE**: we are skipping figure titled 'Didactic example of a DAG: search space of FERRARI\\n(topological ordering x)' in [Reachability labels for version control graphs.ipynb](_Reachability_labels_for_version_control_graphs.ipynb). If it would be added, it would be added in the notebook describing various reachability indices."
+    "**NOTE**: we are skipping figure titled 'Didactic example of a DAG: search space of FERRARI\\n(topological ordering x)' in [Reachability labels for version control graphs.ipynb](_Reachability_labels_for_version_control_graphs.ipynb). If it is to be added, it would be added in the notebook describing various reachability indices."
    ]
   },
   {
@@ -703,7 +703,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Create an example DAG used among others for showing how Reachability Contracton Hierarchies (RCH) labeling works. This graph is shown on Figures 1 and 2 in the PReaCH paper.\n",
+    "Create an example DAG used among others for showing how Reachability Contraction Hierarchies (RCH) labeling works. This graph is shown on Figures 1 and 2 in the PReaCH paper.\n",
     "\n",
     "The graph as shown in Figure 1 in the PReaCH paper (preprint) can be seen below:\n",
     "\n",
@@ -714,7 +714,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "_Caption:_ Example RCH. Edges in the forward search space are light green and those in the\n",
+    "_Caption:_ Example RCH. Edges in the forward search space are light green, and those in the\n",
     "backward search space are dark blue. The search spaces for a query from $s$ to $t$ are circled.\n",
     "Node labels specify the RCH node ordering."
    ]
@@ -732,7 +732,7 @@
     "    Positions of nodes in the drawing from Figure 1 and 2 in PReaCH paper\n",
     "    is stored in `pos` attribute of returned graph object.\n",
     "    \n",
-    "    Backard topological levels (i.e. with level equal to 0 for nodes\n",
+    "    Backward topological levels (i.e. with level equal to 0 for nodes\n",
     "    with no outgoing edges, that is with out-degree of 0) are stored\n",
     "    in `lvl` attribute of returned graph object.\n",
     "    \n",
@@ -946,7 +946,7 @@
    "source": [
     "Draw using node positions created with the help of `pydot` module and Graphviz, using 'dot' layout algorithm, if the module is present (installed).\n",
     "\n",
-    "The resulting positioning is transformed from vertical to horizontal, and flipped along horizontal axis to better match the original draving in the Stolee blog post(s)."
+    "The resulting positioning is transformed from vertical to horizontal, and flipped along horizontal axis to better match the original drawing in the Stolee blog post(s)."
    ]
   },
   {