Added recipe for average path lenght, related to #511

docs/source/api/recipes/recipes.ipynb

@@ -542,8 +542,8 @@
      "data": {
       "text/plain": [
        "(<Axes3D: >,\n",
-       " (<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x7faad10a17f0>,\n",
-       "  <mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x7faaf0fbf7f0>))"
+       " (<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x7f8ee06cf0a0>,\n",
+       "  <mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x7f8f10c1fb50>))"
       ]
      },
      "execution_count": 20,
@@ -744,6 +744,51 @@
     "pos = {inv_mapping[k]: v for k, v in pos.items()}\n",
     "xgi.draw(S, pos=pos);"
    ]
+  },
+  {
+   "attachments": {},
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 14. Compute the average path length in a hypergraph\n",
+    "This recipe shows how to compute the average path lenght in a hypergraph.\n",
+    "You can compute all shortest path lenghts with [`xgi.shortest_path_length()`](https://xgi.readthedocs.io/en/stable/api/algorithms/xgi.algorithms.shortest_path.html#xgi.algorithms.shortest_path.shortest_path_length). \n",
+    "This gives and infinite length for disconnected nodes, to allow the computation in any case we replace `np.inf` by 0 for disconnected nodes and remove lengths 0 for self-loops."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The average shortest path length is 4.48\n"
+     ]
+    }
+   ],
+   "source": [
+    "import xgi\n",
+    "import numpy as np\n",
+    "\n",
+    "H = xgi.random_hypergraph(N=100, ps=[0.2, 0.02], seed=1)\n",
+    "spl = xgi.shortest_path_length(H)\n",
+    "\n",
+    "lens = []\n",
+    "for tup in spl:\n",
+    "    lens += tup[1].values()\n",
+    "\n",
+    "# remove lengths 0 for self-loops\n",
+    "lens = [i for i in lens if i!=0] \n",
+    "\n",
+    "# replace inf by 0 for disconnected nodes\n",
+    "lens = [0 if i==np.inf else i for i in lens] \n",
+    "\n",
+    "avg_shortest_path = np.sum(lens) / (N * (N-1))\n",
+    "print(\"The average shortest path length is\", avg_shortest_path)"
+   ]
   }
  ],
  "metadata": {