Repository: xgi-org/xgi (language: python)

Issue:
Returning node positions from `xgi.draw`
I want to use the same node positions to draw a few different hypergraphs on the same set of nodes. My lazy approach was to draw the first hypergraph with `xgi.draw`, then get node positions from the return and use them for the subsequent draw calls. However, it was surprisingly difficult to get the positions, despite the fact that `xgi.draw` computes positions and returns something called `node_collection`. The difficulty is that the return object is a `matplotlib.PathCollection`, so it doesn't contain `pos` in the same semantics (at least as far as I can tell). One might be able to use `PathCollection.get_offsets()` or similar to get them, I'm not sure.

This is not urgent at all because really I should compute the layout first, then use the same positions throughout, which is also what the example in the documentation points towards. Not trying to encourage bad design, but it still might be nice to return `pos` explicitly for convenience. I think the main question is whether adding another value to the return will somehow break other pieces of code or be otherwise inconvenient.

May relate to #280 in the future.


Discussion / hints:
Thanks Tim!
Yea my first thought is exactly what you wrote: if you need to reuse the positions, it's best to pre-compute them outside of `draw` and then pass them as an argument. We even have random seed for layout functions, so you could even have the same positions across different scripts. 

About potentially returning positions, we can certainly think about it. I'm not sure about it because we are already returning many things (1 axis and 3 collections). We could make it not break things for sure. Let's talk with the others.
I'm against returning positions. I think that it will unnecessarily clutter the code. Maybe we can make a recipe for this? I will note that the [code](https://github.com/nwlandry/filtering-higher-order-datasets/blob/main/fig1.ipynb) corresponding to my recent paper does exactly what is described here.
What about this recipe lifted from the example I mentioned? My worry is that it is too big for a recipe.

```python


import xgi
import matplotlib.pyplot as plt
from matplotlib import gridspec
import numpy as np
import itertools

links = [[1, 2], [1, 3], [5, 6], [1, 7]]
triangles = [[3, 5, 7], [2, 7, 1], [6, 10, 15]]
squares = [[7, 8, 9, 10]]
pentagons = [[1, 11, 12, 13, 14]]
edges = links + triangles + squares + pentagons

H = xgi.Hypergraph(edges)
pos = xgi.barycenter_spring_layout(H, seed=2)

link_color = "#000000"
triangle_color = "#648FFF"
square_color = "#785EF0"
pentagon_color = "#DC267F"
colors = [link_color, triangle_color, square_color, pentagon_color]

def color_edges(H):
    return [colors[i - 2] for i in H.edges.filterby("order", 1, "gt").size.aslist()]

H = xgi.Hypergraph(edges)

filtering_parameters = np.arange(
    H.edges.size.min(), H.edges.size.max() + 1, 1, dtype=int
)

uniform_filtering = [
    xgi.subhypergraph(H, edges=H.edges.filterby("size", k, "eq")).copy()
    for k in filtering_parameters
]
geq_filtering = [
    xgi.subhypergraph(H, edges=H.edges.filterby("size", k, "geq")).copy()
    for k in filtering_parameters
]
leq_filtering = [
    xgi.subhypergraph(H, edges=H.edges.filterby("size", k, "leq")).copy()
    for k in filtering_parameters
]
exclusion_filtering = [
    xgi.subhypergraph(H, edges=H.edges.filterby("size", k, "neq")).copy()
    for k in filtering_parameters
]
filterings = [uniform_filtering, geq_filtering, leq_filtering, exclusion_filtering]


pos = xgi.pca_transform(xgi.pairwise_spring_layout(H, seed=3))

fig = plt.figure(layout="constrained", figsize=(8, 4))

gs_leftright = gridspec.GridSpec(1, 3, figure=fig, wspace=0.075)

gs_panels = gridspec.GridSpecFromSubplotSpec(4, 4, subplot_spec=gs_leftright[1:])

ax_left = fig.add_subplot(gs_leftright[0])
xgi.draw(
    H, pos=pos, ax=ax_left, edge_fc=color_edges(H), node_size=7, node_lw=0.5, dyad_lw=0.75, alpha=1
)

labels = [r"$H_{(=, k)}$", r"$H_{(\geq, k)}$", r"$H_{(\leq, k)}$", r"$H_{(\neq, k)}$"]

for i, j in itertools.product(range(4), repeat=2):
    ax = fig.add_subplot(gs_panels[i, j])
    ec = color_edges(filterings[i][j])
    xgi.draw(
        filterings[i][j],
        pos=pos,
        ax=ax,
        node_size=4,
        dyad_lw=0.75,
        node_lw=0.5,
        edge_fc=ec,
        alpha=1,
    )
    if i == 0:
        ax.set_title(rf"$k={j + 2}$")

    if j == 0:
        ax.text(-3.5, 0, labels[i], fontsize=16)
plt.show()
```

Fix patch:
diff --git a/docs/source/api/recipes/recipes.ipynb b/docs/source/api/recipes/recipes.ipynb
index fe2990f1..e7ff4a0e 100644
--- a/docs/source/api/recipes/recipes.ipynb
+++ b/docs/source/api/recipes/recipes.ipynb
@@ -530,8 +530,8 @@
      "data": {
       "text/plain": [
        "(<Axes3DSubplot: >,\n",
-       " (<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x144a8a690>,\n",
-       "  <mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x144fe5bd0>))"
+       " (<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x16b916b10>,\n",
+       "  <mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x16b9e83d0>))"
       ]
      },
      "execution_count": 20,
@@ -808,6 +808,8 @@
     }
    ],
    "source": [
+    "import xgi\n",
+    "\n",
     "H = xgi.Hypergraph([[1, 2, 3, 4], [1, 2, 3], [1, 2]])\n",
     "\n",
     "[k for k, v in H.degree().items() if v == H.nodes.degree.max()]"
@@ -835,6 +837,8 @@
     }
    ],
    "source": [
+    "import xgi\n",
+    "\n",
     "H = xgi.load_xgi_data(\"email-enron\")\n",
     "ids = H.nodes.degree.argsort()\n",
     "i = ids[-100]\n",
@@ -927,6 +931,119 @@
     "e = H.edges.filterby_attr(\"timestamp\", [date1, date2], mode=datecompare)\n",
     "print(f\"The number of hyperedges between 01JAN2000 and 01JAN2001 is {len(e)}\")"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 19. Plot many hypergraphs using the same nodal positions\n",
+    "\n",
+    "It can be desirable to plot many hypergraphs with different color schemes or subsets of the original hypergraph, but with the same node positions."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 800x400 with 17 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import xgi\n",
+    "import matplotlib.pyplot as plt\n",
+    "from matplotlib import gridspec\n",
+    "import numpy as np\n",
+    "import itertools\n",
+    "\n",
+    "link_color = \"#000000\"\n",
+    "triangle_color = \"#648FFF\"\n",
+    "square_color = \"#785EF0\"\n",
+    "pentagon_color = \"#DC267F\"\n",
+    "colors = [link_color, triangle_color, square_color, pentagon_color]\n",
+    "\n",
+    "def color_edges(H):\n",
+    "    return [colors[i - 2] for i in H.edges.filterby(\"order\", 1, \"gt\").size.aslist()]\n",
+    "\n",
+    "links = [[1, 2], [1, 3], [5, 6], [1, 7]]\n",
+    "triangles = [[3, 5, 7], [2, 7, 1], [6, 10, 15]]\n",
+    "squares = [[7, 8, 9, 10]]\n",
+    "pentagons = [[1, 11, 12, 13, 14]]\n",
+    "edges = links + triangles + squares + pentagons\n",
+    "H = xgi.Hypergraph(edges)\n",
+    "\n",
+    "# This computes the positions used for all of the subplots\n",
+    "pos = xgi.pca_transform(xgi.pairwise_spring_layout(H, seed=3))\n",
+    "\n",
+    "filtering_parameters = np.arange(\n",
+    "    H.edges.size.min(), H.edges.size.max() + 1, 1, dtype=int\n",
+    ")\n",
+    "\n",
+    "uniform_filtering = [\n",
+    "    xgi.subhypergraph(H, edges=H.edges.filterby(\"size\", k, \"eq\")).copy()\n",
+    "    for k in filtering_parameters\n",
+    "]\n",
+    "geq_filtering = [\n",
+    "    xgi.subhypergraph(H, edges=H.edges.filterby(\"size\", k, \"geq\")).copy()\n",
+    "    for k in filtering_parameters\n",
+    "]\n",
+    "leq_filtering = [\n",
+    "    xgi.subhypergraph(H, edges=H.edges.filterby(\"size\", k, \"leq\")).copy()\n",
+    "    for k in filtering_parameters\n",
+    "]\n",
+    "exclusion_filtering = [\n",
+    "    xgi.subhypergraph(H, edges=H.edges.filterby(\"size\", k, \"neq\")).copy()\n",
+    "    for k in filtering_parameters\n",
+    "]\n",
+    "filterings = [uniform_filtering, geq_filtering, leq_filtering, exclusion_filtering]\n",
+    "\n",
+    "fig = plt.figure(layout=\"constrained\", figsize=(8, 4))\n",
+    "\n",
+    "gs_leftright = gridspec.GridSpec(1, 3, figure=fig, wspace=0.075)\n",
+    "gs_panels = gridspec.GridSpecFromSubplotSpec(4, 4, subplot_spec=gs_leftright[1:])\n",
+    "\n",
+    "ax_left = fig.add_subplot(gs_leftright[0])\n",
+    "xgi.draw(\n",
+    "    H,\n",
+    "    pos=pos,\n",
+    "    ax=ax_left,\n",
+    "    edge_fc=color_edges(H),\n",
+    "    node_size=7,\n",
+    "    node_lw=0.5,\n",
+    "    dyad_lw=0.75,\n",
+    "    alpha=1,\n",
+    ")\n",
+    "\n",
+    "labels = [r\"$H_{(=, k)}$\", r\"$H_{(\\geq, k)}$\", r\"$H_{(\\leq, k)}$\", r\"$H_{(\\neq, k)}$\"]\n",
+    "\n",
+    "for i, j in itertools.product(range(4), repeat=2):\n",
+    "    ax = fig.add_subplot(gs_panels[i, j])\n",
+    "    ec = color_edges(filterings[i][j])\n",
+    "    xgi.draw(\n",
+    "        filterings[i][j],\n",
+    "        pos=pos,\n",
+    "        ax=ax,\n",
+    "        node_size=4,\n",
+    "        dyad_lw=0.75,\n",
+    "        node_lw=0.5,\n",
+    "        edge_fc=ec,\n",
+    "        alpha=1,\n",
+    "    )\n",
+    "    if i == 0:\n",
+    "        ax.set_title(rf\"$k={j + 2}$\")\n",
+    "\n",
+    "    if j == 0:\n",
+    "        ax.text(-3.5, 0, labels[i], fontsize=16)\n",
+    "plt.show()"
+   ]
   }
  ],
  "metadata": {
diff --git a/docs/source/contributors.rst b/docs/source/contributors.rst
index 5597937e..76eebd55 100644
--- a/docs/source/contributors.rst
+++ b/docs/source/contributors.rst
@@ -57,6 +57,13 @@ Core team
         <a href="https://github.com/nwlandry">@nwlandry</a>
     </p>
 
+    <p>
+        <img src="https://github.com/tlarock.png"
+            width="50" height="50" hspace="5"
+            style="border-radius: 50%; vertical-align: middle;"/>
+        <a href="https://github.com/tlarock">@tlarock</a>
+    </p>
+
     <p>
         <img src="https://github.com/thomasrobiglio.png"
             width="50" height="50" hspace="5"
@@ -144,10 +151,3 @@ Contributors
             style="border-radius: 50%; vertical-align: middle;"/>
         <a href="https://github.com/saad1282">@saad1282</a>
     </p>
-
-    <p>
-        <img src="https://github.com/tlarock.png"
-            width="50" height="50" hspace="5"
-            style="border-radius: 50%; vertical-align: middle;"/>
-        <a href="https://github.com/tlarock">@tlarock</a>
-    </p>
\ No newline at end of file


Test patch:
diff --git a/tests/algorithms/test_centrality.py b/tests/algorithms/test_centrality.py
index e28ec60e..80fecabe 100644
--- a/tests/algorithms/test_centrality.py
+++ b/tests/algorithms/test_centrality.py
@@ -193,4 +193,5 @@ def test_katz_centrality(edgelist1, edgelist8):
         5: 0.07147345362079142,
         6: 0.03614424740207708,
     }
-    assert c == expected_c
+    for n in c:
+        assert np.allclose(c[n], expected_c[n])