From fb01e187eb60bfcc761d49398eb4f2d5f2c91c2b Mon Sep 17 00:00:00 2001
From: adamjanovsky
Date: Wed, 20 Dec 2023 18:12:39 +0100
Subject: code to compute reach/eal correlations
---
notebooks/cc/references.ipynb | 39327 +++++++++++++++++++++++++++++++++++++++-
1 file changed, 39279 insertions(+), 48 deletions(-)
diff --git a/notebooks/cc/references.ipynb b/notebooks/cc/references.ipynb
index 4b027a55..c62f84e9 100644
--- a/notebooks/cc/references.ipynb
+++ b/notebooks/cc/references.ipynb
@@ -17,7 +17,7 @@
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 90,
"metadata": {
"pycharm": {
"name": "#%%\n"
@@ -26,6 +26,7 @@
"outputs": [],
"source": [
"import itertools\n",
+ "import json\n",
"import warnings\n",
"from collections.abc import Iterable\n",
"from pathlib import Path\n",
@@ -36,11 +37,15 @@
"import networkx.algorithms.community as nx_comm\n",
"import numpy as np\n",
"import pandas as pd\n",
+ "import plotly.express as px\n",
+ "import plotly.graph_objects as go\n",
"import seaborn as sns\n",
"from notebooks.fixed_sankey_plot import sankey\n",
+ "from scipy import stats\n",
"from tqdm import tqdm\n",
"\n",
"from sec_certs.dataset.cc import CCDataset\n",
+ "from sec_certs.utils.parallel_processing import process_parallel\n",
"\n",
"# Surpress user warnings\n",
"warnings.filterwarnings(\"ignore\", category=UserWarning)\n",
@@ -98,7 +103,7 @@
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
@@ -106,6 +111,12 @@
" return len(x) if pd.notnull(x) else 0\n",
"\n",
"\n",
+ "def get_label_subgraph(graph: nx.DiGraph, label: str | Iterable[str]) -> nx.DiGraph:\n",
+ " label = label if isinstance(label, Iterable) else [label]\n",
+ " sub_edges = [(u, v) for u, v, d in graph.edges(data=True) if d.get(\"reference_label\") in label]\n",
+ " return graph.edge_subgraph(sub_edges)\n",
+ "\n",
+ "\n",
"def compute_reference_numbers(df__: pd.DataFrame) -> pd.DataFrame:\n",
" \"\"\"\n",
" Creates new columns with number of references for each certificate.\n",
@@ -148,9 +159,7 @@
" \"\"\"\n",
" Limits the columns with references to a given label.\n",
" \"\"\"\n",
- " label = label if isinstance(label, Iterable) else [label]\n",
- " sub_edges = [(u, v) for u, v, d in graph.edges(data=True) if d.get(\"reference_label\") in label]\n",
- " subgraph = graph.edge_subgraph(sub_edges)\n",
+ " subgraph = get_label_subgraph(graph, label)\n",
"\n",
" return cc_df.assign(\n",
" refs=lambda df_: df_.apply(\n",
@@ -185,7 +194,102 @@
" target=\"reference\",\n",
" create_using=nx.DiGraph,\n",
" edge_attr=[\"reference_label\"],\n",
- " )"
+ " )\n",
+ "\n",
+ "\n",
+ "def get_plotly_node_edge_traces(G: nx.DiGraph, cc_dset: CCDataset) -> tuple[go.Scatter, go.Scatter]:\n",
+ " pos = nx.spring_layout(G)\n",
+ "\n",
+ " edge_x = []\n",
+ " edge_y = []\n",
+ " for edge in G.edges():\n",
+ " x0, y0 = pos[edge[0]]\n",
+ " x1, y1 = pos[edge[1]]\n",
+ " edge_x.append(x0)\n",
+ " edge_x.append(x1)\n",
+ " edge_x.append(None)\n",
+ " edge_y.append(y0)\n",
+ " edge_y.append(y1)\n",
+ " edge_y.append(None)\n",
+ "\n",
+ " edge_trace = go.Scatter(x=edge_x, y=edge_y, line={\"width\": 0.5, \"color\": \"#888\"}, hoverinfo=\"none\", mode=\"lines\")\n",
+ "\n",
+ " node_x = []\n",
+ " node_y = []\n",
+ " for node in G.nodes():\n",
+ " x, y = pos[node]\n",
+ " node_x.append(x)\n",
+ " node_y.append(y)\n",
+ "\n",
+ " node_trace = go.Scatter(\n",
+ " x=node_x,\n",
+ " y=node_y,\n",
+ " mode=\"markers\",\n",
+ " hoverinfo=\"text\",\n",
+ " marker={\n",
+ " \"showscale\": True,\n",
+ " \"colorscale\": \"Viridis\",\n",
+ " \"reversescale\": True,\n",
+ " \"color\": [],\n",
+ " \"size\": 10,\n",
+ " \"colorbar\": {\"thickness\": 15, \"title\": \"Node Connections\", \"xanchor\": \"left\", \"titleside\": \"right\"},\n",
+ " \"line_width\": 2,\n",
+ " },\n",
+ " )\n",
+ "\n",
+ " node_adjacencies = []\n",
+ " node_text = []\n",
+ " node_name_mapping = dict(enumerate(G.nodes()))\n",
+ " cert_id_to_dgst = {x.heuristics.cert_id: x.dgst for x in cc_dset}\n",
+ " for node, adjacencies in enumerate(G.adjacency()):\n",
+ " node_adjacencies.append(len(adjacencies[1]))\n",
+ " node_text.append(\n",
+ " f\"{node_name_mapping[node]} ({cert_id_to_dgst[node_name_mapping[node]]}) (# conns: {len(adjacencies[1])})\"\n",
+ " )\n",
+ "\n",
+ " node_trace.marker.color = node_adjacencies\n",
+ " node_trace.text = node_text\n",
+ "\n",
+ " return node_trace, edge_trace\n",
+ "\n",
+ "\n",
+ "def plotly_draw(graph: nx.DiGraph, cc_dset: CCDataset):\n",
+ " plt.figure(figsize=(12, 12))\n",
+ " node_trace, edge_trace = get_plotly_node_edge_traces(graph, cc_dset)\n",
+ " fig = go.Figure(\n",
+ " data=[edge_trace, node_trace],\n",
+ " layout=go.Layout(\n",
+ " title=\"
Network graph made with Python\",\n",
+ " titlefont_size=16,\n",
+ " showlegend=False,\n",
+ " hovermode=\"closest\",\n",
+ " margin={\"b\": 20, \"l\": 5, \"r\": 5, \"t\": 40},\n",
+ " annotations=[\n",
+ " {\n",
+ " \"text\": \"Python code: https://plotly.com/ipython-notebooks/network-graphs/\",\n",
+ " \"showarrow\": False,\n",
+ " \"xref\": \"paper\",\n",
+ " \"yref\": \"paper\",\n",
+ " \"x\": 0.005,\n",
+ " \"y\": -0.002,\n",
+ " }\n",
+ " ],\n",
+ " xaxis={\"showgrid\": False, \"zeroline\": False, \"showticklabels\": False},\n",
+ " yaxis={\"showgrid\": False, \"zeroline\": False, \"showticklabels\": False},\n",
+ " ),\n",
+ " )\n",
+ " fig.update_layout(\n",
+ " autosize=False,\n",
+ " width=1600,\n",
+ " height=1000,\n",
+ " )\n",
+ " fig.show()\n",
+ "\n",
+ "\n",
+ "def find_reach_over_time(df_: pd.DataFrame, cert_id: str, date_range: pd.DatetimeIndex) -> pd.Series:\n",
+ " df = df_.copy().loc[lambda df_: df_.trans_refs.apply(lambda x: pd.notnull(x) and cert_id in x)]\n",
+ " dct = {date: df.loc[(date >= df.not_valid_before) & (date <= df.not_valid_after)].shape[0] for date in date_range}\n",
+ " return pd.Series(dct, name=cert_id)"
]
},
{
@@ -197,7 +301,7 @@
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
@@ -214,6 +318,8 @@
" edge_attr=\"reference_label\",\n",
" create_using=nx.DiGraph,\n",
")\n",
+ "comp_subgraph = get_label_subgraph(graph, \"COMPONENT_USED\")\n",
+ "prev_subgraph = get_label_subgraph(graph, \"PREVIOUS_VERSION\")\n",
"\n",
"cc_df = compute_reference_numbers(compute_references(cc_df, graph, unique_labels))\n",
"cc_df_comp = compute_reference_numbers(compute_references(cc_df, graph, \"COMPONENT_USED\"))\n",
@@ -237,13 +343,6 @@
"g.fig.show()"
]
},
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Common processing functions"
- ]
- },
{
"attachments": {},
"cell_type": "markdown",
@@ -327,13 +426,6 @@
"\n",
"\n",
"def compute_certs_top_reach(df__: pd.DataFrame):\n",
- " def find_reach_over_time(df_: pd.DataFrame, cert_id: str, date_range: pd.DatetimeIndex) -> pd.Series:\n",
- " df = df_.copy().loc[lambda df_: df_.trans_refs.apply(lambda x: pd.notnull(x) and cert_id in x)]\n",
- " dct = {\n",
- " date: df.loc[(date >= df.not_valid_before) & (date <= df.not_valid_after)].shape[0] for date in date_range\n",
- " }\n",
- " return pd.Series(dct, name=cert_id)\n",
- "\n",
" df = df__.copy()\n",
" top_10_certs = df.sort_values(by=\"n_in_trans_refs\", ascending=False).head(10)\n",
" print(top_10_certs[[\"cert_id\", \"n_in_trans_refs\"]])\n",
@@ -371,9 +463,37748 @@
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 4,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Preparing inputs for average reach computation...\n",
+ "Computing average reach in parallel...\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "100%|██████████| 543/543 [01:39<00:00, 5.46it/s]\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Preparing inputs for average reach computation...\n",
+ "Computing average reach in parallel...\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "100%|██████████| 110/110 [00:24<00:00, 4.58it/s]\n"
+ ]
+ },
+ {
+ "data": {
+ "text/html": [
+ " \n",
+ " "
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "application/vnd.plotly.v1+json": {
+ "config": {
+ "plotlyServerURL": "https://plot.ly"
+ },
+ "data": [
+ {
+ "hovertemplate": "category=smartcard reach
date=%{x|%Y-%m-%d}
n_references=%{y}",
+ "legendgroup": "smartcard reach",
+ "line": {
+ "color": "#636efa",
+ "dash": "solid"
+ },
+ "marker": {
+ "symbol": "circle"
+ },
+ "mode": "lines",
+ "name": "smartcard reach",
+ "showlegend": true,
+ "type": "scattergl",
+ "x": [
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"source": [
"def compute_avg_references(df__: pd.DataFrame, variable: str, date_range: pd.DatetimeIndex) -> dict:\n",
" df = df__.copy()\n",
@@ -383,6 +38214,29 @@
" }\n",
"\n",
"\n",
+ "def compute_avg_reach(df__: pd.DataFrame, category: str, date_range: pd.DatetimeIndex) -> dict:\n",
+ " certs_from_category = (\n",
+ " df__.copy().loc[df__.category == SMARTCARD_CATEGORY]\n",
+ " if category == \"smartcards\"\n",
+ " else df__.copy().loc[df__.category != SMARTCARD_CATEGORY]\n",
+ " )\n",
+ " certs_with_reach = certs_from_category.loc[certs_from_category.n_in_trans_refs > 0].cert_id.tolist()\n",
+ "\n",
+ " print(\"Preparing inputs for average reach computation...\")\n",
+ " parallel_processing_inputs = [(df__.copy(), x, date_range) for x in certs_with_reach]\n",
+ " print(\"Computing average reach in parallel...\")\n",
+ " outputs = process_parallel(\n",
+ " find_reach_over_time, parallel_processing_inputs, max_workers=200, use_threading=False, unpack=True\n",
+ " )\n",
+ " reach_dict = dict(zip(certs_with_reach, outputs))\n",
+ "\n",
+ " averages = {}\n",
+ " for date in date_range:\n",
+ " averages[date] = np.mean([reach_dict[x][date] for x in reach_dict])\n",
+ "\n",
+ " return averages\n",
+ "\n",
+ "\n",
"def compute_avg_references_over_time(df__: pd.DataFrame) -> dict:\n",
" df = df__.copy()\n",
" date_range = pd.date_range(df.not_valid_before.min(), df.not_valid_before.max())\n",
@@ -409,10 +38263,15 @@
" )\n",
"\n",
" plt.figure()\n",
- " g = sns.lineplot(data=df_avg_num_refs_melted, x=\"date\", y=\"n_references\", hue=\"category\")\n",
- " g.set(title=\"Average number of references in certificates\", xlabel=\"Time\", ylabel=\"Number of references\")\n",
- " g.figure.savefig(RESULTS_DIR / \"lineplot_avg_n_references.pdf\", bbox_inches=\"tight\")\n",
- " g.figure.show()\n",
+ " fig = px.line(\n",
+ " df_avg_num_refs_melted,\n",
+ " x=\"date\",\n",
+ " y=\"n_references\",\n",
+ " color=\"category\",\n",
+ " hover_data={\"date\": \"|%Y-%m-%d\"},\n",
+ " title=\"Timestamp vs Value\",\n",
+ " )\n",
+ " fig.show()\n",
"\n",
" return {}\n",
"\n",
@@ -420,8 +38279,8 @@
"def compute_avg_reach_over_time(df__: pd.DataFrame) -> dict:\n",
" df = df__.copy()\n",
" date_range = pd.date_range(df.not_valid_before.min(), df.not_valid_before.max())\n",
- " reach_smartcards = compute_avg_references(df.loc[df.category == SMARTCARD_CATEGORY], \"n_in_trans_refs\", date_range)\n",
- " reach_others = compute_avg_references(df.loc[df.category != SMARTCARD_CATEGORY], \"n_in_trans_refs\", date_range)\n",
+ " reach_smartcards = compute_avg_reach(df, \"smartcards\", date_range)\n",
+ " reach_others = compute_avg_reach(df, \"others\", date_range)\n",
"\n",
" df_avg_num_refs_melted = (\n",
" pd.concat(\n",
@@ -436,15 +38295,15 @@
" .melt(id_vars=[\"date\"], var_name=\"category\", value_name=\"n_references\")\n",
" )\n",
"\n",
- " plt.figure()\n",
- " g = sns.lineplot(data=df_avg_num_refs_melted, x=\"date\", y=\"n_references\", hue=\"category\")\n",
- " g.set(\n",
- " title=\"Average certificate reach over time\",\n",
- " xlabel=\"Time\",\n",
- " ylabel=\"Number of (transitively) referencing certificates\",\n",
+ " fig = px.line(\n",
+ " df_avg_num_refs_melted,\n",
+ " x=\"date\",\n",
+ " y=\"n_references\",\n",
+ " color=\"category\",\n",
+ " hover_data={\"date\": \"|%Y-%m-%d\"},\n",
+ " title=\"Timestamp vs Value\",\n",
" )\n",
- " g.figure.savefig(RESULTS_DIR / \"lineplot_avg_n_references.pdf\", bbox_inches=\"tight\")\n",
- " g.figure.show()\n",
+ " fig.show()\n",
"\n",
" return {}\n",
"\n",
@@ -893,7 +38752,9 @@
" return {}\n",
"\n",
"\n",
+ "print(\"Countplot of sub-component references\")\n",
"plot_direct_refs_per_category(cc_df_comp)\n",
+ "print(\"Countplot of previous version references\")\n",
"plot_direct_refs_per_category(cc_df_prev)"
]
},
@@ -1172,6 +39033,24 @@
")"
]
},
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Evaluate cycles in the graph"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Ideally there should be none, but there are some BAC, EAC cycles badly annotated.\n",
+ "for cycle in nx.simple_cycles(prev_subgraph):\n",
+ " print(cycle)"
+ ]
+ },
{
"attachments": {},
"cell_type": "markdown",
@@ -1197,7 +39076,7 @@
},
"outputs": [],
"source": [
- "cert_id = \"ANSSI-CC-2014/07\"\n",
+ "cert_id = \"BSI-DSZ-CC-0753-2012\"\n",
"\n",
"for component in nx.weakly_connected_components(graph):\n",
" if cert_id in component:\n",
@@ -1205,7 +39084,7 @@
"else:\n",
" raise ValueError(f\"Certificate with id {cert_id} not found in graph.\")\n",
"\n",
- "view = nx.subgraph_view(graph, lambda node: node in component)\n",
+ "view = nx.subgraph_view(prev_subgraph, lambda node: node in component)\n",
"print(f\"Certificate with id {cert_id}:\")\n",
"print(f\" - is in a component with {len(view.nodes)} certificates and {len(view.edges)} references.\")\n",
"print(f\" - references {list(view[cert_id].keys())}\")\n",
@@ -1218,15 +39097,6 @@
"print(f\" - its page is at https://seccerts.org/cc/{cert.dgst}/\")"
]
},
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "nx.draw(view, with_labels=True)"
- ]
- },
{
"attachments": {},
"cell_type": "markdown",
@@ -1322,6 +39192,1367 @@
"# print(f\"\\\\newcommand{{\\\\numCCUSReferencing}}{{{len(df_id_rich.loc[(df_id_rich.scheme == 'US') & (df_id_rich.directly_referencing.notnull())])}}}\")\n",
"# print(f\"\\\\newcommand{{\\\\numCCUS}}{{{len(df_id_rich.loc[(df_id_rich.scheme == 'US')])}}}\")\n"
]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Correlation between EAL and number of references / reach"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 100,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "eal_mapping = {cat: i for i, cat in enumerate(cc_df_comp.eal.dtype.categories)}\n",
+ "cc_df_comp_eal = cc_df_comp.loc[cc_df_comp.eal.notnull()]\n",
+ "cc_df_comp_eal[\"eal_int\"] = cc_df_comp_eal.eal.map(lambda x: eal_mapping[x])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 132,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "smartcard_trans_refs = stats.spearmanr(\n",
+ " cc_df_comp_eal.loc[cc_df_comp_eal.category == SMARTCARD_CATEGORY].eal_int,\n",
+ " cc_df_comp_eal.loc[cc_df_comp_eal.category == SMARTCARD_CATEGORY].n_trans_refs,\n",
+ " nan_policy=\"omit\",\n",
+ " alternative=\"less\",\n",
+ ")\n",
+ "smartcard_reach = stats.spearmanr(\n",
+ " cc_df_comp_eal.loc[cc_df_comp_eal.category == SMARTCARD_CATEGORY].eal_int,\n",
+ " cc_df_comp_eal.loc[cc_df_comp_eal.category == SMARTCARD_CATEGORY].n_in_trans_refs,\n",
+ " nan_policy=\"omit\",\n",
+ " alternative=\"greater\",\n",
+ ")\n",
+ "others_trans_refs = stats.spearmanr(\n",
+ " cc_df_comp_eal.loc[cc_df_comp_eal.category != SMARTCARD_CATEGORY].eal_int,\n",
+ " cc_df_comp_eal.loc[cc_df_comp_eal.category != SMARTCARD_CATEGORY].n_trans_refs,\n",
+ " nan_policy=\"omit\",\n",
+ " alternative=\"greater\",\n",
+ ")\n",
+ "others_reach = stats.spearmanr(\n",
+ " cc_df_comp_eal.loc[cc_df_comp_eal.category != SMARTCARD_CATEGORY].eal_int,\n",
+ " cc_df_comp_eal.loc[cc_df_comp_eal.category != SMARTCARD_CATEGORY].n_in_trans_refs,\n",
+ " nan_policy=\"omit\",\n",
+ " alternative=\"greater\",\n",
+ ")\n",
+ "\n",
+ "df_corr = pd.DataFrame(\n",
+ " {\n",
+ " \"transitive references corr\": [smartcard_trans_refs.statistic, others_trans_refs.statistic],\n",
+ " \"transitive references p-value\": [smartcard_trans_refs.pvalue, others_trans_refs.pvalue],\n",
+ " \"reach corr\": [smartcard_reach.statistic, others_reach.statistic],\n",
+ " \"reach p-value\": [smartcard_reach.pvalue, others_reach.pvalue],\n",
+ " },\n",
+ " index=[\"smartcards\", \"other categories\"],\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 133,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | \n",
+ " transitive references corr | \n",
+ " transitive references p-value | \n",
+ " reach corr | \n",
+ " reach p-value | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | smartcards | \n",
+ " -0.146789 | \n",
+ " 3.538119e-10 | \n",
+ " 0.233111 | \n",
+ " 2.733572e-23 | \n",
+ "
\n",
+ " \n",
+ " | other categories | \n",
+ " 0.251177 | \n",
+ " 5.579787e-44 | \n",
+ " 0.153535 | \n",
+ " 2.529777e-17 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ " transitive references corr transitive references p-value \\\n",
+ "smartcards -0.146789 3.538119e-10 \n",
+ "other categories 0.251177 5.579787e-44 \n",
+ "\n",
+ " reach corr reach p-value \n",
+ "smartcards 0.233111 2.733572e-23 \n",
+ "other categories 0.153535 2.529777e-17 "
+ ]
+ },
+ "execution_count": 133,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "df_corr"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Examine re-evaluation graph"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "nodes_with_long_paths = set()\n",
+ "min_path_len = 12\n",
+ "\n",
+ "for source in tqdm(prev_subgraph.nodes()):\n",
+ " ancestors = nx.ancestors(prev_subgraph, source)\n",
+ " if len(ancestors) > min_path_len - 1:\n",
+ " nodes_with_long_paths.add(source)\n",
+ " continue\n",
+ "\n",
+ "print(f\"Found: {len(nodes_with_long_paths)} nodes with path of len >={min_path_len}\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Save nodes with high betweenness centrality for each of the components\n",
+ "\n",
+ "Iterate over all components and save top-2 nodes w.r.t. their betweeness centrality into json."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 89,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "components = list(nx.weakly_connected_components(comp_subgraph))\n",
+ "large_components = [x for x in components if len(x) > 10]\n",
+ "\n",
+ "nodes_with_high_betweenness = {}\n",
+ "for i, comp in enumerate(large_components):\n",
+ " subg = comp_subgraph.subgraph(comp)\n",
+ " betweenness_centrality_vals = sorted((nx.betweenness_centrality(subg).items()), key=lambda x: x[1], reverse=True)\n",
+ " nodes_with_high_betweenness[f\"component_{i} with size {len(comp)}\"] = [\n",
+ " betweenness_centrality_vals[0],\n",
+ " betweenness_centrality_vals[1],\n",
+ " ]\n",
+ "\n",
+ "with Path(RESULTS_DIR / \"nodes_with_high_betweenness.json\").open(\"w\") as f:\n",
+ " json.dump(nodes_with_high_betweenness, f, indent=4)"
+ ]
+ },
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