{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"pycharm": {
"name": "#%% md\n"
}
},
"source": [
"# Katz centrality"
]
},
{
"cell_type": "markdown",
"metadata": {
"pycharm": {
"name": "#%% md\n"
}
},
"source": [
"This notebook illustrates the ranking of the nodes of a graph by [Katz centrality](https://en.wikipedia.org/wiki/Katz_centrality), a weighted average of number of paths of different lengths to each node."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [],
"source": [
"from IPython.display import SVG"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [],
"source": [
"from sknetwork.data import karate_club, painters, movie_actor\n",
"from sknetwork.ranking import Katz\n",
"from sknetwork.visualization import visualize_graph, visualize_bigraph"
]
},
{
"cell_type": "markdown",
"metadata": {
"pycharm": {
"name": "#%% md\n"
}
},
"source": [
"## Graphs"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [],
"source": [
"graph = karate_club(metadata=True)\n",
"adjacency = graph.adjacency\n",
"position = graph.position"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [],
"source": [
"katz = Katz()\n",
"scores = katz.fit_predict(adjacency)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [
{
"data": {
"image/svg+xml": [
""
],
"text/plain": [
""
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"image = visualize_graph(adjacency, position, scores=scores)\n",
"SVG(image)"
]
},
{
"cell_type": "markdown",
"metadata": {
"pycharm": {
"name": "#%% md\n"
}
},
"source": [
"## Directed graphs"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"ExecuteTime": {
"end_time": "2019-07-15T12:29:58.542147Z",
"start_time": "2019-07-15T12:29:58.529699Z"
},
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [],
"source": [
"graph = painters(metadata=True)\n",
"adjacency = graph.adjacency\n",
"names = graph.names\n",
"position = graph.position"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [],
"source": [
"katz = Katz()\n",
"scores = katz.fit_predict(adjacency)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [
{
"data": {
"image/svg+xml": [
""
],
"text/plain": [
""
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"image = visualize_graph(adjacency, position, scores=scores, names=names)\n",
"SVG(image)"
]
},
{
"cell_type": "markdown",
"metadata": {
"pycharm": {
"name": "#%% md\n"
}
},
"source": [
"## Bipartite graphs"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [],
"source": [
"graph = movie_actor(metadata=True)\n",
"biadjacency = graph.biadjacency\n",
"names_row = graph.names_row\n",
"names_col = graph.names_col"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [],
"source": [
"katz = Katz()\n",
"katz.fit(biadjacency)\n",
"scores_row = katz.scores_row_\n",
"scores_col = katz.scores_col_"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [
{
"data": {
"image/svg+xml": [
""
],
"text/plain": [
""
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"image = visualize_bigraph(biadjacency, names_row, names_col, scores_row=scores_row, scores_col=scores_col)\n",
"SVG(image)\n"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.13"
},
"pycharm": {
"stem_cell": {
"cell_type": "raw",
"metadata": {
"collapsed": false
},
"source": []
}
},
"toc": {
"base_numbering": 1,
"nav_menu": {},
"number_sections": true,
"sideBar": true,
"skip_h1_title": false,
"title_cell": "Table of Contents",
"title_sidebar": "Contents",
"toc_cell": false,
"toc_position": {},
"toc_section_display": true,
"toc_window_display": false
}
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"nbformat": 4,
"nbformat_minor": 4
}