{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"pycharm": {
"name": "#%% md\n"
}
},
"source": [
"# Triangles and cliques"
]
},
{
"cell_type": "markdown",
"metadata": {
"pycharm": {
"name": "#%% md\n"
}
},
"source": [
"This notebook illustrates clique counting and evaluation of the [clustering coefficient](https://en.wikipedia.org/wiki/Clustering_coefficient) of a graph."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [],
"source": [
"from IPython.display import SVG"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"ExecuteTime": {
"end_time": "2019-07-15T12:29:50.554431Z",
"start_time": "2019-07-15T12:29:50.414075Z"
},
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [],
"source": [
"import numpy as np"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [],
"source": [
"from sknetwork.data import karate_club\n",
"from sknetwork.topology import count_triangles, get_clustering_coefficient, count_cliques\n",
"from sknetwork.visualization import visualize_graph"
]
},
{
"cell_type": "markdown",
"metadata": {
"pycharm": {
"name": "#%% md\n"
}
},
"source": [
"## Triangles"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"ExecuteTime": {
"end_time": "2019-07-15T12:29:51.261957Z",
"start_time": "2019-07-15T12:29:51.249107Z"
},
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [],
"source": [
"graph = karate_club(metadata=True)\n",
"adjacency = graph.adjacency\n",
"position = graph.position"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"scrolled": true,
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [
{
"data": {
"image/svg+xml": [
""
],
"text/plain": [
""
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# graph\n",
"image = visualize_graph(adjacency, position)\n",
"SVG(image)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [
{
"data": {
"text/plain": [
"45"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# number of triangles\n",
"count_triangles(adjacency)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"scrolled": true,
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [
{
"data": {
"text/plain": [
"0.26"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# coefficient of clustering\n",
"np.round(get_clustering_coefficient(adjacency), 2)"
]
},
{
"cell_type": "markdown",
"metadata": {
"pycharm": {
"name": "#%% md\n"
}
},
"source": [
"## Cliques"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [
{
"data": {
"text/plain": [
"11"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# number of 4-cliques\n",
"count_cliques(adjacency, 4)\n"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.8.3"
},
"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
}
},
"nbformat": 4,
"nbformat_minor": 2
}