1021 lines
276 KiB
Plaintext
1021 lines
276 KiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "1ee388e8",
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"metadata": {},
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"source": [
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"# Графы"
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]
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},
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{
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"cell_type": "markdown",
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"id": "31fe6bcc",
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"metadata": {},
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"source": [
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"## Определение графов. "
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]
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},
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{
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"cell_type": "markdown",
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"id": "6cbbbe70",
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"metadata": {},
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"source": [
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"\n",
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" Неориентированным графом (или графом) называется пара $(V,E)$, где $V = \\{v_1, v_2,... \\}$ — множество вершин, $E = \\{e_1, e_2,... \\}$ — множество ребер, в котором каждый элемент $e_k$ является неупорядоченной парой $\\{v_i, v_j\\}$. Пара $(V,E)$, в которой множество $E$ состоит из упорядоченных пар $(v_i, v_j )$, называется ориентированным графом, а элементы из $E$ — дугами, или ориентированными ребрами. Вершины $v_i$ и $v_j$ , составляющие ребро или дугу, называются концевыми вершинами ребра или дуги, а про ребро и дугу говорят, что они соединяют свои концевые вершины.<br/> <br/>\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "26e31d3b",
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"metadata": {},
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"source": [
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"## Локальные характеристики"
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]
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},
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{
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"cell_type": "markdown",
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"id": "ccdb2118",
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"metadata": {},
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"source": [
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"Если $ e=\\{v_i, v_j\\} $– ребро графа, то вершина $ v_i $ и ребро е инцидентны. Вершина $ v_j $ и ребро е также инцидентны.<br/>\n",
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"Вершины, инцидентные одному ребру, называются смежными.<br/>\n",
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"Два ребра смежные, если инцидентны одной вершине.<br/>\n",
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"Число вершин графа называется его порядком.<br/>\n",
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"Число ребер графа, инцидентных данной вершине $vi$ , называется степенью $p(v_i)$ вершины $vi$ (другое обозначение $deg(v_i)$).<br/>\n",
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"Если $ p(v_i)$ то $v_i$ – изолированная вершина, если $p(v_i)=1$, то $v_i$ – висячая вершина.<br/>\n",
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"Если концевые вершины совпадают, то дугу $e=(v_i, v_j)$ называют петлей. <br/>\n",
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"Очевидно, что для неориентированного графа $\\{v_i, v_j\\}=\\{v_j, v_i\\}$, а для ориентированного $(v_i, v_j)\\neq (v_j, v_i)$ .\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "5eb6495a",
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"metadata": {},
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"source": [
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"Нетрудно подсчитать число графов с фиксированным множеством вершин. Обозначим через $ N_g $ число неориентированных графов без петель с множеством вершин n.\n",
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"<dt>Теорема (О количестве графов)</dt>\n",
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" $$ N_g = 2^{\\frac{n(n-1)}{2}} $$\n",
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"\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "e8785f8f",
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"metadata": {},
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"source": [
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"<dt>Теорема (Лемма о рукопожатиях)</dt> Сумма степеней всех вершин графа равна удвоенному числу ребер: \n",
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" $$ \\sum p(v_i)=2|E| $$\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "b4003ab7",
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"metadata": {},
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"source": [
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"<dt>Следствие</dt> Сумма степеней вершин графа всегда четное число."
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]
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},
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{
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"cell_type": "markdown",
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"id": "9d0d01ae",
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"metadata": {},
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"source": [
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"<dt>Теорема</dt>\tВ любом графе число вершин нечетной степени четно.\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "8efea77a",
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"metadata": {},
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"source": [
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"## Способы представления графов"
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]
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},
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{
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"cell_type": "markdown",
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"id": "a53868fa",
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"metadata": {},
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"source": [
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"### Графическое представление графов. представление в виде списков смежности"
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]
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},
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{
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"cell_type": "markdown",
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"id": "7e31a24f",
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"metadata": {},
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"source": [
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"Обычно граф изображают на плоскости в виде множества точек, соответствующих вершинам, и множества линий, которые соединяют вершины и соответствуют ребрам. При изображении ориентированных графов линии снабжаются стрелками, указывающими ориентацию дуги, т. е. порядок вершин в паре."
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]
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},
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{
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"cell_type": "markdown",
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"id": "eb9279ad",
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"metadata": {},
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"source": [
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"Для работы с графами можно использовать библиотеку NetworkX, предназначенную для создания, манипуляции и изучения структуры, динамики и функционирования сложных сетевых структур. Внутреннее представление графов реализовано в виде списков смежности. <br/>\n",
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"Основные возможности библиотеки:\n",
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"<ol>\n",
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" <li>Классы для работы с простыми, ориентированными и взвешенными графами</li>\n",
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" <li>Узлом может быть практически что угодно: time-series, текст, изображение, XML</li>\n",
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" <li>Сохранение / загрузка графов в/из наиболее распространённых форматов файлов хранения графов</li>\n",
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" <li>Встроенные процедуры для создания графов базовых типов</li>\n",
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" <li>Методы для обнаружения подграфов, клик и К-дольных графов (K-core) ( максимальный подграф в котором каждая вершина имеет по крайней мере уровень К )</li>\n",
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" <li>Получение таких характеристик графа как степени вершин, высота графа, диаметр, радиус, длинны путей, центр, промежуточности, и т. д.</li>\n",
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" <li>Визуализировать сети в виде 2D и 3D графиков</li>\n",
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"</ol>\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 24,
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"id": "98e1dde0",
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"metadata": {},
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"outputs": [],
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"source": [
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"#Если требуется установить библиотеку\n",
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"# !pip install networkx"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 25,
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"id": "b254ada3",
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"metadata": {},
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"outputs": [],
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"source": [
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"import networkx as nx \n",
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"import matplotlib.pyplot as plt\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 26,
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"id": "519b710b",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": "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"text/plain": [
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"<Figure size 700x1000 with 1 Axes>"
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]
|
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},
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"metadata": {},
|
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"output_type": "display_data"
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},
|
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{
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"data": {
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|
|
"image/png": "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
|
|||
|
|
"text/plain": [
|
|||
|
|
"<Figure size 700x1000 with 1 Axes>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "display_data"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"G = nx.Graph() # пустой неориентированный граф\n",
|
|||
|
|
"G1 = nx.DiGraph() # пустой ориентированный граф\n",
|
|||
|
|
"GG = nx.MultiGraph() # пустой мультиграф\n",
|
|||
|
|
"GG1 = nx.MultiDiGraph() # пустой ориентированный мультиграф\n",
|
|||
|
|
"\n",
|
|||
|
|
"G.add_node(1) # добавляем одину вершину, получаем тоже пустой граф\n",
|
|||
|
|
"G.add_nodes_from([3, 4, 5, 6, 7]) # добавляем еще шесть вершин сразу\n",
|
|||
|
|
"\n",
|
|||
|
|
"# В качестве обозначений вершин можем использовать ярлыки:\n",
|
|||
|
|
"G1.add_nodes_from([\"node_1\", \"node_2\"]) # пустой ориентированный граф\n",
|
|||
|
|
"\n",
|
|||
|
|
"plt.figure(figsize =(7, 10))\n",
|
|||
|
|
"plt.subplot(211)\n",
|
|||
|
|
"nx.draw_networkx(G)\n",
|
|||
|
|
"plt.show()\n",
|
|||
|
|
"\n",
|
|||
|
|
"plt.figure(figsize =(7, 10))\n",
|
|||
|
|
"plt.subplot(212)\n",
|
|||
|
|
"nx.draw_networkx(G1, with_labels = True)\n",
|
|||
|
|
"plt.show()\n"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 27,
|
|||
|
|
"id": "283ba2d2",
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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
|
|||
|
|
"text/plain": [
|
|||
|
|
"<Figure size 700x1000 with 1 Axes>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "display_data"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"# добавляем в графы ребра и дуги\n",
|
|||
|
|
"G.add_edges_from([(1, 2), (1, 3), (1, 4), (2, 4), (2, 6), (3, 6), (4,7), (5, 7)]) # для неориентированного графа\n",
|
|||
|
|
"G.add_edge(8,9) # добавление ребра с новыми вершинами, добавит их тоже\n",
|
|||
|
|
"\n",
|
|||
|
|
"plt.figure(figsize =(7, 10))\n",
|
|||
|
|
"plt.subplot(211)\n",
|
|||
|
|
"nx.draw_networkx(G)\n",
|
|||
|
|
"plt.show()\n"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 28,
|
|||
|
|
"id": "d273c0ff",
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"NodeView((1, 3, 4, 5, 6, 7, 2, 8, 9))"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 28,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"G.nodes()"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 29,
|
|||
|
|
"id": "98549f52",
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"9"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 29,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"# Количество вершин в графе G\n",
|
|||
|
|
"G.number_of_nodes()\n",
|
|||
|
|
"# G.order\n",
|
|||
|
|
"# len(G)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 30,
|
|||
|
|
"id": "b8d574e8",
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"G.edges()\n",
|
|||
|
|
"nx.write_edgelist(G, \"Graf.txt\")"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 31,
|
|||
|
|
"id": "ea2178eb",
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"9"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 31,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"# количество ребер\n",
|
|||
|
|
"G.number_of_edges()"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 46,
|
|||
|
|
"id": "2925c211",
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"DiGraph with 9 nodes and 9 edges\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"# создание графа из файла\n",
|
|||
|
|
"G2 = nx.read_edgelist(\"Graf.txt\", nodetype = int, create_using = nx.DiGraph()) #считываем список ребер из файла, по умолчанию неориентированный\n",
|
|||
|
|
"nx.is_directed(G2)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 33,
|
|||
|
|
"id": "4316a607",
|
|||
|
|
"metadata": {
|
|||
|
|
"scrolled": true
|
|||
|
|
},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"[2, 3, 4]\n",
|
|||
|
|
"[5, 6, 7, 8, 9]\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"# список соседей вершины графа\n",
|
|||
|
|
"#list(G.neighbors(1))\n",
|
|||
|
|
"print(list(nx.all_neighbors(G, 1))) # список соседних вершин\n",
|
|||
|
|
"print(list(nx.non_neighbors(G, 1))) # список остальных вершин"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 34,
|
|||
|
|
"id": "be070e29",
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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
|
|||
|
|
"text/plain": [
|
|||
|
|
"<Figure size 700x1000 with 1 Axes>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "display_data"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"G1.add_edges_from([(\"node_1\", \"node_2\")]) # для ориентированного графа\n",
|
|||
|
|
"\n",
|
|||
|
|
"plt.figure(figsize =(7, 10))\n",
|
|||
|
|
"plt.subplot(212)\n",
|
|||
|
|
"nx.draw_networkx(G1)\n",
|
|||
|
|
"plt.show()\n"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 35,
|
|||
|
|
"id": "04767bda",
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"3\n"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"DegreeView({1: 3, 3: 2, 4: 3, 5: 1, 6: 2, 7: 2, 2: 3, 8: 1, 9: 1})"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 35,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"# степени вершин\n",
|
|||
|
|
"print(G.degree(1))\n",
|
|||
|
|
"G.degree()"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": null,
|
|||
|
|
"id": "bd241395",
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": []
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"id": "de4d11f9",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"### Представление графов виде матриц"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"id": "ad160898",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"#### Матрица смежности"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"id": "c35cad09",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"Матрицей смежности $A=A(a_{ij})$ графа G называется матрица порядка n, определенная следующим образом:\n",
|
|||
|
|
"$$a_{ij}=\\begin{cases} 1, &если& e_{ij} \\in E \\\\ 0, &если& e_{ij} \\notin E \\end{cases} $$\n",
|
|||
|
|
" \n",
|
|||
|
|
"Матрица смежности для неориентированного графа будет симметрична относительно главной диагонали. Матрица смежности для ориентированного графа в общем случае не симметрична относительно главной диагонали."
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 36,
|
|||
|
|
"id": "b9ef4b36",
|
|||
|
|
"metadata": {
|
|||
|
|
"scrolled": true
|
|||
|
|
},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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
|
|||
|
|
"text/plain": [
|
|||
|
|
"<Figure size 700x1000 with 1 Axes>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "display_data"
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"[[0 1 1 0 0 0 1 0 0]\n",
|
|||
|
|
" [1 0 0 0 1 0 0 0 0]\n",
|
|||
|
|
" [1 0 0 0 0 1 1 0 0]\n",
|
|||
|
|
" [0 0 0 0 0 1 0 0 0]\n",
|
|||
|
|
" [0 1 0 0 0 0 1 0 0]\n",
|
|||
|
|
" [0 0 1 1 0 0 0 0 0]\n",
|
|||
|
|
" [1 0 1 0 1 0 0 0 0]\n",
|
|||
|
|
" [0 0 0 0 0 0 0 0 1]\n",
|
|||
|
|
" [0 0 0 0 0 0 0 1 0]]\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"plt.figure(figsize =(7, 10))\n",
|
|||
|
|
"plt.subplot(212)\n",
|
|||
|
|
"nx.draw_networkx(G)\n",
|
|||
|
|
"plt.show()\n",
|
|||
|
|
"\n",
|
|||
|
|
"a= nx.adjacency_matrix(G) # список вершин, которые соединены попарно, и веса связывающих их ребер.\n",
|
|||
|
|
"A=a.todense() # Формируем матрицу смежности\n",
|
|||
|
|
"print(A)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 37,
|
|||
|
|
"id": "22c6a448",
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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
|
|||
|
|
"text/plain": [
|
|||
|
|
"<Figure size 700x1000 with 1 Axes>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "display_data"
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"[[0 1 1 1 0 0 0]\n",
|
|||
|
|
" [0 0 0 1 1 0 0]\n",
|
|||
|
|
" [0 0 0 0 1 0 0]\n",
|
|||
|
|
" [0 0 0 0 0 1 0]\n",
|
|||
|
|
" [0 0 0 0 0 0 0]\n",
|
|||
|
|
" [0 0 0 0 0 0 0]\n",
|
|||
|
|
" [0 0 0 0 0 1 0]]\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"G2 = nx.DiGraph()\n",
|
|||
|
|
"G2.add_edges_from([('q', 'w'), ('q', 'e'), ('q', 'r'), ('w', 'r'), ('w', 'y'), ('e', 'y'), ('r','u'), ('t', 'u')])\n",
|
|||
|
|
"\n",
|
|||
|
|
"plt.figure(figsize =(7, 10))\n",
|
|||
|
|
"plt.subplot(212)\n",
|
|||
|
|
"nx.draw_networkx(G2)\n",
|
|||
|
|
"plt.show()\n",
|
|||
|
|
"\n",
|
|||
|
|
"a= nx.adjacency_matrix(G2) # список вершин, которые соединены попарно.\n",
|
|||
|
|
"A=a.todense() # Формируем матрицу смежности\n",
|
|||
|
|
"print(A)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"id": "94a7923d",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"<dt>Теорема</dt>\tГрафы изоморфны тогда и только тогда, когда их матрицы смежности получаются друг из друга одновременными перестановками строк и столбцов (т.е. одновременно с перестановкой $i$-й и $j$-й строк переставляются $i$-й и $j$-й столбцы)."
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"id": "904e294c",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"#### Матрица инцидености"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"id": "685333ab",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"Матрицей инцидентности $B=(b_{ij})$ неориентированного графа G называется матрица размера $ |V|\\times|E|$ , в которой столбцы матрицы соответствуют ребрам, строки — вершинам. Ненулевое значение в ячейке матрицы указывает связь между вершиной и ребром определяемую следующим образом: \n",
|
|||
|
|
"$$b_{ij}=\\begin{cases} 1, &если& e_{j} &инцидентна\\space вершине& a_i \\\\ 0, &иначе& \\end{cases} $$ \n",
|
|||
|
|
"<br/>\n",
|
|||
|
|
"В случае наличия ориентированных дуг, начало и конец обозначаются противоположныти знаками\n",
|
|||
|
|
"$$b_{ij}=\\begin{cases} 1, &если& e_{j} &исходит\\space из\\space вершины& a_i \\\\ -1, &если& e_{j} &заходит\\space в\\space вершину& a_i &и\\space не\\space является\\space петлей& \\\\0, &иначе& \\end{cases} $$\n",
|
|||
|
|
" \n"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 38,
|
|||
|
|
"id": "5d0d0824",
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"[[1. 1. 1. 0. 0. 0. 0. 0. 0.]\n",
|
|||
|
|
" [0. 1. 0. 1. 0. 0. 0. 0. 0.]\n",
|
|||
|
|
" [0. 0. 1. 0. 1. 1. 0. 0. 0.]\n",
|
|||
|
|
" [0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
|
|||
|
|
" [0. 0. 0. 1. 0. 0. 0. 1. 0.]\n",
|
|||
|
|
" [0. 0. 0. 0. 0. 1. 1. 0. 0.]\n",
|
|||
|
|
" [1. 0. 0. 0. 1. 0. 0. 1. 0.]\n",
|
|||
|
|
" [0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
|
|||
|
|
" [0. 0. 0. 0. 0. 0. 0. 0. 1.]]\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"a= nx.incidence_matrix(G) # список вершин, которые соединены попарно.\n",
|
|||
|
|
"A=a.todense() # Формируем матрицу инцидентности\n",
|
|||
|
|
"print(A)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 39,
|
|||
|
|
"id": "afa251b7",
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"[[ 1. 1. 1. 0. 0. 0. 0. 0.]\n",
|
|||
|
|
" [-1. 0. 0. 1. 1. 0. 0. 0.]\n",
|
|||
|
|
" [ 0. -1. 0. 0. 0. 1. 0. 0.]\n",
|
|||
|
|
" [ 0. 0. -1. -1. 0. 0. 1. 0.]\n",
|
|||
|
|
" [ 0. 0. 0. 0. -1. -1. 0. 0.]\n",
|
|||
|
|
" [ 0. 0. 0. 0. 0. 0. -1. -1.]\n",
|
|||
|
|
" [ 0. 0. 0. 0. 0. 0. 0. 1.]]\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"b= -nx.incidence_matrix(G2, oriented=True) # список вершин, которые соединены попарно.\n",
|
|||
|
|
"B=b.todense() # Формируем матрицу инцидентности\n",
|
|||
|
|
"print(B)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"id": "d7a85452",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"<dt>Теорема</dt>\tГрафы и изоморфны тогда и только тогда, когда их матрицы инцидентности получаются друг из друга некоторыми перестановками строк и столбцов."
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"id": "d838ad99",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"## Операции над графами"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"id": "dc315442",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"В результате операции добавления к графу $G=\\langle V,E \\rangle$ вершины $a$ a образуется граф $G1=\\langle V\\cup \\{a\\},E \\rangle$ .<br/> В результате операции добавления дуги $e$ к графу G образуется графа $G2=\\langle V,E\\cup \\{e\\} \\rangle$.<br/>\n",
|
|||
|
|
"Под операцией удаления дуги $e$ из графа $G$ понимается операция, заключающаяся в удалении пары $(a_i, a_j)$ из множества дуг $E$. <br/>Операция удаления вершины a из графа $G$ заключается в удалении вершины a вместе с инцидентными ей дугами.<br/> При замыкании двух вершин, эти вершины удаляются из графа и заменяются одной новой, при этом ребра, инцидентные исходным вершинам, теперь будут инцидентны новой вершине. В случае, когда отождествляемые вершины соединены дугой, операцию отождествления называют стягиванием дуги.\n"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 40,
|
|||
|
|
"id": "85892ea0",
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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
|
|||
|
|
"text/plain": [
|
|||
|
|
"<Figure size 640x480 with 1 Axes>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "display_data"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"import numpy as np\n",
|
|||
|
|
"A=np.array([[1, 0, 1, 0], \n",
|
|||
|
|
" [1, 1, 0, 0], \n",
|
|||
|
|
" [0, 1, 1, 0], \n",
|
|||
|
|
" [0, 1, 1, 1]])\n",
|
|||
|
|
"G = nx.DiGraph(A)\n",
|
|||
|
|
"plt.subplot(212)\n",
|
|||
|
|
"nx.draw_networkx(G)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 41,
|
|||
|
|
"id": "059ef702",
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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
|
|||
|
|
"text/plain": [
|
|||
|
|
"<Figure size 640x480 with 1 Axes>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "display_data"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"# Удаление ребра\n",
|
|||
|
|
"G.remove_edge(3,1) \n",
|
|||
|
|
"plt.subplot(212)\n",
|
|||
|
|
"nx.draw_networkx(G)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 42,
|
|||
|
|
"id": "c17ab9ba",
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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
|
|||
|
|
"text/plain": [
|
|||
|
|
"<Figure size 640x480 with 1 Axes>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "display_data"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"# Удаление вершины\n",
|
|||
|
|
"G.remove_node(2) \n",
|
|||
|
|
"plt.subplot(212)\n",
|
|||
|
|
"nx.draw_networkx(G)\n"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 43,
|
|||
|
|
"id": "2d012b55",
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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
|
|||
|
|
"text/plain": [
|
|||
|
|
"<Figure size 640x480 with 1 Axes>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "display_data"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"# Дополнение графа\n",
|
|||
|
|
"H = nx.complement(G)\n",
|
|||
|
|
"plt.subplot(212)\n",
|
|||
|
|
"nx.draw_networkx(H)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"id": "fe9a389c",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"Очевидно, имеем следующие утверждения:<br/>\n",
|
|||
|
|
"У всякого графа имеется пустой подграф.<br/>\n",
|
|||
|
|
"Всякий граф является подграфом полного графа.<br/>\n",
|
|||
|
|
"Если граф G является подграфом графа G1, а граф G2 – подграфом графа G1, то G2 – подграф графа G, (то есть отношение «быть\n",
|
|||
|
|
"подграфом» транзитивно).\n"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"id": "7a893bea",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"## Задание"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"id": "f177290d",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"**Задание 1.** Сгенерировать несколько ориентированных и несколько неориентированных графов различными способами (включая считывание из файла). Выполнить с ними все известные операции. Получить для них матрицы смежности и инцидентности. Вывести степени вершин, списки ребер и вершин."
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 59,
|
|||
|
|
"id": "424ba7bc",
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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
|
|||
|
|
"text/plain": [
|
|||
|
|
"<Figure size 640x480 with 1 Axes>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "display_data"
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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
|
|||
|
|
"text/plain": [
|
|||
|
|
"<Figure size 640x480 with 1 Axes>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "display_data"
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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
|
|||
|
|
"text/plain": [
|
|||
|
|
"<Figure size 640x480 with 1 Axes>"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "display_data"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"# Генерируем ориентированные и неориентированные графы\n",
|
|||
|
|
"G_directed = nx.DiGraph()\n",
|
|||
|
|
"G_undirected = nx.Graph()\n",
|
|||
|
|
"\n",
|
|||
|
|
"# Добавляем ребра в ориентированный граф\n",
|
|||
|
|
"G_directed.add_edges_from([(1, 2), (2, 3), (3, 2), (4, 2)])\n",
|
|||
|
|
"\n",
|
|||
|
|
"# Добавляем ребра в неориентированный граф\n",
|
|||
|
|
"G_undirected.add_edges_from([(1, 2), (2, 3), (3, 4), (4, 1)])\n",
|
|||
|
|
"\n",
|
|||
|
|
"# Считываем граф из файла\n",
|
|||
|
|
"G_from_file = nx.read_edgelist('Задание_9_graph.txt', nodetype=int)\n",
|
|||
|
|
"\n",
|
|||
|
|
"# Визуализируем графы\n",
|
|||
|
|
"nx.draw(G_directed, with_labels=True, font_weight='bold')\n",
|
|||
|
|
"plt.title('Ориентированный Граф')\n",
|
|||
|
|
"plt.show()\n",
|
|||
|
|
"\n",
|
|||
|
|
"nx.draw(G_undirected, with_labels=True, font_weight='bold')\n",
|
|||
|
|
"plt.title('Неориентированный Граф')\n",
|
|||
|
|
"plt.show()\n",
|
|||
|
|
"\n",
|
|||
|
|
"nx.draw(G_from_file, with_labels=True, font_weight='bold')\n",
|
|||
|
|
"plt.title('Граф из файла')\n",
|
|||
|
|
"plt.show()"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 45,
|
|||
|
|
"id": "8eea3b07",
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"Матрица смежности ориентированного графа:\n",
|
|||
|
|
"[[0 1 0 0]\n",
|
|||
|
|
" [0 0 1 0]\n",
|
|||
|
|
" [0 1 0 0]\n",
|
|||
|
|
" [0 1 0 0]]\n",
|
|||
|
|
"Матрица смежности неориентированного графа:\n",
|
|||
|
|
"[[0 1 0 1]\n",
|
|||
|
|
" [1 0 1 0]\n",
|
|||
|
|
" [0 1 0 1]\n",
|
|||
|
|
" [1 0 1 0]]\n",
|
|||
|
|
"Матрица инцидентности ориентированного графа:\n",
|
|||
|
|
"[[1. 0. 0. 0.]\n",
|
|||
|
|
" [1. 1. 1. 1.]\n",
|
|||
|
|
" [0. 1. 1. 0.]\n",
|
|||
|
|
" [0. 0. 0. 1.]]\n",
|
|||
|
|
"Матрица инцидентности неориентированного графа:\n",
|
|||
|
|
"[[1. 1. 0. 0.]\n",
|
|||
|
|
" [1. 0. 1. 0.]\n",
|
|||
|
|
" [0. 0. 1. 1.]\n",
|
|||
|
|
" [0. 1. 0. 1.]]\n",
|
|||
|
|
"Степени вершин ориентированного графа:\n",
|
|||
|
|
"[(1, 0), (2, 3), (3, 1), (4, 0)]\n",
|
|||
|
|
"Степени вершин неориентированного графа:\n",
|
|||
|
|
"[(1, 2), (2, 2), (3, 2), (4, 2)]\n",
|
|||
|
|
"Список ребер ориентированного графа:\n",
|
|||
|
|
"[(1, 2), (2, 3), (3, 2), (4, 2)]\n",
|
|||
|
|
"Список ребер неориентированного графа:\n",
|
|||
|
|
"[(1, 2), (1, 4), (2, 3), (3, 4)]\n",
|
|||
|
|
"Список вершин ориентированного графа:\n",
|
|||
|
|
"[1, 2, 3, 4]\n",
|
|||
|
|
"Список вершин неориентированного графа:\n",
|
|||
|
|
"[1, 2, 3, 4]\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"# Получаем матрицы смежности и инцидентности\n",
|
|||
|
|
"print(\"Матрица смежности ориентированного графа:\")\n",
|
|||
|
|
"print(nx.adjacency_matrix(G_directed).todense())\n",
|
|||
|
|
"\n",
|
|||
|
|
"print(\"Матрица смежности неориентированного графа:\")\n",
|
|||
|
|
"print(nx.adjacency_matrix(G_undirected).todense())\n",
|
|||
|
|
"\n",
|
|||
|
|
"print(\"Матрица инцидентности ориентированного графа:\")\n",
|
|||
|
|
"print(nx.incidence_matrix(G_directed).todense())\n",
|
|||
|
|
"\n",
|
|||
|
|
"print(\"Матрица инцидентности неориентированного графа:\")\n",
|
|||
|
|
"print(nx.incidence_matrix(G_undirected).todense())\n",
|
|||
|
|
"\n",
|
|||
|
|
"# Выводим степени вершин каждого графа\n",
|
|||
|
|
"print(\"Степени вершин ориентированного графа:\")\n",
|
|||
|
|
"print(G_directed.in_degree())\n",
|
|||
|
|
"\n",
|
|||
|
|
"print(\"Степени вершин неориентированного графа:\")\n",
|
|||
|
|
"print(G_undirected.degree())\n",
|
|||
|
|
"\n",
|
|||
|
|
"# Выводим списки ребер\n",
|
|||
|
|
"print(\"Список ребер ориентированного графа:\")\n",
|
|||
|
|
"print(G_directed.edges())\n",
|
|||
|
|
"\n",
|
|||
|
|
"print(\"Список ребер неориентированного графа:\")\n",
|
|||
|
|
"print(G_undirected.edges())\n",
|
|||
|
|
"\n",
|
|||
|
|
"# Выводим списки вершин\n",
|
|||
|
|
"print(\"Список вершин ориентированного графа:\")\n",
|
|||
|
|
"print(G_directed.nodes())\n",
|
|||
|
|
"\n",
|
|||
|
|
"print(\"Список вершин неориентированного графа:\")\n",
|
|||
|
|
"print(G_undirected.nodes())"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"id": "2087767b",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"**Задание 2.** Проверить любой из графов из задания 1 на наличие Эйлерова цикла, эйлерова пути, гамильтонова цикла."
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 63,
|
|||
|
|
"id": "0e8216f7",
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"Граф содержит Эйлеров цикл.\n",
|
|||
|
|
"Граф содержит Эйлеров путь.\n",
|
|||
|
|
"Граф содержит Гамильтонов цикл, цикл: (1, 2, 3, 4)\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"import itertools\n",
|
|||
|
|
"\n",
|
|||
|
|
"\n",
|
|||
|
|
"# Проверка на наличие Эйлерова цикла\n",
|
|||
|
|
"if nx.is_eulerian(G_undirected):\n",
|
|||
|
|
" print(\"Граф содержит Эйлеров цикл.\")\n",
|
|||
|
|
"else:\n",
|
|||
|
|
" print(\"Граф не содержит Эйлеров цикл.\")\n",
|
|||
|
|
"\n",
|
|||
|
|
"# Проверка на наличие Эйлерова пути\n",
|
|||
|
|
"if nx.has_eulerian_path(G_undirected):\n",
|
|||
|
|
" print(\"Граф содержит Эйлеров путь.\")\n",
|
|||
|
|
"else:\n",
|
|||
|
|
" print(\"Граф не содержит Эйлеров путь.\")\n",
|
|||
|
|
"\n",
|
|||
|
|
"# Проверка на наличие Гамильтонова цикла\n",
|
|||
|
|
"def is_hamiltonian(graph: any) -> None:\n",
|
|||
|
|
" for p in itertools.permutations(list(graph.nodes())):\n",
|
|||
|
|
" if all(p[i] in graph[p[i - 1]] for i in range(len(p))) and p[0] in graph[p[-1]]:\n",
|
|||
|
|
" print(f\"Граф содержит Гамильтонов цикл, цикл: {p}\")\n",
|
|||
|
|
" return\n",
|
|||
|
|
"\n",
|
|||
|
|
"is_hamiltonian(G_undirected)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"id": "2e168a74",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"**Задание 3.** Подсчитать количество циклов в любом из графов из задания 1."
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 67,
|
|||
|
|
"id": "2ffaa940",
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"Количество циклов: 1\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"from networkx.algorithms import cycle_basis\n",
|
|||
|
|
"\n",
|
|||
|
|
"# Находим все циклы в графе\n",
|
|||
|
|
"cycles = cycle_basis(G_undirected)\n",
|
|||
|
|
"\n",
|
|||
|
|
"# Подсчет количества циклов\n",
|
|||
|
|
"number_of_cycles = len(cycles)\n",
|
|||
|
|
"\n",
|
|||
|
|
"# Выводим количество циклов\n",
|
|||
|
|
"print(f'Количество циклов: {number_of_cycles}')"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"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": "3.11.0"
|
|||
|
|
}
|
|||
|
|
},
|
|||
|
|
"nbformat": 4,
|
|||
|
|
"nbformat_minor": 5
|
|||
|
|
}
|