initial upload of all course files
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Joe James
175
Section_5/Graph Implementation Using Adjacency Matrix.ipynb
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175
Section_5/Graph Implementation Using Adjacency Matrix.ipynb
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Graph Implementation Using Adjacency Matrix\n",
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"for undirected graph, with weighted or unweighted edges. \n",
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"© Joe James, 2019."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Vertex Class\n",
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"A vertex object only needs to store its name. "
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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": 4,
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"metadata": {},
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"outputs": [],
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"source": [
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"class Vertex:\n",
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" def __init__(self, n):\n",
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" self.name = n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Graph Class\n",
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"A graph object has three attributes: \n",
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"**vertices** - a dictionary with vertex_name:vertex_object. \n",
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"**edges** - a 2-dimensional list (ie. a matrix) of edges. for an unweighted graph it will contain 0 for no edge and 1 for edge. \n",
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"**edge_indices** - a dictionary with vertex_name:list_index (eg. A:0) to access edges. \n",
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"add_vertex updates all three of these attributes. \n",
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"add_edge only needs to update the edges matrix."
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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": 5,
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"metadata": {},
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"outputs": [],
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"source": [
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"class Graph:\n",
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" vertices = {}\n",
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" edges = []\n",
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" edge_indices = {}\n",
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" \n",
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" def add_vertex(self, vertex):\n",
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" if isinstance(vertex, Vertex) and vertex.name not in self.vertices:\n",
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" self.vertices[vertex.name] = vertex\n",
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" # for loop appends a column of zeros to the edges matrix\n",
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" for row in self.edges:\n",
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" row.append(0)\n",
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" # append a row of zeros to the bottom of the edges matrix\n",
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" self.edges.append([0] * (len(self.edges)+1))\n",
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" self.edge_indices[vertex.name] = len(self.edge_indices)\n",
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" return True\n",
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" else:\n",
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" return False\n",
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" \n",
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" def add_edge(self, u, v, weight=1):\n",
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" if u in self.vertices and v in self.vertices:\n",
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" self.edges[self.edge_indices[u]][self.edge_indices[v]] = weight\n",
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" self.edges[self.edge_indices[v]][self.edge_indices[u]] = weight\n",
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" return True\n",
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" else:\n",
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" return False\n",
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" \n",
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" def print_graph(self):\n",
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" for v, i in sorted(self.edge_indices.items()):\n",
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" print(v + ' ', end='')\n",
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" for j in range(len(self.edges)):\n",
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" print(self.edges[i][j], end=' ')\n",
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" print(' ')"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Test Code\n",
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"Here we create a new Graph object. We create a new vertex named A. We add A to the graph. Then we add new vertex B to the graph. Then we iterate from A to K and add a bunch of vertices to the graph. Since the add_vertex method checks for duplicates, A and B are not added twice.\n",
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"This is exactly the same test code we used for the graph with adjacency lists."
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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": 8,
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"metadata": {},
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"outputs": [],
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"source": [
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"g = Graph()\n",
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"a = Vertex('A')\n",
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"g.add_vertex(a)\n",
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"g.add_vertex(Vertex('B'))\n",
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"for i in range(ord('A'), ord('K')):\n",
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" g.add_vertex(Vertex(chr(i)))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"An edge consists of two vertex names. Here we iterate through a list of edges and add each to the graph. \n",
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"\n",
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"This print_graph method doesn't give a very good visualization of the graph, but it does show the adjacency matrix so we can see each vertex's neighbors."
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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": 7,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"A 0 1 0 0 1 0 0 0 0 0 \n",
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"B 1 0 0 0 0 1 0 0 0 0 \n",
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"C 0 0 0 0 0 0 1 0 0 0 \n",
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"D 0 0 0 0 1 0 0 1 0 0 \n",
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"E 1 0 0 1 0 0 0 1 0 0 \n",
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"F 0 1 0 0 0 0 1 0 1 1 \n",
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"G 0 0 1 0 0 1 0 0 0 1 \n",
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"H 0 0 0 1 1 0 0 0 1 0 \n",
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"I 0 0 0 0 0 1 0 1 0 0 \n",
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"J 0 0 0 0 0 1 1 0 0 0 \n"
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]
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}
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],
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"source": [
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"edges = ['AB', 'AE', 'BF', 'CG', 'DE', 'DH', 'EH', 'FG', 'FI', 'FJ', 'GJ', 'HI']\n",
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"for edge in edges:\n",
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" g.add_edge(edge[0], edge[1])\n",
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"\n",
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"g.print_graph()"
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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": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"file_extension": ".py",
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"pygments_lexer": "ipython3",
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"version": "3.7.0"
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}
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"nbformat": 4,
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"nbformat_minor": 2
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}
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