{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Basic Tutorial: Embedded graph class \n", "\n", "In this notebook, we'll walk through the basic functionality of the `EmbeddedGraph` class. See [here](../modules/reeb/embedgraph.rst)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import networkx as nx\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "# The main class for the embedded graph\n", "from cereeberus import EmbeddedGraph" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Constructing the embedded graph\n", "\n", "We assume our input is an undirected graph $G$ with an embedding in 2D given by a map on the vertices $f: V(G) \\to \\mathbb{R}^2$. A graph can be constructed as follows. \n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Construct an example graph \n", "\n", "G = EmbeddedGraph()\n", "\n", "G.add_node('A', 1, 2)\n", "G.add_node('B', 3, 4)\n", "G.add_node('C', 5, 7)\n", "G.add_node('D', 3, 6)\n", "G.add_node('E', 4, 3)\n", "G.add_node('F', 4, 5)\n", "G.add_node('G', 2, 5)\n", "\n", "G.add_edge('A', 'B')\n", "G.add_edge('B', 'C')\n", "G.add_edge('B', 'D')\n", "G.add_edge('B', 'E')\n", "G.add_edge('C', 'D')\n", "G.add_edge('E', 'F')\n", "G.add_edge('G', 'D')\n", "G.add_edge('G', 'B')\n", "\n", "G.plot()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The coordinates of all vertices, given as a dictionary, can be accessed using the `coordinates` attribute." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'A': (1, 2),\n", " 'B': (3, 4),\n", " 'C': (5, 7),\n", " 'D': (3, 6),\n", " 'E': (4, 3),\n", " 'F': (4, 5),\n", " 'G': (2, 5)}" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "G.coordinates" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Because of the rotational aspect of the ECT, we often want our graph to be centered, so you can use the `set_mean_centered_coordinates` method shift the graph to have the average of the vertex coordinates be 0. Note that this does overwrite the coordinates of the points. " ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "{'A': (-2.142857142857143, -2.571428571428571), 'B': (-0.1428571428571428, -0.5714285714285712), 'C': (1.8571428571428572, 2.428571428571429), 'D': (-0.1428571428571428, 1.4285714285714288), 'E': (0.8571428571428572, -1.5714285714285712), 'F': (0.8571428571428572, 0.4285714285714288), 'G': (-1.1428571428571428, 0.4285714285714288)}\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "G.set_mean_centered_coordinates()\n", "print(G.coordinates)\n", "G.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Reeb graph from a given direction\n", "\n", "Directions are given in the code by specifying $\\theta \\in [0,2\\pi]$. We often convert this to $\\omega \\in \\mathbb{S}^1$ by defining the unit vector $\\omega = (\\cos(\\theta), \\sin(\\theta))$. Then the function $g_\\omega$ is defined on the vertices of $G$ by taking the dot product of the embedding coordinates with the unit vector, specifically\n", "$$\n", "g_\\omega(v) = \\langle f(v), \\omega\\rangle.\n", "$$\n", "This is done in the code using the `g_omega` method as shown. " ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "G.plot(color_nodes_theta=3*np.pi/4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For this function defined based on the direction, we can then construct the Reeb graph of the graph with the function. Note that the drawing locations no longer have anything to do with the original embedding information other than have the $y$-coordinate the same as the function value. " ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "R = G.reeb_graph_from_direction(3*np.pi/4)\n", "R.draw(cpx = .2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Of course, collapsing of two vertices only happens at degenerate directions (i.e. those where the endpoints of an edge have the same function value in that direction). For most directions, the Reeb graph will look similar to the original graph, but the only information retained is now a 1-d function. " ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "R = G.reeb_graph_from_direction(3*np.pi/7)\n", "R.draw(cpx = .2)" ] } ], "metadata": { "kernelspec": { "display_name": "base", "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": "3.11.7" } }, "nbformat": 4, "nbformat_minor": 2 }