{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Basic tutorial: ``MapperGraph`` class" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import networkx as nx\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "# The main class for the Reeb Graph\n", "from cereeberus import MapperGraph, ReebGraph\n", "\n", "# Some built in example graphs\n", "import cereeberus.data.ex_reebgraphs as ex_rg\n", "import cereeberus.data.ex_mappergraphs as ex_mg" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Mapper graphs are similar to Reeb graphs, except that: \n", "- The value of $f$ are *integers* in some range, `[n_low, ... , n_high]`.\n", "- We store a `delta` so that we can equivalently think of the function values as being `[delta * n_low, ... , delta * n_high]`.\n", "- All edges have adjacent integers for function values. Equivalently, the inverse image of an integer is only vertices, no internal points of edges. This can be done by subdividing any edge as needed. " ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "<Figure size 640x480 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "MG = MapperGraph( seed = 0, delta = 1)\n", "MG.add_node('A', f_vertex = 3)\n", "MG.add_node('B', f_vertex = 1)\n", "MG.add_node('C', f_vertex = 0)\n", "MG.add_node('D', f_vertex = -2)\n", "MG.add_node('E', f_vertex = 3)\n", "MG.add_node('F', f_vertex = 1)\n", "\n", "MG.add_edge('A','B')\n", "MG.add_edge('B','C')\n", "MG.add_edge('A','D')\n", "MG.add_edge('D','E')\n", "MG.add_edge('D','B')\n", "MG.add_edge('D','B')\n", "MG.add_edge('C','F')\n", "\n", "# These positions are the locations for the drawing\n", "MG.set_pos_from_f(seed = 8)\n", "\n", "MG.draw(cpx = 1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can convert a `ReebGraph` class instance into a `MapperGraph` class instance. Note that this is **NOT** the same as computing the mapper graph of a Reeb graph treated as the input object. " ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "{0: 7, 1: 6, 2: 5, 3: 5, 4: 6, 5: 4, 6: 4, 7: 1}\n" ] }, { "data": { "image/png": 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", "text/plain": [ "<Figure size 640x480 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "R = ex_rg.dancing_man(seed = 0)\n", "R.draw()\n", "print(R.f)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "<Figure size 640x480 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "MG = R.to_mapper()\n", "MG.draw()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, if the Reeb graph has any vertices with a non-integer function value, no mapper graph instance can be created. " ] } ], "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": "3.10.9" } }, "nbformat": 4, "nbformat_minor": 2 }