{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "12870de5",
   "metadata": {},
   "source": [
    "# Mixing Matrix and Benchmarks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "01f6500f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from netseg import freeman\n",
    "import numpy as np \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dcb5e8d2",
   "metadata": {},
   "source": [
    "## Different Ways to Use `netseg`\n",
    "\n",
    "Most of the measures in `netseg` can directly be used with a mixing matrix. These measures have an argument that accept a mixing matrix as total edge counts across groups. For example,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "208ea7de",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.7948717948717948)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "membership = [0 if i < 100 else 1 for i in range(200)]\n",
    "freeman(membership= membership, mixing_matrix= np.array([[140, 16],[16,140]]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e825be10",
   "metadata": {},
   "source": [
    "## Benchmarks\n",
    "\n",
    "`netseg` provides scalable, easy-to-use segregation measures for computational social scientists. By leveraging NumPy's vectorization and igraph's C backend, the package builds upon foundational community implementations to optimize performance for large networks. It consolidates several individually developed metrics into a unified toolkit. \n",
    "\n",
    "The benchmarks below show the scaling of `netseg` alongside the existing packages that inspired this work. It is important to notice that only challenging metrics are considered since some of the metrics are trivial and require obtaining a mixing matrix, which does not require extensive optimization and all of the Python and R packages, more or less, will have similar times if they are develop with care. For assortativity coefficient, `netseg` will perform better than `networkx` but `igraph` will perform orders of magnitude better than `netseg`.\n",
    "\n",
    "All results were obtained on a MacBook Air M3. Times are reported in seconds. Python benchmarks were timed using `perf_counter` and R benchmarks were timed using `system.time()`. Note that if you perform these tests yourself, although the difference ratio will be the same more or less, the slope of the curve might change between time-points according to your L2 cache size.\n",
    "\n",
    "For the Random Walk Controversy (RWC) metric, the number of simulations was set to 10,000. For both RWC and Dipole Moment, `k_top` was set to .3% of the total number of nodes in the graph. Finally, for the previous best implementation of RWC, the number of parallel workers was set to 8.\n",
    "\n",
    "\n",
    "![performed benchmarks for dprwcbp](figures/benchmarks.png)\n"
   ]
  }
 ],
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