Parkinson's Law 1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Parkinson's Law\n",
    "## Quantifying Dissensus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import random"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Setup Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0. 1. 5. 3. 6. 7. 2. 9. 4.]\n",
      " [1. 2. 7. 5. 6. 8. 4. 3. 9.]\n",
      " [2. 3. 9. 5. 8. 7. 6. 1. 4.]\n",
      " [3. 7. 6. 4. 8. 9. 1. 2. 5.]\n",
      " [4. 6. 8. 1. 5. 9. 2. 3. 7.]\n",
      " [5. 2. 8. 9. 6. 1. 7. 3. 4.]\n",
      " [6. 5. 1. 2. 9. 4. 8. 3. 7.]\n",
      " [7. 5. 6. 2. 8. 3. 1. 4. 9.]\n",
      " [8. 4. 6. 3. 5. 7. 2. 1. 9.]\n",
      " [9. 8. 3. 7. 1. 5. 4. 6. 2.]]\n"
     ]
    }
   ],
   "source": [
    "def getOpinions():\n",
    "    \"\"\"\n",
    "        Function randomly assigns opinion states to committee members\n",
    "        Inputs:  None\n",
    "        Returns: committee\"\"\"\n",
    "    committee = np.zeros(N)\n",
    "    for i in range(0,N):\n",
    "        committee[i] = random.randint(0,1)\n",
    "    return committee\n",
    "\n",
    "def getLinks(N):\n",
    "    \"\"\"\n",
    "       Function randomly assigns links between each node and k of its neighbours\n",
    "       Inputs:  None\n",
    "       Returns: links\"\"\"\n",
    "    # Contingency for plots that iterate from N = 0 not N > k+1\n",
    "    if N == k:\n",
    "        links = np.zeros([N,k])\n",
    "        x = k\n",
    "    else:\n",
    "        links = np.zeros([N,k+1])\n",
    "        x = k+1\n",
    "    \n",
    "    # Create left-most collumn as an indicator of each node\n",
    "    for i in range(0,N):\n",
    "        links[i][0] = i\n",
    "    \n",
    "    # Link each node to k different random nodes and store these in a row with the node indicator\n",
    "    for i in range(0,N):\n",
    "        for j in range(1,x):\n",
    "            n = 0\n",
    "            while n < 1:\n",
    "                if N == k:\n",
    "                    choice = random.choice(range(0,N+1))\n",
    "                else:\n",
    "                    choice = random.choice(range(0,N))\n",
    "                if choice != i and choice not in links[i]:\n",
    "                    links[i][j] = int(choice)\n",
    "                    n += 1\n",
    "                else:\n",
    "                    continue\n",
    "    return links\n",
    "\n",
    "# Trial\n",
    "N = 10\n",
    "k = 8\n",
    "links = getLinks(N)\n",
    "print(links)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Iterative Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rewire(links):\n",
    "    \"\"\"\n",
    "       Function rewires links with a probability 'e'\n",
    "       Inputs:  links\n",
    "       Returns: links\"\"\"\n",
    "    if k == N:\n",
    "        x = k\n",
    "    else:\n",
    "        x = k+1\n",
    "    for i in range(0,N):\n",
    "        for j in range(1,x):\n",
    "            # Perform rewiring with likelihood e\n",
    "            if random.random() >= (1-e):\n",
    "                n = 0\n",
    "                while n < 1:\n",
    "                    choice = random.choice(range(0,N))\n",
    "                    if choice != i and choice not in links[i]:\n",
    "                        links[i][j] = int(choice)\n",
    "                        n += 1\n",
    "                    else:\n",
    "                        continue\n",
    "    # Check that no completely independent sub-graphs have formed\n",
    "    graph = createGraph(links)\n",
    "    visited = []\n",
    "    DFS(visited,graph,0)\n",
    "    for i in range(0,N):\n",
    "        if i not in visited:\n",
    "            rewire(links)\n",
    "    return links\n",
    "\n",
    "def newOpinions(committee, links, N):\n",
    "    \"\"\"\n",
    "       Function re-evaluates opinion states if average opinion of connected nodes exceeds threshold\n",
    "       Inputs:  committee, links\n",
    "       Returns: links\"\"\"\n",
    "    # Create random order\n",
    "    order = 100*np.ones(N)\n",
    "    n = 0\n",
    "    while n < N:\n",
    "        y = random.randint(0,N-1)\n",
    "        if y not in order:\n",
    "            order[n] = y\n",
    "            n += 1\n",
    "    \n",
    "    # Iterate over each node\n",
    "    for i in range(0,N):\n",
    "        # Perform the iteration random-sequentially\n",
    "        x = int(order[i])\n",
    "        # Initialise arrays to count number of zeros and ones\n",
    "        ops0 = np.zeros(k)\n",
    "        ops1 = np.zeros(k)\n",
    "        # Contigency for N < k+2\n",
    "        if k == N:\n",
    "            z = k-1\n",
    "        else:\n",
    "            z = k\n",
    "        # Sum the ones and zeros held by connected nodes for each of N nodes\n",
    "        for j in range(1,z):\n",
    "            node = int(links[x][z])\n",
    "            if committee[node] == 0:\n",
    "                ops0[j] = int(1)\n",
    "            elif committee[node] == 1:\n",
    "                ops1[j] = int(1)\n",
    "        # Calculate proportion of ones and zeros with respect to total number of connected nodes\n",
    "        no = np.sum(ops0)/k\n",
    "        yes = np.sum(ops1)/k\n",
    "        # Change opinion if proportion in favour of majority is greater than threshold, h\n",
    "        if no >= h:\n",
    "            committee[x] = int(0)\n",
    "        elif yes >= h:\n",
    "            committee[x] = int(1)\n",
    "        else:\n",
    "            continue\n",
    "    return committee"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### DFS Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "def createGraph(links):\n",
    "    \"\"\"\n",
    "       Function creates a dictionary representation of array 'links' (manual test stage)\n",
    "       Inputs:\n",
    "       links    Adjacency matrix that stores connections between nodes\n",
    "       Returns:\n",
    "       graph   'Links' converted into a dictionary\"\"\"\n",
    "    if k == N:\n",
    "        x = k\n",
    "    else:\n",
    "        x = k+1\n",
    "    graph = {}\n",
    "    for i in range(0,N):\n",
    "        graph[i] = i\n",
    "        connections = np.zeros(k)\n",
    "        for j in range(1,x):\n",
    "            connections[j-1] = links[i][j] \n",
    "        graph[graph[i]] = connections\n",
    "    return graph\n",
    "\n",
    "def DFS(visited, graph, node):\n",
    "    \"\"\"\n",
    "       Function traverses graph via connections and stores each node it visits\n",
    "       Inputs:\n",
    "       Graph    Any graph\n",
    "       Node     Start node\n",
    "       Visited  Array of visited nodes (initially none)\n",
    "       Outputs:\n",
    "       Visited\"\"\"\n",
    "    if node not in visited:\n",
    "        visited.append(node)\n",
    "        for neighbour in graph[int(node)]:\n",
    "            DFS(visited, graph, neighbour)\n",
    "    return visited"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1. 0. 1. 0. 1. 1. 1. 1. 1.]\n",
      "[[0. 5. 6. 7. 8. 3.]\n",
      " [1. 3. 4. 6. 7. 2.]\n",
      " [2. 8. 3. 6. 4. 1.]\n",
      " [3. 8. 1. 5. 7. 6.]\n",
      " [4. 5. 8. 7. 2. 3.]\n",
      " [5. 2. 3. 1. 6. 4.]\n",
      " [6. 4. 7. 5. 1. 8.]\n",
      " [7. 5. 6. 3. 1. 4.]\n",
      " [8. 5. 6. 2. 4. 3.]]\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Test variable set\n",
    "N = 9\n",
    "k = 5\n",
    "e = 0.1\n",
    "h = 0.6\n",
    "\n",
    "# Establish random distribution of opinions and initial connections\n",
    "committee = getOpinions()\n",
    "print(committee)\n",
    "links = getLinks(N)\n",
    "print(links)\n",
    "\n",
    "# Initialise 2D opinion array\n",
    "opinions = np.zeros((4,N))\n",
    "opinions[0] = committee\n",
    "\n",
    "# Iterate re-evaluation and re-wiring 3 times\n",
    "for i in range(1,4):\n",
    "    committee = newOpinions(committee, links, N)\n",
    "    opinions[i] = committee\n",
    "    links = rewire(links)\n",
    "\n",
    "# Plot 2D opinion array to show evolution of committee opinion states\n",
    "plt.imshow(opinions, cmap='Greys')\n",
    "ax = plt.gca()\n",
    "ax.set_xticks(np.arange(-.5,N,1))\n",
    "ax.set_yticks(np.arange(-.5,4,1))\n",
    "ax.set_xticklabels('')\n",
    "ax.set_yticklabels('')\n",
    "ax.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 1296x1296 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1296x1296 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 2592x2592 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k = 8\n",
    "e = 0.1\n",
    "h = 0.6\n",
    "\n",
    "fig1 = plt.figure(figsize=(18,18))\n",
    "\n",
    "N = 15\n",
    "# Establish random distribution of opinions and initial connections\n",
    "committee = getOpinions()\n",
    "links = getLinks(N)\n",
    "\n",
    "# Initialise 2D opinion array\n",
    "opinions = np.zeros((4,N))\n",
    "opinions[0] = committee\n",
    "\n",
    "# Iterate re-evaluation and re-wiring 3 times\n",
    "for i in range(1,4):\n",
    "    committee = newOpinions(committee, links, N)\n",
    "    opinions[i] = committee\n",
    "    links = rewire(links)\n",
    "    \n",
    "a = fig1.add_subplot(1,4,1)\n",
    "plt.imshow(opinions, cmap='Greys')\n",
    "a = plt.gca()\n",
    "a.set_xticks(np.arange(-.5,N,1))\n",
    "a.set_yticks(np.arange(-.5,4,1))\n",
    "a.set_xticklabels('')\n",
    "a.set_yticklabels('')\n",
    "a.grid()\n",
    "\n",
    "N = 15\n",
    "# Establish random distribution of opinions and initial connections\n",
    "committee = getOpinions()\n",
    "links = getLinks(N)\n",
    "\n",
    "# Initialise 2D opinion array\n",
    "opinions = np.zeros((4,N))\n",
    "opinions[0] = committee\n",
    "\n",
    "# Iterate re-evaluation and re-wiring 3 times\n",
    "for i in range(1,4):\n",
    "    committee = newOpinions(committee, links, N)\n",
    "    opinions[i] = committee\n",
    "    links = rewire(links)\n",
    "    \n",
    "b = fig1.add_subplot(1,4,2)\n",
    "plt.imshow(opinions, cmap='Greys')\n",
    "b = plt.gca()\n",
    "b.set_xticks(np.arange(-.5,N,1))\n",
    "b.set_yticks(np.arange(-.5,4,1))\n",
    "b.set_xticklabels('')\n",
    "b.set_yticklabels('')\n",
    "b.grid()\n",
    "\n",
    "N = 15\n",
    "# Establish random distribution of opinions and initial connections\n",
    "committee = getOpinions()\n",
    "links = getLinks(N)\n",
    "\n",
    "# Initialise 2D opinion array\n",
    "opinions = np.zeros((4,N))\n",
    "opinions[0] = committee\n",
    "\n",
    "# Iterate re-evaluation and re-wiring 3 times\n",
    "for i in range(1,4):\n",
    "    committee = newOpinions(committee, links, N)\n",
    "    opinions[i] = committee\n",
    "    links = rewire(links)\n",
    "    \n",
    "c = fig1.add_subplot(1,4,3)\n",
    "plt.imshow(opinions, cmap='Greys')\n",
    "c = plt.gca()\n",
    "c.set_xticks(np.arange(-.5,N,1))\n",
    "c.set_yticks(np.arange(-.5,4,1))\n",
    "c.set_xticklabels('')\n",
    "c.set_yticklabels('')\n",
    "c.grid()\n",
    "\n",
    "N = 15\n",
    "# Establish random distribution of opinions and initial connections\n",
    "committee = getOpinions()\n",
    "links = getLinks(N)\n",
    "\n",
    "# Initialise 2D opinion array\n",
    "opinions = np.zeros((4,N))\n",
    "opinions[0] = committee\n",
    "\n",
    "# Iterate re-evaluation and re-wiring 3 times\n",
    "for i in range(1,4):\n",
    "    committee = newOpinions(committee, links, N)\n",
    "    opinions[i] = committee\n",
    "    links = rewire(links)\n",
    "    \n",
    "d = fig1.add_subplot(1,4,4)\n",
    "plt.imshow(opinions, cmap='Greys')\n",
    "d = plt.gca()\n",
    "d.set_xticks(np.arange(-.5,N,1))\n",
    "d.set_yticks(np.arange(-.5,4,1))\n",
    "d.set_xticklabels('')\n",
    "d.set_yticklabels('')\n",
    "d.grid()\n",
    "\n",
    "plt.show()\n",
    "\n",
    "fig2 = plt.figure(figsize=(18,18))\n",
    "\n",
    "N = 25\n",
    "# Establish random distribution of opinions and initial connections\n",
    "committee = getOpinions()\n",
    "links = getLinks(N)\n",
    "\n",
    "# Initialise 2D opinion array\n",
    "opinions = np.zeros((4,N))\n",
    "opinions[0] = committee\n",
    "\n",
    "# Iterate re-evaluation and re-wiring 3 times\n",
    "for i in range(1,4):\n",
    "    committee = newOpinions(committee, links, N)\n",
    "    opinions[i] = committee\n",
    "    links = rewire(links)\n",
    "    \n",
    "a = fig2.add_subplot(2,4,1)\n",
    "plt.imshow(opinions, cmap='Greys')\n",
    "a = plt.gca()\n",
    "a.set_xticks(np.arange(-.5,N,1))\n",
    "a.set_yticks(np.arange(-.5,4,1))\n",
    "a.set_xticklabels('')\n",
    "a.set_yticklabels('')\n",
    "a.grid()\n",
    "\n",
    "N = 25\n",
    "# Establish random distribution of opinions and initial connections\n",
    "committee = getOpinions()\n",
    "links = getLinks(N)\n",
    "\n",
    "# Initialise 2D opinion array\n",
    "opinions = np.zeros((4,N))\n",
    "opinions[0] = committee\n",
    "\n",
    "# Iterate re-evaluation and re-wiring 3 times\n",
    "for i in range(1,4):\n",
    "    committee = newOpinions(committee, links, N)\n",
    "    opinions[i] = committee\n",
    "    links = rewire(links)\n",
    "    \n",
    "b = fig2.add_subplot(2,4,2)\n",
    "plt.imshow(opinions, cmap='Greys')\n",
    "b = plt.gca()\n",
    "b.set_xticks(np.arange(-.5,N,1))\n",
    "b.set_yticks(np.arange(-.5,4,1))\n",
    "b.set_xticklabels('')\n",
    "b.set_yticklabels('')\n",
    "b.grid()\n",
    "\n",
    "N = 25\n",
    "# Establish random distribution of opinions and initial connections\n",
    "committee = getOpinions()\n",
    "links = getLinks(N)\n",
    "\n",
    "# Initialise 2D opinion array\n",
    "opinions = np.zeros((4,N))\n",
    "opinions[0] = committee\n",
    "\n",
    "# Iterate re-evaluation and re-wiring 3 times\n",
    "for i in range(1,4):\n",
    "    committee = newOpinions(committee, links, N)\n",
    "    opinions[i] = committee\n",
    "    links = rewire(links)\n",
    "    \n",
    "c = fig2.add_subplot(2,4,3)\n",
    "plt.imshow(opinions, cmap='Greys')\n",
    "c = plt.gca()\n",
    "c.set_xticks(np.arange(-.5,N,1))\n",
    "c.set_yticks(np.arange(-.5,4,1))\n",
    "c.set_xticklabels('')\n",
    "c.set_yticklabels('')\n",
    "c.grid()\n",
    "\n",
    "N = 25\n",
    "# Establish random distribution of opinions and initial connections\n",
    "committee = getOpinions()\n",
    "links = getLinks(N)\n",
    "\n",
    "# Initialise 2D opinion array\n",
    "opinions = np.zeros((4,N))\n",
    "opinions[0] = committee\n",
    "\n",
    "# Iterate re-evaluation and re-wiring 3 times\n",
    "for i in range(1,4):\n",
    "    committee = newOpinions(committee, links, N)\n",
    "    opinions[i] = committee\n",
    "    links = rewire(links)\n",
    "    \n",
    "d = fig2.add_subplot(2,4,4)\n",
    "plt.imshow(opinions, cmap='Greys')\n",
    "d = plt.gca()\n",
    "d.set_xticks(np.arange(-.5,N,1))\n",
    "d.set_yticks(np.arange(-.5,4,1))\n",
    "d.set_xticklabels('')\n",
    "d.set_yticklabels('')\n",
    "d.grid()\n",
    "\n",
    "plt.show()\n",
    "\n",
    "fig3 = plt.figure(figsize=(36,36))\n",
    "\n",
    "N = 35\n",
    "# Establish random distribution of opinions and initial connections\n",
    "committee = getOpinions()\n",
    "links = getLinks(N)\n",
    "\n",
    "# Initialise 2D opinion array\n",
    "opinions = np.zeros((4,N))\n",
    "opinions[0] = committee\n",
    "\n",
    "# Iterate re-evaluation and re-wiring 3 times\n",
    "for i in range(1,4):\n",
    "    committee = newOpinions(committee, links, N)\n",
    "    opinions[i] = committee\n",
    "    links = rewire(links)\n",
    "    \n",
    "a = fig3.add_subplot(3,4,1)\n",
    "plt.imshow(opinions, cmap='Greys')\n",
    "a = plt.gca()\n",
    "a.set_xticks(np.arange(-.5,N,1))\n",
    "a.set_yticks(np.arange(-.5,4,1))\n",
    "a.set_xticklabels('')\n",
    "a.set_yticklabels('')\n",
    "a.grid()\n",
    "\n",
    "N = 35\n",
    "# Establish random distribution of opinions and initial connections\n",
    "committee = getOpinions()\n",
    "links = getLinks(N)\n",
    "\n",
    "# Initialise 2D opinion array\n",
    "opinions = np.zeros((4,N))\n",
    "opinions[0] = committee\n",
    "\n",
    "# Iterate re-evaluation and re-wiring 3 times\n",
    "for i in range(1,4):\n",
    "    committee = newOpinions(committee, links, N)\n",
    "    opinions[i] = committee\n",
    "    links = rewire(links)\n",
    "    \n",
    "b = fig3.add_subplot(3,4,2)\n",
    "plt.imshow(opinions, cmap='Greys')\n",
    "b = plt.gca()\n",
    "b.set_xticks(np.arange(-.5,N,1))\n",
    "b.set_yticks(np.arange(-.5,4,1))\n",
    "b.set_xticklabels('')\n",
    "b.set_yticklabels('')\n",
    "b.grid()\n",
    "\n",
    "N = 35\n",
    "# Establish random distribution of opinions and initial connections\n",
    "committee = getOpinions()\n",
    "links = getLinks(N)\n",
    "\n",
    "# Initialise 2D opinion array\n",
    "opinions = np.zeros((4,N))\n",
    "opinions[0] = committee\n",
    "\n",
    "# Iterate re-evaluation and re-wiring 3 times\n",
    "for i in range(1,4):\n",
    "    committee = newOpinions(committee, links, N)\n",
    "    opinions[i] = committee\n",
    "    links = rewire(links)\n",
    "    \n",
    "c = fig3.add_subplot(3,4,3)\n",
    "plt.imshow(opinions, cmap='Greys')\n",
    "c = plt.gca()\n",
    "c.set_xticks(np.arange(-.5,N,1))\n",
    "c.set_yticks(np.arange(-.5,4,1))\n",
    "c.set_xticklabels('')\n",
    "c.set_yticklabels('')\n",
    "c.grid()\n",
    "\n",
    "N = 35\n",
    "# Establish random distribution of opinions and initial connections\n",
    "committee = getOpinions()\n",
    "links = getLinks(N)\n",
    "\n",
    "# Initialise 2D opinion array\n",
    "opinions = np.zeros((4,N))\n",
    "opinions[0] = committee\n",
    "\n",
    "# Iterate re-evaluation and re-wiring 3 times\n",
    "for i in range(1,4):\n",
    "    committee = newOpinions(committee, links, N)\n",
    "    opinions[i] = committee\n",
    "    links = rewire(links)\n",
    "    \n",
    "d = fig3.add_subplot(3,4,4)\n",
    "plt.imshow(opinions, cmap='Greys')\n",
    "d = plt.gca()\n",
    "d.set_xticks(np.arange(-.5,N,1))\n",
    "d.set_yticks(np.arange(-.5,4,1))\n",
    "d.set_xticklabels('')\n",
    "d.set_yticklabels('')\n",
    "d.grid()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getOpinions(S_i, N):\n",
    "    \"\"\"\n",
    "        Function assigns opinion states to committee members\n",
    "        Inputs: None\n",
    "        Returns: committee\"\"\"\n",
    "    order = np.ones(N)*100\n",
    "    for i in range(0,N):\n",
    "        n = 0\n",
    "        while n < 1:\n",
    "            choice = random.randint(0,N-1)\n",
    "            if choice not in order:\n",
    "                order[i] = choice\n",
    "                n += 1\n",
    "            else:\n",
    "                continue\n",
    "        \n",
    "    committee = np.zeros(N)\n",
    "    for i in range(0,S_i):\n",
    "        committee[int(order[i])] = 1\n",
    "    return committee"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'D(N)')"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k = 8\n",
    "h = 0.6\n",
    "e = 0.1\n",
    "\n",
    "iters = 40\n",
    "\n",
    "D_N = np.zeros(iters - k-1)\n",
    "for N in range(k+2,iters):\n",
    "    d_N = np.zeros(N)\n",
    "\n",
    "    for i in range(0,N):\n",
    "        S_i = i\n",
    "        committee = getOpinions(S_i, N)\n",
    "        links = getLinks(N)\n",
    "\n",
    "        opinions = np.zeros((4,N))\n",
    "\n",
    "        for j in range(1,4):\n",
    "            committee = newOpinions(committee, links, N)\n",
    "            opinions[j] = committee\n",
    "            links = rewire(links)\n",
    "\n",
    "        S_f = np.sum(np.where(committee==1,1,0))\n",
    "\n",
    "        y = np.array((S_f, N-S_f))\n",
    "        x = 1 - np.max(y)/N\n",
    "        if x > 0:\n",
    "            x = 1\n",
    "        elif x == 0:\n",
    "            x = 0\n",
    "        else:\n",
    "            x = 0\n",
    "        d_N[i] = x\n",
    "     \n",
    "    D = np.mean(d_N)\n",
    "    D_N[N-k-1] = D\n",
    " \n",
    "N = np.zeros(iters - k-1)\n",
    "for i in range(k+2,iters+1):\n",
    "    N[i - k-2] = i\n",
    "    \n",
    "plt.scatter(N, D_N)\n",
    "plt.title('Degree of Dissensus Reached for a Range of Committee Sizes')\n",
    "plt.xlabel('N')\n",
    "plt.ylabel('D(N)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I have now managed to create a plot that matches expectation, so I will use this modified approache to gather my results. I do now even see consensus always being reached when N < 10. \n",
    "\n",
    "I corrected the code by only running it for N > k+1 and fixing the DFS error from the previous attempt above. It would therefore seem that the change I made to the 'newOpinions' function at the beginning of this logbook was the main contributer to getting results that more closely resemble expectation and those given in the paper cited by the project description."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Figures for Report"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getOpinions():\n",
    "    \"\"\"\n",
    "        Function randomly assigns opinion states to committee members\n",
    "        Inputs: None\n",
    "        Returns: committee\"\"\"\n",
    "    committee = np.zeros(N)\n",
    "    for i in range(0,N):\n",
    "        committee[i] = random.randint(0,1)\n",
    "    return committee"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 2880x5760 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Percentage of shared opinions among connected nodes: 75.11111111111111 %\n"
     ]
    }
   ],
   "source": [
    "k = 8\n",
    "e = 0.1\n",
    "h = 0.6\n",
    "\n",
    "fig1 = plt.figure(figsize=(40,80))\n",
    "\n",
    "N = 25\n",
    "# Establish random distribution of opinions and initial connections\n",
    "committee = getOpinions()\n",
    "links = getLinks(N)\n",
    "\n",
    "# Initialise 2D opinion array\n",
    "opinions = np.zeros((4,N))\n",
    "opinions[0] = committee\n",
    "\n",
    "# Iterate re-evaluation and re-wiring 3 times\n",
    "for i in range(1,4):\n",
    "    committee = newOpinions(committee, links, N)\n",
    "    opinions[i] = committee\n",
    "    links = rewire(links)\n",
    "    \n",
    "a = fig1.add_subplot(1,4,1)\n",
    "plt.imshow(opinions, cmap='Greys')\n",
    "a = plt.gca()\n",
    "a.set_xticks(np.arange(-.5,N,1))\n",
    "a.set_yticks(np.arange(-.5,4,1))\n",
    "a.set_xticklabels('')\n",
    "a.set_yticklabels('')\n",
    "a.grid()\n",
    "plt.show()\n",
    "\n",
    "# Calculate percentage of nodes that share the opinion state of the majority\n",
    "averages = np.zeros(N)\n",
    "zeros = 0\n",
    "ones = 0\n",
    "for i in range(0,N):\n",
    "    for j in range(0,k+1):\n",
    "        node = int(links[i][j])\n",
    "        if committee[node]==0:\n",
    "            zeros += 1\n",
    "        elif committee[node]==1:\n",
    "            ones +=1\n",
    "    perc = (np.max((zeros,ones))/(k+1))*100\n",
    "averages[i] = perc\n",
    "print('Percentage of shared opinions among connected nodes:', np.mean(averages), '%')"
   ]
  }
 ],
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