{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "def generiranje_matrik(m, n): \n",
    "    d = m * n # število vrstic in stolpcev\n",
    "    rd = range(d) # obseg indeksov\n",
    "    matrika = Matrix(d, d) # matrika samih ničel\n",
    "    for i in rd:\n",
    "        for j in (i-1, i+1, i-n, i+n):\n",
    "            if j in rd:\n",
    "                matrika[i, j] = 1\n",
    "    return matrika\n",
    "\n",
    "def matrika_mreza(m, n):  #že vgrajena funkcija, .am() vrne matriko in ne grafa\n",
    "    return graphs.Grid2dGraph(m, n).am()\n",
    "\n",
    "def izris_grafa(matrika):  #izriše graf za dano matriko\n",
    "    matrika = Matrix(matrika)\n",
    "    G = Graph(matrika)\n",
    "    return G.plot().show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "def prehodna_matrika_M(matrika):   #vrne matriko katere (i,j)-ti element prikazuje verjetnost, da se bomo iz i-tega vozlišča premaknili v j-to\n",
    "    return Matrix([r/v for r, v in zip(matrika, sum(matrika))]) # vrstica / vsota vrstice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "def brisanje(j, matrika):  #izbriše j-ti stolpec in j-to vrstico\n",
    "    return matrika.delete_columns([j]).delete_rows([j])\n",
    "\n",
    "def dodajanje(j, matrika):   #doda j-to vrstico in j-ti stolpec (ničle)\n",
    "    return block_matrix([[matrika[:j, :j], 0, matrika[:j, j:]],\n",
    "                         [0, Matrix(1, 1), 0],\n",
    "                         [matrika[j:, :j], 0, matrika[j:, j:]]])\n",
    "\n",
    "def element_H(i, j, matrika):    #izračuna (i,j)-ti element matrike H\n",
    "    IM = dodajanje(j, (identity_matrix(matrika.nrows()-1) - brisanje(j, matrika))^-2)\n",
    "    return sum(IM[i, k] * matrika[k, j] for k in range(matrika.nrows()) if k != j)\n",
    "\n",
    "def matrika_H(matrika):  #vrne celotno matriko H\n",
    "    return Matrix([next(zip(*dodajanje(j, (identity_matrix(matrika.nrows()-1) - brisanje(j, matrika))^-2) * matrika[:, j]))\n",
    "                   for j in range(matrika.ncols())]).transpose()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "def nakjucni_sprehod_blizine_centralnosti(i,matrika): #sprejme incidenčno matriko!\n",
    "    vsota = 0\n",
    "    n = matrika.nrows()\n",
    "    rd = range(0,n)\n",
    "    M = prehodna_matrika_M(matrika) #izračun matrike M\n",
    "    for j in rd:\n",
    "        vsota += matrika_H(M)[j,i]\n",
    "    return n/vsota\n",
    "\n",
    "#def centralno_po_npbc(matrika):\n",
    "#    n = matrika.nrows()\n",
    "#    rd = range(0,n)\n",
    "#    rez = Matrix(n,1)\n",
    "#    for i in rd: #za vsako vozlišče izračunamo nsbc\n",
    "#        print(nakjucni_sprehod_blizine_centralnosti(i,matrika))\n",
    "#        rez[i] = int(nakjucni_sprehod_blizine_centralnosti(i,matrika))\n",
    "#        print(rez[i])\n",
    "#    return rez\n",
    "\n",
    "def centralno_po_nsbc(matrika):\n",
    "    n = matrika.nrows()\n",
    "    rd = range(0,n)\n",
    "    najvecji = [0,0]\n",
    "    for i in rd:\n",
    "        if nakjucni_sprehod_blizine_centralnosti(i,matrika) > najvecji[1]:\n",
    "            najvecji = [i][nakjucni_sprehod_blizine_centralnosti(i,matrika)]   #ne zna prevest rational v integer, vprašaj vidali\n",
    "    return najvecji"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<class 'sage.rings.rational.Rational'>"
      ]
     },
     "execution_count": 5,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = matrika_mreza(3,6)\n",
    "#show(nakjucni_sprehod_blizine_centralnosti(1,A),nakjucni_sprehod_blizine_centralnosti(2,A))\n",
    "#max(nakjucni_sprehod_blizine_centralnosti(1,A),nakjucni_sprehod_blizine_centralnosti(2,A))\n",
    "#B = [4,5]\n",
    "#show(B[0])\n",
    "#centralno_po_nobc(A)\n",
    "#centralno_po_npbc(A)\n",
    "#rez = Matrix(18,1)\n",
    "#type(A)\n",
    "#(A^3)[1][1]\n",
    "type(nakjucni_sprehod_blizine_centralnosti(1,A))\n",
    "#rez[1] = tuple(nakjucni_sprehod_blizine_centralnosti(1,A))\n",
    "#show(rez)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "def oddaljenost_i(i,matrika):   #vrne oddaljenost (najkrajšo pot) i-tega vozlišča do vseh ostalih vozlišč\n",
    "    n = matrika.nrows()\n",
    "    rd = range(0,n)\n",
    "    vektor = Matrix(n,1)\n",
    "    for j in rd:  #j != i\n",
    "        if j == i:  #spusti\n",
    "            vektor = vektor\n",
    "        elif matrika[i,j] != 0:  #sosednja vozlišča\n",
    "            vektor[j] = 1\n",
    "        else:\n",
    "            for l in range(1,n):\n",
    "                if vektor[j] != 0:\n",
    "                    vektor = vektor\n",
    "                elif (matrika^l)[i,j] != 0:\n",
    "                    vektor[j] = l\n",
    "    return vektor\n",
    "\n",
    "def centralnost_i(i,matrika):  #centralno vozlišče\n",
    "    return 1/sum(oddaljenost_i(i,matrika))   #sum() ne zna delit, vprašaj vidali"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "[1]\n",
       "[0]\n",
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       "[3]\n",
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       "[4]\n",
       "[5]\n",
       "[6]"
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     },
     "execution_count": 7,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
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       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(51\\right)</script></html>"
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      "text/plain": [
       "(51)"
      ]
     },
     "execution_count": 7,
     "metadata": {
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     "data": {
      "text/plain": [
       "<class 'sage.modules.vector_integer_dense.Vector_integer_dense'>"
      ]
     },
     "execution_count": 7,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = matrika_mreza(3,6)\n",
    "v=oddaljenost_i(1,A)\n",
    "show(v)\n",
    "s=sum(v)\n",
    "#C=centralnost_i(1,A)\n",
    "show(s)\n",
    "type(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "cannot add edge from 2 to 2 in graph without loops",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-4-7e73a075fc87>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     35\u001b[0m         \u001b[0msez2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     36\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mC\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 37\u001b[0;31m \u001b[0mkrozni_graf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m8\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     38\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     39\u001b[0m \u001b[0;31m#C.show() # long time\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-4-7e73a075fc87>\u001b[0m in \u001b[0;36mkrozni_graf\u001b[0;34m(n, k)\u001b[0m\n\u001b[1;32m     32\u001b[0m                     \u001b[0mk\u001b[0m \u001b[0;34m-=\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     33\u001b[0m             \u001b[0;32mfor\u001b[0m \u001b[0mj\u001b[0m \u001b[0;32min\u001b[0m \u001b[0msez2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 34\u001b[0;31m                  \u001b[0mC\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd_edges\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     35\u001b[0m         \u001b[0msez2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     36\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mC\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/ext/sage/sage-9.1/local/lib/python3.7/site-packages/sage/graphs/generic_graph.py\u001b[0m in \u001b[0;36madd_edges\u001b[0;34m(self, edges, loops)\u001b[0m\n\u001b[1;32m  10925\u001b[0m                 \u001b[0;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"cannot interpret {!r} as graph edge\"\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m  10926\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mloops\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mu\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mv\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m> 10927\u001b[0;31m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_backend\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd_edge\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mu\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mv\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_directed\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m  10928\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m  10929\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0msubdivide_edge\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/ext/sage/sage-9.1/local/lib/python3.7/site-packages/sage/graphs/base/sparse_graph.pyx\u001b[0m in \u001b[0;36msage.graphs.base.sparse_graph.SparseGraphBackend.add_edge (build/cythonized/sage/graphs/base/sparse_graph.c:16220)\u001b[0;34m()\u001b[0m\n\u001b[1;32m   1358\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1359\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mu_int\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mv_int\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_loops\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1360\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mf\"cannot add edge from {u!r} to {v!r} in graph without loops\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1361\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1362\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmultiple_edges\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: cannot add edge from 2 to 2 in graph without loops"
     ]
    }
   ],
   "source": [
    "\n",
    "#def 3Dmreza(m,n,z):\n",
    "#    d = m*n*z #dimenzije matrike\n",
    "#    rd = range(d)\n",
    "#    matrika = Matrix(d, d) # matrika samih ničel\n",
    "\n",
    "\n",
    "def generator_binarnih_dreves(k): #vrne binarno drevo \n",
    "    G = graphs.BalancedTree(2,k)\n",
    "    show(G)\n",
    "    return G\n",
    "\n",
    "#def bd_matrika(k):\n",
    "#    return graphs.Grid2dGraph(m, n).am()\n",
    "\n",
    "\n",
    "import networkx\n",
    "import random\n",
    "\n",
    "#def krozni_graf(n,k): #n vozlisc, vsako ima k povezav\n",
    "#    sez1 = list(range(0,n))\n",
    "#    #n = networkx.cycle_graph(n)\n",
    "#    C = graphs.CycleGraph(n)\n",
    "#    sez2 = []\n",
    "#    if k < n - 2:\n",
    "#        for i in C:\n",
    "#            while k>0:\n",
    "#                r = random.choice(sez1)\n",
    "#                if r == i-1 or r == i+1 or r == i:\n",
    "#                    pass\n",
    "#                else:\n",
    "#                    sez2.append(r)\n",
    "#                    k -= 1\n",
    "#            for j in sez2:\n",
    "#                 C.add_edges([(j, i)])\n",
    "        sez2 = []\n",
    "    return C.show()\n",
    "krozni_graf(8,2)\n",
    "    \n",
    "#C.show() # long time\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "#def sprehod(matrika,v1,v2):\n",
    "#    a = 0\n",
    "#    while v1 < v2:\n",
    "#        for v1 in matrika:\n",
    "#            for j in matrika:\n",
    "#                while j < matrika.nrows():\n",
    "#                    b = 0\n",
    "#                    if matrika[v1][j] == 1:\n",
    "#                        j += 1\n",
    "#                        b = j\n",
    "#                    else:\n",
    "#                        j += 1\n",
    "#        v1 = b\n",
    "#        a += 1\n",
    "#    return a\n",
    "\n",
    "\n",
    "def oddaljenost_i_j(matrika,i,j):  #izračuna dolžino najkrajše poti med i in j\n",
    "    n = matrika.nrows()\n",
    "    rd = range(0,n)\n",
    "    razdalja = 0\n",
    "    if matrika[i,j] != 0:\n",
    "        razdalja = 1\n",
    "    else:\n",
    "        for l in range(2,n):\n",
    "            if (matrika^l)[i,j] != 0:\n",
    "                while razdalja == 0:\n",
    "                    razdalja = l\n",
    "    return razdalja\n",
    "\n",
    "def povprecje_sprehodov(matrika,k):   #sešteje najkrajše razdalje do drugih vozlišč in to deli s številom vozlišč-1\n",
    "    koraki = 0\n",
    "    for i in range(0, matrika.nrows):\n",
    "        if i != k:\n",
    "            koraki += oddaljenost_i_j(matrika,i,k)\n",
    "        else:\n",
    "            pass\n",
    "    return koraki/(matrika.nrows()-1)  #se poglej malo mislim da ne klices prav funkcije\n",
    "\n",
    "\n",
    "\n",
    "import random\n",
    "\n",
    "def nakljucni_sprehod(matrika, k):\n",
    "    sez2 = list(range(0, (matrika.nrows())))  #seznam neobiskanih vozlišč\n",
    "    zacetno = k\n",
    "    a = len(sez2)\n",
    "    koraki = 0\n",
    "    koncni_sez = [0] * a\n",
    "    koncni_sez[zacetno] = 1  #v to vozlišče ni potrebno priti, na koncu popravimo na 0\n",
    "    sez2.remove(zacetno)  #odstranimo začetno vozlišče, ker v njega ni potrebno priti\n",
    "    while len(sez2) > 0:\n",
    "        sez3 = []\n",
    "        for k in range(0,matrika.nrows()):\n",
    "            for j in range(0,matrika.nrows()):\n",
    "                if matrika[k,j] != 0:  #naredimo seznam sosednjih vozlišč\n",
    "                    sez3.append(j)\n",
    "                else:\n",
    "                    pass\n",
    "        c = random.choice(sez3)  #naključno izbere v kako vozlišče se premaknemo\n",
    "        k = c   #k označuje trenutno vozlišče\n",
    "        sez3 = []\n",
    "        koraki += 1\n",
    "        if koncni_sez[c] == 0:\n",
    "            koncni_sez[c] = koraki   #dodamo število korakov, ki smo jih potrebovali, da smo prišli do tega vozlišča\n",
    "            sez2.remove(c)    #in ga odstranimo iz seznama neobiskanih vozlišč\n",
    "        else:\n",
    "            pass\n",
    "        #for i in sez2:\n",
    "         #   if sez2[i] == c:\n",
    "          #      sez2.pop(c)\n",
    "           # else:\n",
    "            #    pass\n",
    "    koncni_sez[zacetno] = 0 #nastavimo začetno vozlišče nazaj na 0\n",
    "    return koncni_sez\n",
    "\n",
    "\n",
    "def n_nakljucnih_sprehodov(matrika,k,n):   #funkcija naredi n naključnih sprehodov iz k-tega vozlišča\n",
    "    d = matrika.nrows()\n",
    "    povp = [0] * d\n",
    "    for ponovitev in range(0,n):\n",
    "        v = nakljucni_sprehod(matrika,k)\n",
    "        for i in range(0,d):\n",
    "            povp[i] += v[i]\n",
    "    povp[:] = [x / n for x in povp]  #deli vse elemente z n; da dobimo povprečno dolžino\n",
    "    return povp\n",
    "\n",
    "def dolzina_vseh(matrika,n):  #naredi n naključnih sprehodov; vrne povprečno hitrost, s katero procesi naključnega sprehajanja dosežejo vozlišče iz drugih vozlišč v omrežju\n",
    "    d = matrika.nrows()\n",
    "    povp = [0] * d\n",
    "    for vozlisce in range(0,d):\n",
    "        v = n_nakljucnih_sprehodov(matrika,vozlisce,n)\n",
    "        for i in range(0,d):\n",
    "            povp[i] += v[i]\n",
    "    povp[:] = [x / (n-1)*d for x in povp]  #deli vse elemente s številom sprehodov; da dobimo povprečno dolžino\n",
    "    return povp\n",
    "\n",
    "def nsbc(matrika,n):\n",
    "    rez = dolzina_vseh(matrika,n)\n",
    "    rez[:] = [1 / x for x in rez]\n",
    "    return rez"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5/2103"
      ]
     },
     "execution_count": 91,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#v=oddaljenost_i(1,A)\n",
    "#u=oddaljenost_i_j(A,1,15)\n",
    "#show(v)\n",
    "#show(u)\n",
    "#izris_grafa(A)\n",
    "#nakljucni_sprehod(A, 2)\n",
    "#n_nakljucnih_sprehodov(A,2,500)\n",
    "a=nsbc(A,10)\n",
    "max(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1320}{62341} \\frac{220}{6651} \\frac{1320}{30781}</script></html>"
      ],
      "text/plain": [
       "1320/62341 220/6651 1320/30781"
      ]
     },
     "execution_count": 89,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show(nakjucni_sprehod_blizine_centralnosti(0,A),nakjucni_sprehod_blizine_centralnosti(1,A),nakjucni_sprehod_blizine_centralnosti(2,A))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
   ]
  }
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