{"cells":[{"metadata":{},"cell_type":"markdown","source":"![En tête general](https://raw.githubusercontent.com/PythonLycee/PyLyc/master/img/En_tete_general.png)\n\n\n© Copyright Franck CHEVRIER 2019-2021 https://www.python-lycee.com.
\nLes activités partagées sur Capytale sont sous licence Creative Commons.\n\n Pour exécuter une saisie Python, sélectionner la cellule et valider avec SHIFT+Entrée.\n"},{"metadata":{},"cell_type":"markdown","source":"# Réseaux sociaux et graphes (corrigé)"},{"metadata":{},"cell_type":"markdown","source":"*Le but de l’activité est de modéliser les relations d'un réseau social à l'aide de graphes, et d'introduire les notions de matrice d'adjacence et de diamètre d'un graphe.*\n"},{"metadata":{},"cell_type":"markdown","source":"## 1. Relation d'amitié réflexive : Graphe non orienté"},{"metadata":{},"cell_type":"markdown","source":"![Reseau_social_amities](https://raw.githubusercontent.com/PythonLycee/PyLyc/master/SNT/img/ReseauSocial_1.png)\n\n__1. a. Des relations d'amitiés au sein d'un réseau social sont présentées ci-dessus. La relation d'amitié considérée est une relation réflexive (réciproque). A l'aide de la vidéo suivante, donner:__\n\n\n\n - la matrice d'adjacence associée à ce graphe ;
\n - la distance de C à E ;
\n - le diamètre de ce graphe.
\n
\n\n Pour les corrections de cette question, voir les résultats des saisies Python.\n\n\n\n"},{"metadata":{},"cell_type":"markdown","source":"__1. b. On code en Python le graphe précédent à l'aide de la structure G1 ci-dessous. Expliquer brièvement comment sont stockées les informations du graphe dans G1.__\n\n G1 donne la correspondance entre chaque sommet et la liste des sommets qui lui sont adjacents.\n\n\nAttention : Penser ensuite à exécuter la zone ci-dessous (et les suivantes) avec SHIFT+Entrée."},{"metadata":{"trusted":false},"cell_type":"code","source":"G1 = { 'A':['C','F'] , \n 'B':['C','D','E','F'] , \n 'C':['A','B','F'] , \n 'D':['B','E'] , \n 'E':['B','D'] , \n 'F':['A','B','C'] \n }","execution_count":1,"outputs":[]},{"metadata":{},"cell_type":"markdown","source":"__1. c. La fonction Python repr_graphe ci-dessous permet de représenter un graphe à partir de sa structure en Python. Tester l'appel à cette fonction pour G1 et vérifier qu'on obtient bien le graphe initial.__\n"},{"metadata":{"trusted":false},"cell_type":"code","source":"#import des modules pour les calculs et graphiques\nfrom math import*\nimport numpy as np\nimport matplotlib.pyplot as plt\n\ndef non_oriente(Graphe):\n \"\"\"\n Fonction qui indique si un graphe n'est pas orienté\n \"\"\"\n for S in Graphe:\n for adj in Graphe[S]:\n if S not in Graphe[adj]: return False\n return True\n \ndef repr_graphe(Graphe, r_sommets=0.1):\n \"\"\"\n Fonction qui représente un graphe stocké sous forme d'un dictionnaire\n (la fonction trace des arêtes orientées si le graphe est orienté)\n \"\"\"\n #couleurs du graphique\n col_p='black' \n col_t='white' \n \n #récupération du nombre de sommets\n n_sommets=len(Graphe)\n \n #préparation du graphique: axes masqués\n fig, ax = plt.subplots() ; axes = plt.gca()\n for dir in ['left','right','bottom','top']: ax.spines[dir].set_visible(False)\n aff=1+r_sommets*1.1\n plt.xlim(-aff,aff) ; axes.xaxis.set_ticks_position('none') ; axes.xaxis.set_ticklabels([])\n plt.ylim(-aff,aff) ; axes.yaxis.set_ticks_position('none') ; axes.yaxis.set_ticklabels([])\n \n #calcul des coordonnées des sommets:\n x_sommet={} ; y_sommet={}\n k=0\n for S in Graphe:\n angle=2*pi*k/n_sommets\n x_sommet[S]=cos(angle)\n y_sommet[S]=sin(angle)\n k+=1\n \n #tracé des arêtes\n for S in Graphe:\n for adj in Graphe[S]:\n if non_oriente(Graphe):\n #arête simple si le graphe n'est pas orienté\n plt.plot([x_sommet[S],x_sommet[adj]],[y_sommet[S],y_sommet[adj]],color=col_p)\n else:\n #arête orientée sinon\n x_vect=x_sommet[adj]-x_sommet[S] ; y_vect=y_sommet[adj]-y_sommet[S]\n ax.arrow( x_sommet[S] , y_sommet[S] , x_vect*(1-2*r_sommets/sqrt(x_vect**2+y_vect**2)) , y_vect*(1-2*r_sommets/sqrt(x_vect**2+y_vect**2)) , head_width=r_sommets*2/3, head_length=r_sommets, fc=col_p, ec=col_p)\n \n #tracé des sommets\n k=0\n for S in Graphe:\n ax.add_patch(plt.Circle((x_sommet[S],y_sommet[S]), radius=r_sommets , color=col_p )) #disque représentant le sommet\n plt.text(x_sommet[S]-r_sommets/4,y_sommet[S]-r_sommets/4,S, color=col_t) #nom du sommet\n k+=1 \n \n #affichage général\n plt.show()","execution_count":2,"outputs":[]},{"metadata":{"trusted":false},"cell_type":"code","source":"#Appel à la fonction pour le graphe G1\nrepr_graphe(G1)","execution_count":3,"outputs":[{"data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAWQAAADuCAYAAAAOR30qAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAAIABJREFUeJzt3XlwlPX9B/D3s0eyR0hC5IiCEG4iQQkghwJBEVGwFCE4IwidERgvmPFCW8rhWCQtYu0oMDpYSxUrFFCpVZGCnHJUY6yEGxIhytFAEok5dzef3x/8Nl0g4Xmefe7n+bxmdqbaffb7DQlvN5993s8jEBEYY4wZz2X0BhhjjF3CgcwYYybBgcwYYybBgcwYYybBgcwYYybBgcwYYybBgcwYYybBgcwYYybBgcwYYybhkfl8rvUxxph8gpQn8TtkxhgzCQ5kxhgzCQ5kxhgzCQ5kxhgzCQ5kxhgzCQ5kxhgzCQ5kxhgzCQ5kxhgzCQ5kxhgzCQ5kxhgzCQ5kxhgzCQ5kxhgzCbkXF2IaiEQiOHr0KIqKilBcXIzTp0+jrq4ObrcbaWlpyMjIQKdOnZCZmYnk5GSjt8sspK6uDocOHUJxcTGKi4tRWlqKuro6eL1etGnTBp07d2782UpMTDR6u47HgWyQqqoqrFmzBmvXrsXOnTshCALcbjfq6upQW1vb+DyPxwO/3w9BEFBbW4tu3bph3LhxmDp1Krp3727gV8DM6ty5c1i1ahXWr1+P/Px8+Hw+AEBtbS3q6+sbn5eQkACfzwciQl1dHfr164fx48djypQpaNu2rVHbdzYikvNgCp0+fZpmzZpFwWCQgsEg4dIlTWU9PB4P+f1+Gjp0KG3ZssXoL4mZRGFhIT3wwAPk8/nI5/PF9bMVPTY3N5f2799v9JdkJ5IyViCSdYljvh5ynIgIy5Ytw/PPP49wOHzZOxUlAoEA7rjjDvzlL39B69atVXlNZi21tbV4/vnnsWLFCtTV1aGhoUHxa7pcLiQmJmL69OlYvHhx47tsFjdJ10PmQNZBKBTCxIkTsXnzZlRVVan++gkJCWjRogV27tyJzMxM1V+fmVdZWRmGDh2K4uJi1NTUqP76fr8fGRkZ2LVrF9LS0lR/fQfhQDaDcDiMX/ziF9ixYweqq6s1W0cQBKSkpGDnzp3IysrSbB1mHmVlZRg0aBBOnjyp2m9cTfF6vejQoQP27t2LVq1aabaOzfEdQ8xg8eLFssK4bdu2eP/993H8+HEcOHAAn3zyCbp16yZ6HBGhoqICY8eO1fQvJzOPhx9+WFYYh8NhFBQU4Ntvv0V+fj4GDx4s6bhQKIRTp07h4YcfVrJdJoXUYTPxh3qyff/99+T3+2V9qLJ792565JFHGv/5lltuoSFDhkg+PhAI0Isvvmj0l840tmnTJgoEArJ+tiorKxv/9913303btm2TdXwgEKDPPvvM6C/dqiRlLL9D1tB7770n6wOWO+64A6FQCG+++Wbjv/vPf/6DXbt2SX6N6upqLF++HCRvFMUs5rXXXlM0AktOTkZ5ebmsY6qrq/Haa6/FvSYTx+cha2j16tWoq6uT/PysrCzk5+crXvfixYs4duwYn6dsU5FIBFu2bJF9nN/vR0FBAXw+H66//nrceeedsl9j69atCIfD8Hg4OrTAf6oaOnPmjCHrVldXo2/fvvyXxqaIKK4zKmpqapCdnQ0AGDRoEN555x3ZHwATEX766Sdcd911stdn4nhkoSGv1yvr+QcOHEC/fv002g2zC0GQ9IH9NUXPmJB77nokEuGKtYb4LZSGhgwZgrVr10p+/hdffIFFixZh+vTpeOuttwAA/fv3RyAQwI4dOyS/TmJiIs6ePYukpCTZe2bW0LlzZxQXF8d9fI8ePeB2u3HhwgVZx7Vv355/rjTE75A1NGnSJNk/vPfffz9GjhyJ48ePo7CwEC+88AJOnz4t+XhBEDB48GD+S2NzkyZNkv1ONTpDLigowJo1a/CrX/1K1ofOCQkJePDBB+VulcnAxRANRSIR9OnTBwcOHNDtrIfExETs3bsXffr00WU9ZoyysjJ07twZP/30k25rpqSk4MSJEzw/jg8XQ4zmdrvx/vvvw+/367ZmfX09nnrqKVkjDmYtx44dwyOPPKJJVbo5gUAAK1as4DDWGAeyxrKysvDpp58iEAhouo7P50PPnj2RmpqKbdu2IScnBy1btsSMGTNw9uxZTddm2quursb8+fPRvn17dO/eHevWrYPb7UafPn00/5DN7/djyZIlmDhxoqbrMHBTTy979+6lNm3axH1ZxOYegiCQ3++nefPmUUNDAxER7dq1i0aMGEEej6fxeV27dqU//elPFAqFDP6TYHJ88MEH1K9fP3K5XI3f7+zsbFq9enXjc1avXk3BYPCy77caD4/HQ8FgkN5//30D/wRsQ1LGciDr6OLFi/TEE08oul5t7MPv99PNN99M+fn5Ta4XiURo+fLl1KNHj8v+kg0fPpy2b9+u81fPpDp69Cjl5uZeVo2+/vrr6Te/+Q1VVlY2eUxJSQmNGTOGfD4fCYKgOIh9Ph/de++9dOrUKZ2/etviQDarc+fO0fz586lly5YUDAYlh7PL5aLk5OTGfx44cGDju2IxpaWl9Nhjj1FaWlrj8ampqTR9+nQ6c+aMxl8xE1NVVUXz5s2jdu3aXfYf3PHjx9PBgwclv87MmTMbj09KSiKv1yvpZ8vr9VJycjL5/X6aMWMGHTlyRMOv1pE4kM2uoaGBvvvuO1qyZAmNGjWKunTpQoFAgFwuF3k8HnK73eTxeCg9PZ0GDhxIs2bNos8++4wqKiqoY8eOBIAeeeQR2evu3r2b7rrrrsv+svJIwxjNjSTWrFkj+7VWrlzZeBGgkpIS+vLLL2nevHk0bNgw6tChA3m9XnK73ZeF8I033khDhw6luXPn0q5du6i+vl6Dr5IRB7J11dbWUmVlJVVXV1MkEmnyOZWVldSyZUsCQHl5eXGtwyMNY8QzkhCzefNmEgSBPB5Ps7deamhooJqaGkpOTqaUlBTJv10xVXAg293Jkycbxx1/+9vfFL0WjzS0pdZIoimFhYXk8XhIEATauHGj6PNTUlIoJSVF0ZpMNg5kJ8jPzye3200ul4t27typymvySEM969atU20k0ZRz58413ix3xYoVko7hQDYEB7JTbNiwgQRBoISEBDp69Khqr8sjjfhoMZJoSk1NDbVu3ZoA0Jw5cyQfx4FsCA5kJ3n99dcbP1m/cOGC6q/PI41r03Ik0ZRIJELdu3cnADRp0iRZx3IgG4ID2WmefvrpxndjdXV1mq3DI43/aWok0bdvX9VGEs0ZPnw4AaAhQ4bIPpYD2RAcyE40YcIEAkBZWVnNnqGhFqeONJobScyZM4eqqqo0X3/q1KmN/xGM53vMgWwIDmSnuvXWWwkAjRo1Src17T7S0Hsk0ZwFCxYQAGrVqlXc4c+BbAgOZKcKhUKKiiNK2WmkYdRIoimxxQ8l/5HjQDYEB7KTqVEcUcqqIw2jRxJNkVL8kIoD2RAcyE6nZnFEKbOPNMwykmiK3OKHGA5kQ3AgM22KI0qZaaRhppFEU+IpfojhQDYEBzK7RKviiFJGjTTMOJJoSrzFDzEcyIbgQGb/o3VxRCmtRxpmHkk0RUnxQwwHsiE4kNnlnn32WV2KI0qpOdIw+0iiOUqKH2I4kA3BgcyupmdxRKl4RxpWGUk0R2nxQwwHsiE4kFnTjCiOKCU20qiqqqK5c+fSDTfcYImRRHPUKH6I4UA2BAcya1pscWTGjBlGb0e2pkYa0YdVRhJNefvtt1UpfojhQDaEpIx1gTmOx+NBYWEhWrZsiRUrViAvL8/oLcnSqlUrpKamwuv1XvX/uVwuJCcnIz093YCdxW/Lli2YNm0aPB4P9u3bZ7n9M5VITW7id8i2Y6biiBixkYTZiyfXonbxQwy/QzYEjyyYODMWR2JFz5KI3tpeykjCTMUTMVoUP8RwIBuCA5lJY7biiFpnSZj9WhqxxY+5c+fqti4HsiE4kJl0RhdHtD5LwmwjDS2LH2I4kA3BgczkMaI4Es9IQikzjDRycnI0K36I4UA2BAcyk0+P4sjhw4dpwoQJ5Pf7DS1uGDXS0Lr4IYYD2RAcyCw+AwYMIAB09913q/aaZi9u6DXS0KP4IYYD2RAcyCw+oVCIMjIyVCmOGDGSUEqrkYZexQ8xHMiG4EBm8Yu948iiRYtkHWuWkYRSao401Lzjh1IcyIbgQGbKyCmOmH0koZSSkYbexQ8xHMiG4EBmysUWR5p6V2jFkYRSckYaZ86caTyfWq/ihxgOZENwIDN1XFkcsctIQqnmRho5OTm0fft2w4ofYjiQDSEpYwUiknXpCzlPZvbxxz/+Ec888wwEQUD0Z8bv9+Pee+/FwoULkZmZafAOjXX+/HnMnz8fa9asQVlZGQA0/lmNHz8e69evN3iH/5OamgoAqKioMHgnjiJIehIHMruW9evXIy8vD998801jEHs8Hvz1r3/FpEmTDN6dOe3ZswejR4++LPC6du2KmTNn4oknnoDH4zFwdxzIBpEUyHz5TXaVI0eOIDc3F4FAALm5ucjPz0d6ejrmzJmDcePGIRwOIy8vDw0NDUZv1ZTeeOMNVFRUoGvXrli6dCl69OiB48eP48knn4Tf78fw4cOxY8cOo7fJzEjqbIN4hmxrcs6S0KI4YhfNFT+aOksjJSWFpk2bpvs5yTxDNgR/qMfExXOWhJrFETuRWvxo6iyNLl260KuvvqrLtTQ4kA3BgcyapsZZEkqKI3YUT/FD7CwNrXAgG4IDmf2PFsWN2OLIqlWrVN6xdahR/NBzpMGBbAgOZKZ9cUOsOGJ3WhQ/tB5pcCAbggPZqfQubnz88cemuuOIXrQufmg10uBANgQHspMYfS2JZcuWGXrHEb3F3vFj8uTJmq+n5kiDA9kQHMhOYKZrSRhxxxGjRO/4MXToUN3XVjrS4EA2BAeyXZn5WhJ63HHEaNE7fnTr1s3QrzHekQYHsiE4kO3E6JGEHHYujsybN8/wO340Rc5IgwPZEBzIdmCmkYRUdi2OmOWOH2L27t1LI0eObHakwYFsCA5kqzLzSEIquxVHzHTHD6kikQi98cYbV4003G43BYNBo7fnNBzIVmKlkYRUJSUltiiOxBY/Nm3aZPR24mKma2k4FAeyFVhxJCGH1YsjscWPt956y+jtqCIpKYk8Ho9h19JwKA5ks7LDSEIOqxZHzHrHD6WiM+TmRho5OTm0detWo7dpNxzIZmLHkYQcViuO6F380FNTH+rxSENzHMhmYPeRhBzR4kh6errpiyNGFj+0JnaWhdhZGiwuHMhGaWokccMNN9DcuXNtOZKQI1oc6dWrl2mLI1OmTDFF8UMrUk97i440evbsySMN5TiQ9XStkcThw4eN3p6pmLk4Ytbih5riOQ+5tLSUHn/8cR5pxI8DWQ88kpDPrMURqxQ/lFJaDOGRRlw4kLXCIwnlzFYcsWLxI15qNfV4pCELB7KamhtJTJgwgUcScTJLccQOxQ85tKhO80hDFAeyGpoaSfTr14/Wrl1r9NZswejiiB2LH2K0vpYFjzSaxIEcLx5J6CtaHPF6vbr+tlFVVWXL4ocYvS4uxCONy3Agy8EjCWPFFkdKS0s1Xy8SiVC3bt1sWfwQY8TV3nikwYEsCY8kzGP27Nm6FUfsXPwQY/TlNx060uBAbg6PJMwrNzdX8+KI3YsfYowO5CiHjTQ4kGPxSMI6tCyOOKH4IcYsgRzLASMNDmQiorVr1/JIwmJiiyPTp09X7XXfeustRxQ/xJgxkGPZdKTh3EDmkYT1qV0c2bRpk2OKH2LMHshRNhtpSMpYgYggg6Qnh8NhfP311ygsLMSxY8dw8OBBVFRUoKGhAV6vFx06dECvXr3QuXNnDB48GO3bt5ezhyZVV1cjLy8Pb7/9Nk6fPg0A8Pv9GD16NF566SX06NFD8RpMXz/88AO6deuG2tparFq1CpMnT47rdQoLC5GdnY1IJILPP/8cI0eOVHmn1pKamgoAqKioMHgn0p0/fx4LFizA6tWrUVZWBgBISUlBbm4uFi5ciPT0dMVrlJeX48svv8SxY8dw+PBhnDhxAjU1NRAEAcFgED179kT37t3Rs2dP3HbbbfD7/XJeXpD0LKnJTSLvkEOhEP3973+nESNGkN/vp+TkZAoEAo2jgisfHo+HkpOTyefzUbt27eiJJ56Ia5bLIwl7U1occWLxQ4xV3iE3R82RxtmzZ+mFF16gnj17UkJCAiUnJ1NCQkKTmQWAfD5f43P69+9PS5cupcrKSilL6TOyqKuro5dffpmuu+46SkpKavYLEXt4PB7y+/00ZMgQ2rt37zW/Mh5JOEu8xZHY4se8efM03KG1WD2Qo5SMNIqKiuiBBx4gn8/XWN+P5xEMBikQCNCsWbOorKzsWktqH8hff/01dezYsfEdiFoPv99P06dPvyxc+SwJZ5NbHHFy8UOMXQI5ltSzNCKRCC1ZsoT8fj95PB7VMisxMZFSUlLogw8+aG6L2gbyJ598onoQX/mrQe/evWnlypU8kmBEJK844uTihxg7BnKs5kYaS5YsoYkTJ1IwGNQstwKBQHMfQmsXyJ9++qmmYdzUg0cSjEhaccTpxQ8xdg/kqKZGGno8AoEAvfTSS1duR5tAvnDhAqWkpMjaYDgcpoKCAiosLKRvv/2WnnrqqWY/7Lvy4XK5aNKkSdp+55ilRIsjI0eOvOr/4+KHOKcEcqxly5bJHlGMGzeOiOiyu3JLffj9fvrmm29it6BNIE+bNo0SExNlba6ysrLxf7du3Zr+9a9/0QsvvCDriztw4IDG3zJmFc0VR7j4IY3TArmqqoqSk5Nlh+qaNWtox44dtGDBAtnHCoJAvXv3jt2G+oEcDoepRYsWsjcXG8gAqFOnTnT+/HnJx3u9Xvrtb3+rx/eOWcSVxREufkjntEDesGGD7EAOBoP0ww8/ULdu3ejQoUOyMw+49DlYUVFRdBuSMtYFGQoKCuQ8vVnFxcVwuVxo06aNpOeHQiGsX79elbWZPSQlJeG7776Dz+fDnDlzcM899wAAPv30U2RlZRm8O2YmGzZswMWLF2UdM27cOGzcuBHHjh1DWVkZsrOzZa/rcrmwadMmecfIeXJpaSlcLlmHNEsQpBVXoqLtHMai2rdvjw0bNgAAGhoaMHv2bMe38NjVos1dOR588EGsXr0aALB69Wo8+OCDsl+jtrYW58+fl3WMR86Tk5OTL805FOrUqRMikQj++9//Sj4mKSlJ8brMXqqrq/HQQw81/vOrr76Khx9+mGvy7DItW7aU9fy0tDTceeedyMrKAhHB7XaDiPDcc8/Jep2EhAS0aNFC1jGy3u72798f9fX1sha4UqtWrfDGG29g6dKlko9xuVwYPXq0onWZvTQ0NKBPnz4oLS3F5MmTsWzZMoRCIfTv31/2uxJmb2PGjJH1hi43NxfvvPMOMjIy0KlTJ3To0AHFxcUYMmSIrHXdbjfuuOMOeZuVOmz+/weNHTuW3G63rOH2lae9PfPMM5JPe8P/f2q+e/duHcb/zCqGDRtGwOXFDz3vOGJlTvtQr6ys7LLLLIg9tm7dSqNGjbrs382aNYuWL18uK/fat29PDQ0N0W1oc9pbcXGxrqUQr9dLY8eO1ec7xyzhWsUPPe44YnVOC2QiokWLFmna0GvqTeTGjRtjt6BdU2/58uW6hLLL5aJWrVrR2bNntf1uMcuIFj9at27dbPFj4MCBBDRdHGHODORQKER9+/aV3aGIN4ynTp165Ra0C2QioldffVXTUPZ4PNSmTZvY8/iYw0ktfmh1xxG7cGIgExFdvHiR+vfvr+jqblLCePLkyRQOh69cXttAJrp0LeIWLVpc8/qh8TyCwSANHjyYfvzxR/W/K8yS5BY/1L7jiJ04NZCJLrX2pk6dqvqbSZfLRX6/n1588cXmRmXaBzIR0blz5+ihhx5SfF1R4NK8uG3btrRy5crYYThzuP3795PH4yFBEGjTpk2SjyspKWn8mVy1apWGO7QWJwdy1NatW+mmm25S/GbS4/GQz+ej4cOH08GDB6+1pD6BHHXu3DmaP38+tWvXjnw+n6SL1bvdbkpOTiaPx9N45sbLL78c/58ysx2ld/xQescRO+JAvmT79u0kCAIJgkCJiYmSf9v3+/0UCAQoNTWVZsyYQUeOHJGynKSM1eSeeiUlJdiyZQsKCgpw4MABFBUVoaqqqvGeem3atEH37t3Rq1cv3H777RgyZAjOnDmDzMxM1NXVYd26dZgwYYKcfTEbqq6uRkZGBkpLSzFv3jy8+OKLcb3OP//5T4wdOxYejwf79+93fHHEivfUU9uxY8eQlZWFUCiEjz76CGPGjEF+fj62b9+O/fv34/Dhwzh9+jTq6+shCAISExPRsWNHZGZm4uabb8add96JzMxMOY1jfe+pp4bdu3eTy+Uil8slehsnZm9q3/FD7h1H7Mzp75AvXLjQ+Bv866+/rtey+o4s1LJ27VoCLt0S5fvvv9djSWZC0eLHsGHDVHtNLo5c4uRArquro+uvv54A0NNPP63n0tYMZCKiJUuWEHDpnljl5eV6LctMQss7fnBxxLmBHIlEKCsriwDQ+PHj9V7euoFMRPT4448TALrxxhtl39qbWZeU4odSTi+OODWQ7777bgJAt956qxHLWzuQiYjGjBlDAKhv3756L80MoNcdP5xeHHFiIM+YMYMAUMeOHY16g2f9QI5EInTLLbcQAL6ehc3pfceP2OLIwoULNV/PTJwWyIsWLSIA1LJlS6qsrDRqG9YPZKJLQ/h27doRcOmKS8x+4i1+KOXU4oiTAnnVqlUEXLqd0smTJ43cij0CmYiovLy88Z5Yr7zyilHbYBpQWvxQyonFEacE8vbt28nlcpHb7ab8/Hyjt2OfQCYiKioqarxS07p164zcClNJVVUVtW7dmgDQvHnzDNvHxx9/TIIgkNfrpcOHDxu2D704IZCPHj1KCQkJJAgCbdiwwejtENktkIm4OGInscWPKVOmGL2dxouPO6E4YvdANqj4IcZ+gUzExRG70KL4oZRTiiN2DuTY4sezzz5r9HZi2TOQibg4YnVaFj+UckJxxK6BHFv8mDBhgtHbuZJ9A5mIaObMmQRcum8VF0esQ4/ih1J2L47YNZANLn6IsXcgE/2vOJKdnW30VpgEehU/lAqFQtSpUyfbFkfsGMgmKH6IsX8gc3HEOmKLH4WFhUZvR1RlZSWlpaXZsjhit0A2SfFDjP0DmYiLI1ZgVPFDKbsWR+wUyCYqfohxRiATcXHEzIwufihlx+KIXQLZZMUPMc4JZCIujpiRWYofStmtOGKHQD58+DB5vV4zFT/EOCuQibg4YiZmK34oZafiiNUDubS01IzFDzHOC2Siy4sjRUVFRm/HscxY/FAqtjhSU1Nj9HbiZuVArquro/T0dDMWP8Q4M5CJuDhitMmTJ5u2+KFUtDhy0003WfZrs2ogRyIR6tWrl1mLH2KcG8hEXBwxihWKH0pZvThi1UCOFj8GDBhg9Fbi4exAJuLiiN6sUvxQyurFESsGcrT4kZGRYdU3WBzIkUiE+vTpw8URHVit+KGUlYsjVgtkixQ/xHAgE116N8PFEW1ZtfihVGxx5N133zV6O5JZKZAtVPwQw4EcxcUR7Vi9+KGUFYsjVglkixU/xHAgx+LiiPrsUvxQymrFESsEcmzx4+OPPzZ6O2rgQL7S3r17uTiiErsVP5SyUnHE7IEcW/xYtmyZ0dtRCwdyU7g4og47Fj+Ueu655yxRHDFzIFu4+CGGA7k5r7zyChdHFLBz8UMpKxRHzBrIFi9+iOFAvhYujsTHCcUPpcxeHDFrIFu8+CGGA1lMtDjSp08f076bMROnFD+Uii2OTJs2zejtXMWMgTx9+nSrFz/EcCCLiS2O3HfffUZvx9ScVvxQyszFEbMFsk2KH2I4kKUIhULUvn17Lo5cg1OLH0qZtThipkCOLX6UlJQYvR0tcSBLVV5eTikpKVwcaUJs8ePtt982ejuWY8biiFkC2WbFDzEcyHJwceRqXPxQh9mKI2YIZBsWP8RwIMvFxZH/4eKHusxUHDE6kG1a/BDDgRwPLo5cwsUP9ZmlOGJkINu4+CGGAzleTi+OcPFDO9HiSGZmpmF/tkYFcmzxIzc3V/f1DcaBrMSsWbMcWRyZO3cuFz80Fi2O3HXXXYasb1Qgjxw50s7FDzEcyErdd999jiqOcPFDH0YXR4wIZAcUP8RwICvlpOIIFz/0ZWRxRO9AdkjxQwwHshqcUByJLX5s3rzZ6O04RklJCfn9ft2LI3oGsoOKH2I4kNVi5+IIFz+MZURxRK9AdljxQwwHsprsWBzh4oc56F0c0SOQHVj8EMOBrLbY4sju3buN3o4iXPwwFz2LI1oHskOLH2I4kLWwbt06WxRHhg4dysUPk9GrOKJlIMcWP2bPnq3JGhbFgawVqxdHuPhhXhMnTtS8OKJVIDu8+CGGA1lLVi2OcPHD/AYNGqRpcUSrQHZ48UMMB7LWrFYc4eKHNUQiEU2LI1oEMhc/RHEgay0SiVB2drYliiNc/LAWLYsjagcyFz8k4UDWgxWKI1z8sCatiiNqBjIXPyTjQNZLbHFkyZIlRm/nMlz8sLZocUQQBNq6dasqr6lWIHPxQxYOZD3FFkfWrl1r9HaI6FLxo1WrVgSAFixYYPR2WJw++eQTVYsjagQyFz9k40DWm5mKI7HFj6lTpxq6F6acmsURpYHMxY+4cCAbwSzFkWjxIycnx7A9MHWpVRxREshc/IgbB7JRjC6ORIsf3bt3t8TpeEw6NYoj8QYyFz8U4UA2UrQ40q5dO13Py+Tih/0pLY7EG8jR4sfAgQPjWtfhOJCNpndxZMWKFVz8cAClxZF4ApmLH4pxIBtNz+LIxo0bufjhILHFkd/97neyjpUbyAsXLuTih3IcyGYQWxyZOXOmJmtw8cOZ4i2OyAlkLn6ohgPZLLQsjnDxw9kKCgpkF0ekBjIXP1TFgWwmWhRHuPjBiOQXR6QEMhc/VMeBbDZqFke4+MFiySmOiAVybPFj+fLlam/VqSRlrEBEkEFj1yfXAAAGsElEQVTWk9nV1q9fj9zcXCQmJuLQoUNo06YNtm/fjl27duHAgQM4fvw4SktLEQ6H4XK5EAwGkZGRgczMTPTv3x933XUXMjIyMGzYMOzcuRM5OTnYtm2b0V8WM4Hnn38eixcvRnp6OoqLi/Hzzz9jy5Yt2LdvHw4cOIATJ07gp59+wvnz5wEAXbp0QefOnZGVlYWBAwdixIgRSEpKQqdOnXD27FnMnj0bixcvNvirsg1B0pM4kPW3ZMkSzJ49G263G4IgIBAIoLKyEmLfi2AwiIaGBhARamtr0aVLFxw9ehQul0unnTOzGz9+PD788EN4vV4QEfx+PyorK0WPa9GiBWpqaiAIAkKhEMaNG4cPP/xQhx07hqRA5r/JOmpoaMCbb76J3//+9/B6vYhEIgiHw7h48aJoGANAVVUVampqUFtbCwAoKSnBlClTcO7cOa23zkyupqYGc+bMwaZNm+ByuRAKhRAOhyWFMQBUVlYiHA4jFArB5XJh06ZN+PWvf43q6mqNd85i8TtknZw6dQr3338/jhw5gqqqKtVeNyEhAQkJCfjzn/+MBx54QLXXZdbx1VdfYdy4cSgvL0dNTY1qr+v3+5GamooPP/wQAwcOVO11HYpHFmZx9OhR3HbbbaioqEAkEtFkjUAggJdeeglPPvmkJq/PzGnz5s345S9/qek72UAggI8++ggjR47UbA0H4EA2gx9//BE333wzysvLJY0llAgEAnjllVfw6KOParoOM4fdu3dj5MiRuowVAoEAPv/8cwwZMkTztWyKA9loRIRRo0Zh69atCIfDko4Jh8PYv39/4z+vXr0af/jDHySvGQgEcPDgQXTs2FH2fpl11NbWomvXrvjxxx8lH3Plz9a4ceNw8uRJycffcMMNOH78OPx+v6y9MgASA9mj9S6cbPv27di9e7fkMAYufTiTnZ0d95r19fV46qmn8MEHH8T9Gsz8li9fjvLyclnHKP3ZKi8vx7Jly/Dss8/G/Rrs2vgsCw299957qn7IIkU4HMbGjRtRX1+v67pMXytXrtT9DIiamhqsXLlS1zWdhgNZQ59//jkaGhpkHeP3+1FQUND4iOfMCa/Xi4KCAtnHMWuoq6vDwYMHZR8X+7MV729QR44c0f1NhpPwyEJD8byDUfprJQAIgoCff/5Z0Wsw86qurobb7ZZ9xo4aP1tutxvV1dU8R9YIv0PWUFpamiHrRiIRtGrVypC1mfaSkpI0P2OnOQ0NDWjRooUhazsBB7KGxo8fD49H/19C3G43evfurfu6TB9erxeDBg0yZO0BAwYgISHBkLWdgANZQw899BC8Xq+sY66cIefl5ck63ufzYcqUKXx9C5t79NFHEQwGdV0zGAzyOe4a4/OQNfbYY49h5cqVjdef0FpaWhqKi4uRnJysy3rMGESEgQMHIj8/X/YHx/FwuVzIzs7Gv//9b/6PfXy4GGIGP//8MwYMGIATJ05ofipaIBDAP/7xD4wYMULTdZg5FBUV4dZbb0VFRYWmoSwIAlJTU/HVV1+hS5cumq1jc3y1NzNISkrCnj170LNnT80+mRYEAcFgkMPYYTp37ox9+/bhuuuukz0ak8rr9SItLQ379u3jMNYBB7IOUlJSsGfPHkyZMkX1UA4Gg+jSpQv27NnDYexAXbt2xf79+zF06FDVZ8rBYBC33347CgsL0a1bN1VfmzWNA1kngUAAb775JrZt24acnBz4fD5F72patGiBtm3bIi8vD4cOHeKzKhysbdu22Lx5M9577z1kZmYiGAxCECT9hnyV6G9bPXv2xLvvvosvvvgC6enpKu+YNYdnyAY5duwYli1bho8++ghnz55FYmIiamtrm5wzR/+SAJc+zMnJycGjjz6K0aNHw+126711ZnL79u3D0qVLsXHjxsYSSU1NTZPXVHG73QgEAohEIvD7/bjnnnswc+ZMw06rszH+UM8qzpw5g71796KoqAiHDh3CqVOnUF9fD7fbjZYtW+Kmm25Cly5d0Lt3b/Tp04c/5WaSEBGOHz+O/Px8FBUV4eDBgzh79ixCoRC8Xi/atm2LXr16oXPnzujXrx+6du0a9ztrJooDmTHGTILPsmCMMSvhQGaMMZPgQGaMMZPgQGaMMZPgQGaMMZPgQGaMMZPgQGaMMZPgQGaMMZPgQGaMMZPgQGaMMZPgQGaMMZPgQGaMMZOQe0tkvhQUY4xphN8hM8aYSXAgM8aYSXAgM8aYSXAgM8aYSXAgM8aYSXAgM8aYSXAgM8aYSXAgM8aYSXAgM8aYSXAgM8aYSfwfygEso+heMccAAAAASUVORK5CYII=\n"},"metadata":{},"output_type":"display_data"}]},{"metadata":{},"cell_type":"markdown","source":"__1. d. Les fonctions Python mat_adjacence, distance et diametre données ci-dessous permettent d'obtenir respectivement la matrice d'adjacence associée à un graphe, la distance entre deux de ses sommets et le diamètre de ce graphe. Effectuer les appels à ces fonctions et vérifier qu'on retrouve les réponses à la question 1.a.__ "},{"metadata":{"trusted":false},"cell_type":"code","source":"#Pour utiliser l'ordre alphabétique\nAlphabet='ABCDEFGHIJKLMNOPQRSTUVWXYZ'\n\ndef mat_adjacence(Graphe):\n \"\"\"\n Fonction qui renvoie la matrice d'adjacence d'un graphe (ordre alphabétique) avec liste ordonnée des noms de sommets\n \"\"\"\n #génération de la liste des sommets dans l'ordre alphabétique\n Liste_sommets = [lettre for lettre in Alphabet if lettre in Graphe]\n \n return np.matrix([ [ 1 if sommet_colonne in Graphe[sommet_ligne] else 0 for sommet_colonne in Liste_sommets ] for sommet_ligne in Liste_sommets ]),Liste_sommets\n \ndef distance(Graphe,debut,fin):\n \"\"\"\n Fonction qui renvoie la distance entre deux sommets\n (renvoie infini par défaut si aucune chaîne n'existe)\n \"\"\"\n ADJ=mat_adjacence(Graphe)\n M=ADJ[0]\n try: rang_deb=ADJ[1].index(debut) ; rang_fin=ADJ[1].index(fin)\n except: return float('inf')\n \n for k in range(len(Graphe)):\n if (M**k)[rang_deb,rang_fin]>0: return k\n \n return float('inf')\n \ndef diametre(Graphe):\n \"\"\"\n Fonction qui renvoie le diamètre d'un graphe\n \"\"\"\n return max(distance(Graphe,s1,s2) for s2 in Graphe for s1 in Graphe)\n","execution_count":4,"outputs":[]},{"metadata":{"trusted":false},"cell_type":"code","source":"#Appel pour obtenir la matrice d'adjacence associée à G1\nmat_adjacence(G1)","execution_count":5,"outputs":[{"data":{},"execution_count":5,"metadata":{},"output_type":"execute_result"}]},{"metadata":{"trusted":false},"cell_type":"code","source":"#Appel pour obtenir la distance entre C et E\ndistance(G1,'C','E')","execution_count":6,"outputs":[{"data":{},"execution_count":6,"metadata":{},"output_type":"execute_result"}]},{"metadata":{"trusted":false},"cell_type":"code","source":"#Appel pour obtenir le diamètre du graphe G1\ndiametre(G1)","execution_count":7,"outputs":[{"data":{},"execution_count":7,"metadata":{},"output_type":"execute_result"}]},{"metadata":{},"cell_type":"markdown","source":"__1. e. Le tableau ci-dessous recense des liens d'amitié existant dans un réseau social.__ \n\n![Reseau_social_amities_2](https://raw.githubusercontent.com/PythonLycee/PyLyc/master/SNT/img/ReseauSocial_2.png)\n\n\n- Réaliser le graphe correspondant à cette nouvelle situation.
\n
\n\n Voir le résultat de la saisie Python."},{"metadata":{},"cell_type":"markdown","source":"\n- Créer une structure Python G2 correspondant à ce graphe, puis effectuer l'appel à la fonction Python repr_graphe permettant de construire le graphe. Vérifier la cohérence avec la réponse précédente.
\n
"},{"metadata":{"trusted":false},"cell_type":"code","source":"#Créer la structure G2 (structure similaire à G1)\nG2 = { 'A':['E','G'] , \n 'B':['C','F'] , \n 'C':['B','D','E','G'] , \n 'D':['C','G'] , \n 'E':['A','C','F'] , \n 'F':['B','E'] ,\n 'G':['A','C','D'] \n }","execution_count":8,"outputs":[]},{"metadata":{"trusted":false},"cell_type":"code","source":"#Effectuer l'appel à la fonction repr_graphe\nrepr_graphe(G2)","execution_count":9,"outputs":[{"data":{"image/png":"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\n"},"metadata":{},"output_type":"display_data"}]},{"metadata":{},"cell_type":"markdown","source":"\n- Déterminer, à la main, la matrice d'adjacence associée à ce graphe et son diamètre, puis vérifier vos résultats à l'aide d'appels aux fonctions Python mat_adjacence et diametre.
\n
\n\n Voir les résultats des saisies Python."},{"metadata":{"trusted":false},"cell_type":"code","source":"#Effectuer l'appel à la fonction mat_adjacence \nmat_adjacence(G2)","execution_count":10,"outputs":[{"data":{},"execution_count":10,"metadata":{},"output_type":"execute_result"}]},{"metadata":{"trusted":false},"cell_type":"code","source":"#Effectuer l'appel à la fonction diametre\ndiametre(G2)","execution_count":11,"outputs":[{"data":{},"execution_count":11,"metadata":{},"output_type":"execute_result"}]},{"metadata":{},"cell_type":"markdown","source":"## 2. Relation de connaissance non réflexive : Graphe orienté"},{"metadata":{},"cell_type":"markdown","source":"__2. a. Certaines relations d'un réseau social ne sont pas réflexives (pas réciproques), c'est le cas par exemple du \"Follow\" sur Twitter. Le tableau ci-dessous recense des connaissances au sein d'un réseau social. Réaliser le graphe correspondant à cette situation (les arêtes seront orientées, représentées par des flèches), ainsi que la matrice d'adjacence associée.__\n\n Pour les réponses à cette question, voir les résultats des saisies Python.\n\n![Reseau_social_connaissance](https://raw.githubusercontent.com/PythonLycee/PyLyc/master/SNT/img/ReseauSocial_3.png)"},{"metadata":{},"cell_type":"markdown","source":"__2. b. Créer une structure Python G3 correspondant à ce graphe. Effectuer ensuite l'appel à la fonction Python repr_graphe permettant de construire le graphe, puis un appel à la fonction mat_adjacence. Pour finir, vérifier la cohérence avec la réponse à la question 2.a.__"},{"metadata":{"trusted":false},"cell_type":"code","source":"#Créer la structure G3 (structure similaire à G1 et G2)\nG3 = { 'A':['B','E','F'] , \n 'B':['D'] , \n 'C':['A','G'] , \n 'D':['B','C'] , \n 'E':['D'] , \n 'F':['B','E'] ,\n 'G':['C','D'] \n }","execution_count":12,"outputs":[]},{"metadata":{"trusted":false},"cell_type":"code","source":"#Effectuer l'appel à la fonction repr_graphe\nrepr_graphe(G3)","execution_count":13,"outputs":[{"data":{"image/png":"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\n"},"metadata":{},"output_type":"display_data"}]},{"metadata":{"trusted":false},"cell_type":"code","source":"#Effectuer l'appel à la fonction mat_adjacence\nmat_adjacence(G3)","execution_count":14,"outputs":[{"data":{},"execution_count":14,"metadata":{},"output_type":"execute_result"}]},{"metadata":{},"cell_type":"markdown","source":"__2. c. Quelle est la propriété d'une matrice d'adjacence d'un graphe non orienté (partie 1) qu'on ne retrouve pas dans le cas d'un graphe orienté (partie 2) ?__\n\n La matrice d'adjacence d'un graphe non orienté a une propriété de symétrie par rapport à sa diagonale principale, alors que ce n'est pas le cas pour la matrice d'adjacence associée à un graphe orienté."},{"metadata":{},"cell_type":"markdown","source":"## 3. Expérience du petit monde de Milgram"},{"metadata":{},"cell_type":"markdown","source":"__3. a. La fonction et l'appel Python suivants permettent de générer une structure G4 correspondant à une situation aléatoire de 20 utilisateurs possédant chacun 5 connaissances vers d'autres utilisateurs (liens non nécessairement réciproques). A l'aide de la fonction Python repr_graphe, obtenir la représentation de ce graphe.__"},{"metadata":{"trusted":false},"cell_type":"code","source":"#Pour le choix au hasard des amis\nfrom random import sample\n\n#Pour utiliser l'ordre alphabétique\nAlphabet='ABCDEFGHIJKLMNOPQRSTUVWXYZ'\n\ndef genere_graphe(n_sommets,n_liens):\n Sommets=Alphabet[:n_sommets]\n return { S:sample( [A for A in Sommets if A!=S] , n_liens ) for S in Sommets } \n \nG4=genere_graphe(20,5)\nG4 ","execution_count":15,"outputs":[{"data":{},"execution_count":15,"metadata":{},"output_type":"execute_result"}]},{"metadata":{"trusted":false},"cell_type":"code","source":"# Effectuer l'appel à la fonction repr_graphe\nrepr_graphe(G4)","execution_count":16,"outputs":[{"data":{"image/png":"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\n"},"metadata":{},"output_type":"display_data"}]},{"metadata":{},"cell_type":"markdown","source":"__3. b. Effectuer un appel à la fonction Python diametre pour ce graphe. Si on choisit deux utilisateurs au hasard, combien d'intermédiaires seront nécessaires pour former une chaîne de connaissances qui les relie?__"},{"metadata":{"trusted":false},"cell_type":"code","source":"#Effectuer l'appel à la fonction diametre\ndiametre(G4)","execution_count":17,"outputs":[{"data":{},"execution_count":17,"metadata":{},"output_type":"execute_result"}]},{"metadata":{},"cell_type":"markdown","source":"__3. c. Relancer les zones Python des questions 3.a et 3.b pour simuler d'autres situations de 20 utilisateurs ayant 5 liens de connaissances, et comparer les résultats obtenus à la question 3.b.__\n\n En dehors de quelques cas où le diamètre est infini (certains utilisateurs ne sont pas reliés), on peut constater qu'il ne suffit souvent que de 2 à 3 utilisateurs intermédiaires pour obtenir une chaîne de connaissance (diamètre 3 ou 4).\n\n\n\n__Synthèse:__\n\n\nL'expérience du petit monde de Milgram est une hypothèse selon laquelle même si des personnes sont très nombreuses et ont un nombre assez limité de connaissances, le nombre de liens nécessaires pour former une chaîne entre deux personnes quelconques sera faible.\n\n\n![Stanley_Milgram](https://raw.githubusercontent.com/PythonLycee/PyLyc/master/SNT/img/Milgram.png)\n\nStanley Milgram, psychologue social américain\n"},{"metadata":{},"cell_type":"markdown","source":"© Copyright Franck CHEVRIER 2019-2021 https://www.python-lycee.com.
\nLes activités partagées sur Capytale sont sous licence Creative Commons."}],"metadata":{"celltoolbar":"Raw Cell Format","kernelspec":{"display_name":"Python 3","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":"3.7.10"}},"nbformat":4,"nbformat_minor":2}