Utilisateur:Leavigouroux/Modélisation des Réseaux (M1, 2018)/Activité E
Graphe p25
a | b | c | d | e | f | g | h | |
---|---|---|---|---|---|---|---|---|
a | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |
b | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 |
c | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
d | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 |
e | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
f | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
g | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
h | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
a | b | c | d | e | f | g | h | |
---|---|---|---|---|---|---|---|---|
a | 0 | 1/8 | 1/8 | 1/8 | 0 | 0 | 0 | 0 |
b | 0 | 0 | 1/8 | 0 | 1/8 | 0 | 0 | 0 |
c | 0 | 0 | 0 | 0 | 0 | 0 | 1/8 | 1/8 |
d | 0 | 0 | 1/8 | 0 | 0 | 1/8 | 0 | 0 |
e | 1/8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
f | 1/8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
g | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1/8 |
h | 0 | 0 | 0 | 0 | 0 | 0 | 1/8 | 0 |
Matrice MT:
a | b | c | d | e | f | g | h | |
---|---|---|---|---|---|---|---|---|
a | 0 | 0 | 0 | 0 | 1/8 | 1/8 | 0 | 0 |
b | 1/8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
c | 1/8 | 1/8 | 0 | 1/8 | 0 | 0 | 0 | 0 |
d | 1/8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
e | 0 | 1/8 | 0 | 0 | 0 | 0 | 0 | 0 |
f | 0 | 0 | 0 | 1/8 | 0 | 0 | 0 | 0 |
g | 0 | 0 | 1/8 | 0 | 0 | 0 | 0 | 1/8 |
h | 0 | 0 | 1/8 | 0 | 0 | 0 | 1/8 | 0 |
p(a) | 1/8 |
---|---|
p(b) | 1/8 |
p(c) | 1/8 |
p(d) | 1/8 |
p(e) | 1/8 |
p(f) | 1/8 |
p(g) | 1/8 |
p(h) | 1/8 |
On résout le système maintenant:
MT x P= P
Pe/8 +Pf/8 = Pa <=> 1/8*1/8 +1/8*1/8= 1/32 <=> Pa= 1/32
Pa/8= Pb <=> Pb=1/64
Pa/8 + Pb/8 + Pd/8= Pc <=> Pc= 1/256
Pa/8= Pd <=> Pd= 1/64
Pb/8= Pe <=> Pe= 1/64
Pd/8= Pf <=> Pf= 1/64
Pc/8 +Ph/8 = Pg <=> Pg= 1/32
Pc/8 +Pg/8 = Ph <=> Ph= 1/32
Les composantes A, G et H sont fortement connexes.
Graphe p 18
On doit calculer la proximité qui est égale à l'inverse de la somme des distances entre le noeud et chacun des autres.
1) proximité sortante:
P1P1= 1
P1P2=2
P1P3=1
P1P4=1
donc Cpout(1)= 1/5
Cpout(2)= 1/4
Cpout(3)= 1/4
Cpout(4)= 1/6
Proximité entrante
P1P1=1
P2P1=1
P3P1=2
P4P1=2
Cpin(1)= 1/6
Cpin(2)= 1/4
Cpin(3)= 1/6
Cpin(4)=1/3
Intermédiarité
g(1)= 1+ 1= 2
g(2)= 1+ 1+ 1= 3
g(3)= 0
g(4)= 1
Tableaux:
noeuds | nb de liens entrants | proximité c(p) | intermédiarité g(p) |
---|---|---|---|
1 | 2 | 1/6 | 1/3 |
2 | 2 | 1/4 | 1/2 |
3 | 1 | 1/6 | 1/6 |
4 | 3 | 1/3 | 1 |
noeuds | nb de liens sortants | proximité c(p) | intermédiarité g(p) |
---|---|---|---|
1 | 3 | 1/5 | 3/5 |
2 | 2 | 1/4 | 1/2 |
3 | 2 | 1/4 | 1/2 |
4 | 1 | 1/6 | 1/6 |