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[ t ]ij ∈ N mi×mj t
i j Xij(t) i
[ t ]ij
i, j ∈ {1, . . . , n} t ∈ N
Xij(t) = [ t ]ij,
t = 0 0 = I i, j ∈ {1, . . . , n} [ 0 ]ii = I
[ 0 ]ij = 0 Xij
t > 0
[ t ]ij =
n
ik[t−1 ]kj =
k=1
k∈{Ni∪i}
ik[ t−1 ]kj,
ik = 0 k /∈ {Ni ∪ i} i, j ∈ {1, . . . , n}
t > 0, Xij(t − 1) = [t−1 ]ij
Xij(t) =
ikXkj(t − 1) =
ik[t−1 ]kj = [t ]ij.
k∈{Ni∪i}
k∈{Ni∪i}
Xij(t) = [ t ]ij t > 0.
Xij(t)
t i j.
.
Gdis
[Xij(t)]r,s > 0
f i r f j s
df
df msum
¯
∼ ¯ , r s
[]r,s > 0 ⇔ [ ¯ ]r,s > 0 []r,s = 0 ⇔ [ ¯ ]r,s = 0.
Xij(t)