When is an n layered network stable? (pseudo-mathematical definition)

  • An n layer network is a strictly ordered set of digraphs G1,G2,…,Gn such that
    • Vn is a subset of Vn-1 is a subset of … V1; where Vi is a set of vertices of Gi
    • For m > 1, a path Pm(i,j) on vertices i, j in Vm exists only if Pm-1(i,j) on Vm-1 exists
  • An n layer network is stable if and only if
    • for all i,j in Vn, all paths Pn(i,j) are stable
  • A path Pm(i,j) is stable if and only if for all q<=m, all Pq(i,j) are stable
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