Sufficient conditions for weighted subdirect sums of Dashnic-Zusmanovich type matrices

The weighted subdirect sum of matrices plays an important role in the description of overlapping groups in complex networks, as well as in the convergence analysis of linear system iterative methods. In this paper, we utilize the classification idea and the inequality scaling technique to give some simple sufficient conditions for the weighted subdirect sum of Dashnic-Zusmanovich type matrices to still be Dashnic-Zusmanovich type matrices. Numerical examples demonstrate the authenticity and validity of the obtained results.