Network analysis with the aid of the path length matrix

Abstract Let a network be represented by simple graph $$\mathcal {G}$$ G with n vertices. A common approach to investigate properties of is use the adjacency matrix $$A=[a_{ij}]_{i,j=1}^n\in \mathbb {R}^{n\times n}$$ A = [ a ij ] i , j 1 n ∈ R × associated , where $$a_{ij}>0$$ > 0 if there an edge pointing from vertex $$v_i$$ v $$v_j$$ and $$a_{ij}=0$$ otherwise. Both its positive integer powers reveal important graph. This paper proposes study also using path length for The $$(ij)^{th}$$ ( ) th entry shortest ; no between these vertices, then value $$\infty $$ ∞ . Powers are formed min-plus multiplication exhibiting We show how several known measures communication such as closeness centrality, harmonic eccentricity related matrix, we introduce new communication, K -centrality global -efficiency, only (short) paths made up at most edges taken into account. sensitivity -efficiency changes entries considered.