TY - JOUR
T1 - Kirchhoffian indices for weighted digraphs
AU - Bianchi, Monica
AU - Palacios, José Luis
AU - Torriero, Anna
AU - Wirkierman, Ariel Luis
PY - 2019
Y1 - 2019
N2 - The resistance indices, namely the Kirchhoff index and its generalisations, have undergone intense critical scrutiny in recent years. Based on random walks, we derive three Kirchhoffian indices for strongly connected and weighted digraphs. These indices are expressed in terms of (i) hitting times and (ii) the trace and eigenvalues of suitable matrices associated to the graph, namely the asymmetric Laplacian, the diagonally scaled Laplacian and their Moore–Penrose inverses. The appropriateness of the generalised Kirchhoff index as a measure of network robustness is discussed, providing an alternative interpretation which is supported by an empirical application to the World Trade Network.
AB - The resistance indices, namely the Kirchhoff index and its generalisations, have undergone intense critical scrutiny in recent years. Based on random walks, we derive three Kirchhoffian indices for strongly connected and weighted digraphs. These indices are expressed in terms of (i) hitting times and (ii) the trace and eigenvalues of suitable matrices associated to the graph, namely the asymmetric Laplacian, the diagonally scaled Laplacian and their Moore–Penrose inverses. The appropriateness of the generalised Kirchhoff index as a measure of network robustness is discussed, providing an alternative interpretation which is supported by an empirical application to the World Trade Network.
KW - Applied Mathematics
KW - Discrete Mathematics and Combinatorics
KW - Kirchhoff index
KW - Moore–Penrose inverse
KW - Random walk on graphs
KW - Weighted digraphs
KW - Applied Mathematics
KW - Discrete Mathematics and Combinatorics
KW - Kirchhoff index
KW - Moore–Penrose inverse
KW - Random walk on graphs
KW - Weighted digraphs
UR - http://hdl.handle.net/10807/130153
U2 - 10.1016/j.dam.2018.08.024
DO - 10.1016/j.dam.2018.08.024
M3 - Article
SN - 0166-218X
VL - 255
SP - 142
EP - 154
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
ER -