  In this article we present Miuz, a robustness index for complex networks.
Miuz measures the impact of disconnecting a node from the network while
comparing the sizes of the remaining connected components. Strictly speaking,
Miuz for a node is defined as the inverse of the size of the largest connected
component divided by the sum of the sizes of the remaining ones. We tested our
index in attack strategies where the nodes are disconnected in decreasing order
of a specified metric. We considered Miuz and other well-known centrality
measures such as betweenness, degree , and harmonic centrality. All of these
metrics were compared regarding the behavior of the robust-ness (R-index)
during the attacks. In an attempt to simulate the internet backbone, the
attacks were performed in complex networks with power-law degree distributions
(scale-free networks). Preliminary results show that attacks based on
disconnecting a few number of nodes Miuz are more dangerous (decreasing the
robustness) than the same attacks based on other centrality measures. We
believe that Miuz, as well as other measures based on the size of the largest
connected component, provides a good addition to other robustness metrics for
complex networks.
