  We propose a new measure of vulnerability of a node in a complex network. The
measure is based on the analogy in which the nodes of the network are
represented by balls and the links are identified with springs. We define the
measure as the node displacement, or the amplitude of vibration of each node,
under fluctuation due to the thermal bath in which the network is supposed to
be submerged. We prove exact relations among the thus defined node
displacement, the information centrality and the Kirchhoff index. The relation
between the first two suggests that the node displacement has a better
resolution of the vulnerability than the information centrality, because the
latter is the sum of the local node displacement and the node displacement
averaged over the entire network.
