  We propose an entropy measure for the analysis of chaotic attractors through
recurrence networks which are un-weighted and un-directed complex networks
constructed from time series of dynamical systems using specific criteria. We
show that the proposed measure converges to a constant value with increase in
the number of data points on the attractor (or the number of nodes on the
network) and the embedding dimension used for the construction of the network,
and clearly distinguishes between the recurrence network from chaotic time
series and white noise. Since the measure is characteristic to the network
topology, it can be used to quantify the information loss associated with the
structural change of a chaotic attractor in terms of the difference in the link
density of the corresponding recurrence networks. We also indicate some
practical applications of the proposed measure in the recurrence analysis of
chaotic attractors as well as the relevance of the proposed measure in the
context of the general theory of complex networks.
