  We propose a general method for the construction and analysis of unweighted
$\epsilon$ - recurrence networks from chaotic time series. The selection of the
critical threshold $\epsilon_c$ in our scheme is done empirically and we show
that its value is closely linked to the embedding dimension $M$. In fact, we
are able to identify a small critical range $\Delta \epsilon$ numerically that
is approximately the same for the random and several standard chaotic time
series for a fixed $M$. This provides us a uniform framework for the non
subjective comparison of the statistical measures of the recurrence networks
constructed from various chaotic attractors. We explicitly show that the degree
distribution of the recurrence network constructed by our scheme is
characteristic to the structure of the attractor and display statistical scale
invariance with respect to increase in the number of nodes $N$. We also present
two practical applications of the scheme, detection of transition between two
dynamical regimes in a time delayed system and identification of the
dimensionality of the underlying system from real world data with limited
number of points, through recurrence network measures. The merits, limitations
and the potential applications of the proposed method have also been
highlighted.

Chaotic Dynamics