Recurrence Network Analysis of the Synchronous EEG Time Series in Normal and Epileptic Brains

We sought to analyze the dynamic properties of brain electrical activity from healthy volunteers and epilepsy patients using recurrence networks. Phase-space trajectories of synchronous electroencephalogram signals were obtained through embedding dimension in phase-space reconstruction based on the distance set of space points. The recurrence matrix calculated from phase-space trajectories was identified with the adjacency matrix of a complex network. Then, we applied measures to characterize the complex network to this recurrence network. A detailed analysis revealed the following: (1) The recurrence networks of normal brains exhibited a sparser connectivity and smaller clustering coefficient compared with that of epileptic brains; (2) the small-world property existed in both normal and epileptic brains consistent with the previous empirical studies of structural and functional brain networks; and (3) the assortative property of the recurrence network was found by computing the assortative coefficients; their values increased from normal to epileptic brain which accurately suggested the difference of the states. These universal and non-universal characteristics of recurrence networks might help clearly understand the underlying neurodynamics of the brain and provide an efficient tool for clinical diagnosis.