Network centrality and multiscale transition asymmetry in the heart rate variability analysis of normal and preeclamptic pregnancies E. Tejera a, * , A.I. Rodrigues c , M.J. Areias c , I. Rebelo a , J.M. Nieto-Villar b a Biochemical Department, Pharmacy Faculty Porto University, Portugal/Institute for Molecular and Cell Biology (IBMC), Porto, Portugal b Chemical-Physics Department, Havana University, Cuba c Maternal Hospital ‘‘Julio Dinis”, Porto, Portugal article info Article history: Received 29 March 2010 Received in revised form 5 July 2010 Accepted 6 July 2010 Available online 11 July 2010 Keywords: HRV Complexity Asymmetry Network Pregnancy Preeclampsia abstract In the present work we define and apply a new methodology for the analysis of time series that involves a network representation. In this methodology, time series are transformed into a network with the subsequent calculation of some centrality indexes as well as the asymmetry of the transition frequency matrix, across different scales. The properties of the proposed indexes were analyzed with short-length simulated and physiological time series. In this case, we use RR time intervals, obtained from electrocardiographic records. The proposed indexes are compared with common complexity indexes in the analysis of the RR time series in normal and preeclamptic pregnancies. Ó 2010 Elsevier B.V. All rights reserved. 1. Introduction The complexity of the time series (TS) generated by physiological systems could be presented under two approaches: the presence/absence of self-organized structures and the roughness or unpredictability of the TS. For random TS, the complexity based on entropy measure (like approximated entropy [1], Shannon entropy or even Higushi fractal dimension [2]) is max- imal, which means that irregularities as well as unpredictability are also maximal. However, in this kind of TS there are not organized or fractal structures and therefore, in this sense, the complexity is minimal [3]. For example, the complexity values of the RR intervals of healthy subjects and patients with previous myocardium infarct, calculated using the approximated entropy (ApEn) or the sample entropy index, are smaller than the values obtained from subjects with atrial fibrillation. How- ever, in the last case the autonomic control is reduced and almost no correlation or fractal structure is detected [3]. In the last decade, novel and innovated procedures have been developed for the TS analysis based on the TS-network translation with the subsequent network description [4–10]. The objective with the conversion of TS to network is to bring the possibility of apply the tools and mathematical knowledge of the graphs and networks theory to understand the corre- lation structure and dynamical properties of the TS. The major problem in this TS-network translation is, specifically, the methodology inherent to the transformation procedure. This means, the appropriated definitions of the nodes and edges in the generated network. The common approaches to networks construction consider as starting points: (1) the autocorre- lation matrix of the TS [4–7], (2) the relative magnitude between the TS points [8,9], (3) the distance between the phase space points [9] and (4) the similarity between non-overlapping segments of specific length in the TS or general number 1007-5704/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.cnsns.2010.07.009 * Corresponding author. E-mail addresses: edutp00@yahoo.com (E. Tejera), irebelo@ff.up.pt (I. Rebelo). Commun Nonlinear Sci Numer Simulat 16 (2011) 1589–1596 Contents lists available at ScienceDirect Commun Nonlinear Sci Numer Simulat journal homepage: www.elsevier.com/locate/cnsns