Publications

References to peer-reviewed publications, theses and reports describing in detail and applying the methods implemented in the pyunicorn package.

General complex networks

Review papers

[Newman2003], [Boccaletti2006], [Costa2007].

Newman2003

M.E.J. Newman. “The structure and function of complex networks”. In SIAM Review, vol. 45 (no. 2), p167-256 (2003) doi:10.1137/S003614450342480

Boccaletti2006

S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.U. Hwang. “Complex networks: structure and dynamics”. In Physics Reports, vol. 424 (no. 4-5), p175-308 (2006) doi:10.1016/j.physrep.2005.10.009

Costa2007

L.D.F. Costa, F.A. Rodrigues, G. Travieso, P.R. Villas Boas. “Characterization of complex networks: A survey of measurements”. In Advances in Physics, vol. 56(1), 167-242 (2007) doi:10.1080/00018730601170527

Further network papers

[Watts1998], [Newman2001], [Newman2002], [Arenas2003], [Newman2005], [Soffer2005], [Holme2007], [Tsonis2008a], [Ueoka2008].

Watts1998

D.J. Watts and S.H. Strogatz. “Collective dynamics of small-world networks”. In Nature vol. 393, 440–442 (1998) doi:10.1038/30918

Newman2001

M.E.J. Newman. “Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality”. In Physical Review E vol. 64.1, 016132 (2001) doi:10.1103/PhysRevE.64.016132

Newman2002

M.E.J. Newman. “Assortative mixing in networks”. In Physical Review Letters, vol. 89.20, 208701 (2002) doi:10.1103/PhysRevLett.112.068103

Arenas2003

A. Arenas, A. Cabrales, A. Díaz-Guilera, R. Guimerà, F. Vega-Redondo. “Search and Congestion in Complex Networks”. In “Statistical Mechanics of Complex Networks”, In Lecture Notes in Physics, vol. 625, p175-194 (2003) doi:10.1007/978-3-540-44943-0_11

Newman2005

M.E.J. Newman. “A measure of betweenness centrality based on random walks”. In Social Networks, vol 27 (no. 1), p39–54 (2005) doi:10.1016/j.socnet.2004.11.009

Soffer2005

S.N. Soffer and A. Vázquez “Network clustering coefficient without degree-correlation biases”. In Physical Review E, vol. 71, 057101 (2005) doi:10.1103/PhysRevE.71.057101

Holme2007

P. Holme, S.M. Park, B.J. Kim, C.R. Edling. “Korean university life in a network perspective: Dynamics of a large affiliation network”. In Physica A: Statistical Mechanics and its Applications, vol. 373, p821-830 (2007) doi:10.1016/j.physa.2006.04.066

Tsonis2008a

A.A. Tsonis, K.L. Swanson, G. Wang. “Estimating the clustering coefficient in scale-free networks on lattices with local spatial correlation structure”. In Physica A: Statistical Mechanics and its Applications, vol. 387 (no. 21) p5287-5294 (2008) doi:10.1016/j.physa.2008.05.048

Ueoka2008

Y. Ueoka, T. Suzuki, T. Ikeguchi, Y. Horio. “Efficiency of Statistical Measures to Estimate Network Structure of Chaos Coupled Systems”. Proceedings of NOLTA (2008) http://tsuzuki.ise.ibaraki.ac.jp/MyPaper/Meeting/08NOLTA.pdf

Spatially embedded networks

[Bartelemy2011].

Bartelemy2011

M. Barthelemy. “Spatial networks”. In Physics Reports, vol. 499 (no. 1-3), p1-101 (2011) doi:10.1016/j.physrep.2010.11.002

Interacting/interdependent networks / networks of networks

Introduction to structural analysis of interacting networks

[Donges2011a].

Donges2011a(1,2)

J.F. Donges, H.C.H. Schultz, N. Marwan, Y. Zou, J. Kurths. “Investigating the topology of interacting networks - Theory and application to coupled climate subnetworks”. In European Physical Journal B: Condensed Matter and Complex Systems, vol. 84 (no. 4) p635-652 (2011) doi:10.1140/epjb/e2011-10795-8

Node-weighted network measures / node-splitting invariance

Introduction

[Heitzig2012].

Heitzig2012

J. Heitzig, J. F. Donges, Y. Zou, N. Marwan, J. Kurths. “Node-weighted measures for complex networks with spatially embedded, sampled, or differently sized nodes”. In European Physical Journal B: Condensed Matter and Complex Systems, vol. 85 p38 (2012) doi:10.1140/epjb/e2011-20678-7

Random graph models and network surrogates for interacting networks

[Schultz2010].

Schultz2010(1,2)

H.C.H. Schultz. “Coupled climate networks: Investigating the terrestrial atmosphere’s dynamical structure”. Diploma thesis, Free University, Berlin (2010)

Analysis of node-weighted interacting networks

[Wiedermann2011], [Wiedermann2013].

Wiedermann2011(1,2)

M. Wiedermann. “Coupled climate network analysis of multidecadal dynamics in the Arctic”. Bachelor’s thesis, Humboldt University, Berlin (2011)

Wiedermann2013

M. Wiedermann, J.F. Donges, J. Heitzig, J. Kurths. “Node-weighted interacting network measures improve the representation of real-world complex systems”. In Europhysics Letters, vol. 102.2, 28007 (2013) doi:10.1209/0295-5075/102/28007

Zemp2014

D.C. Zemp, M. Wiedermann, J. Kurths, A. Rammig, J.F. Donges. “Node-weighted measures for complex networks with directed and weighted edges for studying continental moisture recycling”. In Europhysics Letters, vol. 107.5, p58005 (2014) doi:10.1209/0295-5075/107/58005

Climate data analysis (general)

[Bretherton1992].

Bretherton1992

C.S. Bretherton, C. Smith, J.M. Wallace. “An intercomparison of methods for finding coupled patterns in climate data”. In Journal of Climate, vol. 5, p541-560 (1992) doi:10.1175/1520-0442(1992)005<0541:AIOMFF>2.0.CO;2

Climate networks / Coupled climate networks

Comparing linear and nonlinear construction of climate networks

[Donges2009a].

Donges2009a

J.F. Donges, Y. Zou, N. Marwan, J. Kurths. “Complex networks in climate dynamics”. In European Physical Journal Special Topics, vol. 174 (no. 1), p157-179 (2009) doi:10.1140/epjst/e2009-01098-2

Studying the dynamical structure of the surface air temperature field

[Donges2009b], [Radebach2010].

Donges2009b

J.F. Donges, Y. Zou, N. Marwan, J. Kurths. “The backbone of the climate network”. In Europhysics Letters, vol. 87 (no. 4), 48007 (2009) doi:10.1209/0295-5075/87/48007

Radebach2010

A. Radebach. “Evolving climate networks: Investigating the evolution of correlation structure of the Earth’s climate system”. Diploma thesis, Humboldt University, Berlin (2010)

Introduction to coupled climate networks and applications

[Schultz2010], [Donges2011a], [Wiedermann2011].

Review of climate network analysis (in Chinese!)

[Zou2011].

Zou2011

Y. Zou, J.F. Donges, J. Kurths. “Recent advances in complex climate network analysis”. In Complex Systems and Complexity Science, vol. 8 (no. 1), p27-38 (2011)

Visualization of climate networks

[Tominski2011].

Tominski2011

C. Tominski, J.F. Donges, T. Nocke. “Information Visualization in Climate Research”. In Proceedings of the International Conference on Information Visualisation (IV), London, p298-305 (2011) doi:10.1109/IV.2011.12

Evolving climate networks

[Radebach2013].

Radebach2013

A. Radebach, R.V. Donner, J. Runge, J.F. Donges, J. Kurths. “Disentangling different types of El Nino episodes by evolving climate network analysis”. In Physical Review E, vol. 88, 052807 (2013) doi:10.1103/PhysRevE.88.052807

General

[Tsonis2004], [Tsonis2006], [Gozolchiani2008], [Tsonis2008b], [Tsonis2008c], [Yamasaki2008], [Donges2009c], [Yamasaki2009].

Tsonis2004

A.A. Tsonis and P.J. Roebber. “The architecture of the climate network”. In Physica A: Statistical Mechanics and its Applications, vol. 333, p497-504 (2004) doi:10.1016/j.physa.2003.10.045

Tsonis2006

A.A. Tsonis, K.L. Swanson, P.J. Roebber. “What do networks have to do with climate?”. In Bull. Amer. Meteor. Soc. vol. 87 p585-595 (2006) doi:10.1175/BAMS-87-5-585

Gozolchiani2008

A. Gozolchiani, K. Yamasaki, O. Gazit, S. Havlin. “Pattern of climate network blinking links follows El Niño events”. In Europhysics Letters, vol. 83 (no. 2), 28005 (2008) doi:10.1209/0295-5075/83/28005

Tsonis2008b

A. A. Tsonis and K. L. Swanson. “Topology and Predictability of El Niño and La Niña Networks”. In Physical Review Letters vol 100, 228502 (2008) doi:10.1103/PhysRevLett.100.228502

Tsonis2008c

A. A. Tsonis, K. L. Swanson, G. Wang. “On the role of atmospheric teleconnections in climate”. In Journal of Climate vol. 21, p2990-3001 (2008) doi:10.1175/2007JCLI1907.1

Yamasaki2008

K. Yamasaki, A. Gozolchiani, S. Havlin. “Climate Networks around the Globe are Significantly Affected by El Niño”. In Physical Review Letters, vol. 100, 228501 (2008) doi:10.1103/PhysRevLett.100.228501

Donges2009c

J.F. Donges “Complex networks in the climate system”. Diploma thesis, University of Potsdam (2009) Advisor: Prof. Dr. Dr. h.c. Juergen Kurths. URN: urn:nbn:de:kobv:517-opus-49775.

Yamasaki2009

K. Yamasaki, A. Gozolchiani, S. Havlin. “Climate Networks Based on Phase Synchronization Analysis Track El-Niño”. In Progress Of Theoretical Physics Supplement, vol. 179, p178-188 (2009) doi:10.1143/PTPS.179.178

Power Grids/Power Networks

Resistance based networks

[Schultz2014], [Schultz2014a].

Schultz2014

P. Schultz “Stability Analysis of Power Grid Networks”. M.Sc. Thesis, Humboldt-Universität zu Berlin (2014)

Schultz2014a

P. Schultz, J. Heitzig, J. Kurths A Random Growth Model for Power Grids and Other Spatially Embedded Infrastructure Networks”. In Eur. Phys. J. Special Topics: Resilient Power Grids and Extreme Events (2014)

Time series analysis and synchronization

General

[Pecora1998], [Schreiber2000], [Kraskov2004], [Kantz2006], [Thiel2006], [Bergner2008], [Pompe2011], [Runge2012b].

Pecora1998

L.M. Pecora and T.L. Carroll. “Master Stability Functions for Synchronized Coupled Systems”. In Physical Review Letters, vol. 80, 2109 (1998) doi:10.1103/PhysRevLett.80.2109

Schreiber2000

T. Schreiber and A. Schmitz. “Surrogate time series”. In Physica D vol. 142 (no. 3-4), p346-382 (2000) doi:10.1016/S0167-2789(00)00043-9

Kraskov2004

A. Kraskov, H. Stögbauer, P. Grassberger. “Estimating mutual information”. In Physical Review E, vol. 69(6), 066138 (2004) doi:10.1103/PhysRevE.69.066138

Kantz2006

H. Kantz and T. Schreiber. “Nonlinear Time Series Analysis”. Cambridge University Press, Cambridge, 2nd edition (2006)

Thiel2006

M. Thiel, M.C. Romano, J. Kurths, M. Rolfs, R. Kliegl. “Twin surrogates to test for complex synchronization”. In Europhysics Letters, vol. 75, p535-541 (2006) doi:10.1209/epl/i2006-10147-0

Bergner2008

A. Bergner, R. Meucci, K. Al Naimee, M.C. Romano, M. Thiel, J. Kurths, and F. T. Arecchi. “Continuous wavelet transform in the analysis of burst synchronization in a coupled laser system”. In Physical Review E, vol. 78, 016211 (2008) doi:10.1103/PhysRevE.78.016211

Pompe2011

B. Pompe, J. Runge. “Momentary information transfer as a coupling measure of time series”. In Physical Review E vol. 83, 051122 (2011) doi:10.1103/PhysRevE.83.051122

Runge2012b

J. Runge, J. Heitzig, N. Marwan, J. Kurths. “Quantifying causal coupling strength: A lag-specific measure for multivariate time series related to transfer entropy”. In Physical Review E, vol. 86(6), 1-15 (2012) doi:10.1103/PhysRevE.86.061121

Event synchronization

[Quiroga2002], [Boers2014].

Quiroga2002

R.Q. Quiroga, T. Kreuz, P. Grassberger. “Event synchronization: a simple and fast method to measure synchronicity and time delay patterns.” In Physical Review E, vol. 66(4), 041904 (2002) doi:10.1103/PhysRevE.66.041904

Boers2014

N. Boers, B. Bookhagen, H.M.J. Barbosa, N. Marwan, J. Kurths. J.A. Marengo. “Prediction of extreme floods in the eastern Central Andes based on a complex networks approach”. In Nature communications, vol. 5, 1–7 (2014) doi:10.1038/ncomms6199

Recurrence networks / quantification analysis / plots

Review of recurrence plots and RQA

[Marwan2007].

Marwan2007

N. Marwan, M.C. Romano, M. Thiel, J. Kurths. “Recurrence plots for the analysis of complex systems”. In Physics Reports, vol. 438 (no. 5–6), p237-329 (2007) doi:10.1016/j.physrep.2006.11.001

Introduction and application of recurrence networks in the context of RQA

[Marwan2009].

Marwan2009

N. Marwan, J.F. Donges, Y. Zou, R.V. Donner, J. Kurths. “Complex network approach for recurrence analysis of time series”. In Physics Letters A, vol. 373 (no. 46), p4246-4254 (2009) doi:10.1016/j.physleta.2009.09.042

A thorough introduction to recurrence network analysis

[Donner2010b].

Donner2010b

R.V. Donner, Y. Zou, J.F. Donges, N. Marwan, J. Kurths. “Recurrence networks – A novel paradigm for nonlinear time series analysis”. In New Journal of Physics, vol. 12 (no. 3), 033205 (2010) doi:10.1088/1367-2630/12/3/033025

Discussion of choosing an appropriate recurrence threshold

[Donner2010a], [Zou2010].

Donner2010a

R.V. Donner, Y. Zou, J.F. Donges, N. Marwan, J. Kurths. “Ambiguities in recurrence-based complex network representations of time series”. In Physical Review E, vol. 81 (no. 1), 015101(R) (2010) doi:10.1103/PhysRevE.81.015101

Zou2010

Y. Zou, R.V. Donner, J.F. Donges, N. Marwan, J. Kurths. “Identifying complex periodic windows in continuous-time dynamical systems using recurrence-based methods”. In Chaos, vol. 20 (no. 4), 043130 (2010) doi:10.1063/1.3523304

Review of various methods for network-based time series analysis

[Donner2011a].

Donner2011a

R.V. Donner, M. Small, J.F. Donges, N. Marwan, Y. Zou, R. Xiang, J. Kurths. “Recurrence-based time series analysis by means of complex network methods”. In International Journal of Bifurcation and Chaos, vol. 21 (no. 4), p1019-1046 (2011) doi:10.1142/S0218127411029021

Introduction to measures of (fractal) transitivity dimensions

[Donner2011b].

Donner2011b

R.V. Donner, J. Heitzig, J.F. Donges, Y. Zou, J. Kurths. “The geometry of chaotic dynamics – A complex network perspective”. In European Physical Journal B: Condensed Matter and Complex Systems, vol. 84 (no. 4), p653-672 (2011) doi:10.1140/epjb/e2011-10899-1

Applications of recurrence network analysis to paleoclimate data

[Donges2011b], [Donges2011c], [Feldhoff2012].

Donges2011b

J.F. Donges, R.V. Donner, K. Rehfeld, N. Marwan, M.H. Trauth, J. Kurths. “Identification of dynamical transitions in marine palaeoclimate records by recurrence network analysis”. In Nonlinear Processes in Geophysics, vol. 18 (no. 5), p545-562 (2011) doi:10.5194/npg-18-545-2011

Donges2011c

J.F. Donges, R.V. Donner, M.H. Trauth, N. Marwan, H.J. Schellnhuber, J. Kurths. “Nonlinear detection of paleoclimate-variability transitions possibly related to human evolution”. In Proceedings of the National Academy of Sciences of the United States of America, vol. 108 (no. 51), p20422-20427 (2011) doi:10.1073/pnas.1117052108

Theory of recurrence networks

[Donges2012], [Zou2012].

Donges2012

J.F. Donges, J. Heitzig, R.V. Donner, J. Kurths. “Analytical framework for recurrence network analysis of time series”. In Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, vol. 85, 046105 (2012) doi:10.1103/PhysRevE.85.046105

Zou2012

Y. Zou, J. Heitzig, R.V. Donner, J.F. Donges, J.D. Farmer, R. Meucci, S. Euzzor, N. Marwan, J. Kurths. “Power-laws in recurrence networks from dynamical systems”. In Europhysics Letters, vol. 98, 48001 (2012) doi:10.1209/0295-5075/98/48001

Multivariate extensions of recurrence network analysis

[Feldhoff2012], [Feldhoff2013].

Feldhoff2012(1,2)

J.H. Feldhoff, R.V. Donner, J.F. Donges, N. Marwan, J. Kurths. “Geometric detection of coupling directions by means of inter-system recurrence networks”. In Physics Letters A, vol. 376, 3504-3513 (2012), doi:10.1016/j.physleta.2012.10.008

Feldhoff2013

J.H. Feldhoff, R.V. Donner, J.F. Donges, N. Marwan, J. Kurths. “Geometric signature of complex synchronisation scenarios”. In Europhysics Letters vol. 102, 30007 (2013), doi:10.1209/0295-5075/102/30007

General

[Ngamga2007], [Xu2008], [Schinkel2009].

Ngamga2007

E.J. Ngamga, A. Nandi, R. Ramaswamy, M.C. Romano, M. Thiel, J. Kurths. “Recurrence analysis of strange nonchaotic dynamics”. In Physical Review E, vol. 75, 036222 (2007) doi:10.1103/PhysRevE.75.036222

Xu2008

X. Xu, J. Zhang, M. Small. “Superfamily phenomena and motifs of networks induced from time series”. In Proceedings of the National Academy of Sciences of the United States of America, vol. 105 (no. 50) p19601-19605 (2008) doi:10.1073/pnas.0806082105

Schinkel2009

S. Schinkel, N. Marwan, O. Dimigen, J. Kurths. “Confidence bounds of recurrence-based complexity measures”. In Physics Letters A, vol. 373 (no. 26) p2245–2250 (2009) doi:10.1016/j.physleta.2009.04.045

Visibility graph analysis

Introduction

[Lacasa2008].

Lacasa2008

L. Lacasa, B. Luque, F. Ballesteros, J. Luque, J.C. Nuno. “From time series to complex networks: The visibility graph”. In Proceedings of the National Academy of Sciences of the United States of America, vol. 105 (no. 13), p4972-4975 (2008) doi:10.1073/pnas.0709247105

Application to geophysical time series

[Donner2012].

Donner2012

R.V. Donner and J.F. Donges. “Visibility graph analysis of geophysical time series: Potentials and possible pitfalls”. In Acta Geophysica, vol. 60 p589-623 (2012) doi:10.2478/s11600-012-0032-x

Tests for time series irreversibility

[Donges2013].

Donges2013

J.F. Donges, R.V. Donner, J. Kurths. “Testing time series irreversibility using complex network methods”. In Europhysics Letters, vol. 102.1, 10004 (2013) doi:10.1209/0295-5075/102/10004