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)

Spatially embedded networks


[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](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



[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](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]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]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]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]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]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


[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


[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]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]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]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]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]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


[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



[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]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]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