Force-based Layout of Non-Markovian Temporal Networks

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Force-based Layout of Non-Markovian Temporal Networks Ingo Scholtes ETH Zürich ECCS 2013 Ingo Scholtes 20.09.2013 1 @ ETH Zürich ECCS 2013 Ingo Scholtes 20.09.2013 2 1

@ ETH Zürich ECCS 2013 Ingo Scholtes 20.09.2013 3 An aggregated perspective ECCS 2013 Ingo Scholtes 20.09.2013 4 2

The fallacy of transitivity ECCS 2013 Ingo Scholtes 20.09.2013 5 The time dimension ECCS 2013 Ingo Scholtes 20.09.2013 6 3

Finding Real-world temporal networks are not Markovian! ECCS 2013 Ingo Scholtes 20.09.2013 7 R Pfitzner, I Scholtes, A Garas, CJ Tessone, F Schweitzer: Betweenness Preference: Quantifying Correlations in the Topological Dynamics of Temporal Networks, Phys. Rev. Let., Vol. 110, 198701, May 10 2013 Finding Aggregate networks are poor representations of dynamic (social) systems! ECCS 2013 Ingo Scholtes 20.09.2013 8 R Pfitzner, I Scholtes, A Garas, CJ Tessone, F Schweitzer: Betweenness Preference: Quantifying Correlations in the Topological Dynamics of Temporal Networks, Phys. Rev. Let., Vol. 110, 198701, May 10 2013 4

Effects on dynamical processes Q: How much longer are paths compared to the aggregate network? communities longer paths slower spreading ECCS 2013 Ingo Scholtes 20.09.2013 9 R Pfitzner, I Scholtes, A Garas, CJ Tessone, F Schweitzer: Betweenness Preference: Quantifying Correlations in the Topological Dynamics of Temporal Networks, Phys. Rev. Let., Vol. 110, 198701, May 10 2013 MIT Reality Mining ECCS 2013 Ingo Scholtes 20.09.2013 10 5

time time Aggregate networks G (1) Does not capture non-markovian dynamics False transitivity No reasonable spectral analysis ECCS 2013 Ingo Scholtes 20.09.2013 11 Second-order aggregate networks G (2) State-space expansion Transitivity holds! Spectral analysis of temporal networks ECCS 2013 Ingo Scholtes 20.09.2013 12 I Scholtes, N Wider, R Pfitzner, AGaras, CJ Tessone, F Schweitzer: Slow-Down vs. Speed-Up of Information Diffusion in Non-Markovian Temporal Networks, arxiv:1307.4030, July 15 2013 6

time Second-order aggregate networks G (2) State-space expansion Transitivity holds! Spectral analysis of temporal networks ECCS 2013 Ingo Scholtes 20.09.2013 13 I Scholtes, N Wider, R Pfitzner, AGaras, CJ Tessone, F Schweitzer: Slow-Down vs. Speed-Up of Information Diffusion in Non-Markovian Temporal Networks, arxiv:1307.4030, July 15 2013 Spectra of dynamic networks λ 1 = 1 λ 2 = 0. 873 λ 3 = 0. 873 λ 4 = 0. 61 λ 5 = 0. 54 λ 6 = 0 λ 1 = 1 λ 2 = 0. 816 λ 3 = 0. 816 λ 4 = 0 λ 5 = 0 λ 6 = 0 ECCS 2013 Ingo Scholtes 20.09.2013 14 I Scholtes, N Wider, R Pfitzner, AGaras, CJ Tessone, F Schweitzer: Slow-Down vs. Speed-Up of Information Diffusion in Non-Markovian Temporal Networks, arxiv:1307.4030, July 15 2013 7

Spectra of dynamic networks λ 1 = 1 λ 2 = 0. 873 λ 3 = 0. 873 λ 4 = 0. 61 λ 5 = 0. 54 λ 6 = 0 S = 1. 44 Slow-down factor >1 slow-down <1 speed-up λ 1 = 1 λ 2 = 0. 816 λ 3 = 0. 816 λ 4 = 0 λ 5 = 0 λ 6 = 0 ECCS 2013 Ingo Scholtes 20.09.2013 15 I Scholtes, N Wider, R Pfitzner, AGaras, CJ Tessone, F Schweitzer: Slow-Down vs. Speed-Up of Information Diffusion in Non-Markovian Temporal Networks, arxiv:1307.4030, July 15 2013 Slow-down of information diffusion maximum slow-down ECCS 2013 Ingo Scholtes 20.09.2013 16 I Scholtes, N Wider, R Pfitzner, AGaras, CJ Tessone, F Schweitzer: Slow-Down vs. Speed-Up of Information Diffusion in Non-Markovian Temporal Networks, arxiv:1307.4030, July 15 2013 8

Speed-up of information diffusion minimum speed-up ECCS 2013 Ingo Scholtes 20.09.2013 17 I Scholtes, N Wider, R Pfitzner, AGaras, CJ Tessone, F Schweitzer: Slow-Down vs. Speed-Up of Information Diffusion in Non-Markovian Temporal Networks, arxiv:1307.4030, July 15 2013 Force-based layout of temporal networks 2nd order aggregate network ECCS 2013 Ingo Scholtes 20.09.2013 18 I Scholtes, A Garas, R Pfitzner, CJ Tessone: Using Temporal Correlations in the Visualization of Aggregate Representations of Dynamic Networks, working paper, September 2013 9

Force-based layout of temporal networks ECCS 2013 Ingo Scholtes 20.09.2013 19 I Scholtes, A Garas, R Pfitzner, CJ Tessone: Using Temporal Correlations in the Visualization of Aggregate Representations of Dynamic Networks, working paper, September 2013 Causality-preserving layout ECCS 2013 Ingo Scholtes 20.09.2013 20 10

A simple example ECCS 2013 Ingo Scholtes 20.09.2013 21 A simple example ECCS 2013 Ingo Scholtes 20.09.2013 22 11

MIT RealityMining ECCS 2013 Ingo Scholtes 20.09.2013 23 Causality-preserving layout ECCS 2013 Ingo Scholtes 20.09.2013 24 12

Thank you! R Pfitzner, I Scholtes, A Garas, CJ Tessone, F Schweitzer: Betweenness Preference: Quantifying Correlations in the Topological Dynamics of Temporal Networks, Physical Review Letters, Vol. 110, 198701, May 10 2013 I Scholtes, N Wider, R Pfitzner, A Garas, CJ Tessone, F Schweitzer: Slow-down vs. Speed-up of Information Diffusion in Non-Markovian Temporal Networks, arxiv:1307.4030, July 15 2013 I Scholtes, A Garas, R Pfitzner, CJ Tessone: Force-based Layout of Non-Markovian Temporal Networks, working paper, September 2013 http://www.sg.ethz.ch http://www.ingoscholtes.net Follow @ingo_s ischoltes@ethz.ch ECCS 2013 Ingo Scholtes 20.09.2013 25 13