Force-based Layout of Non-Markovian Temporal Networks
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1 Force-based Layout of Non-Markovian Temporal Networks Ingo Scholtes ETH Zürich ECCS 2013 Ingo Scholtes ETH Zürich ECCS 2013 Ingo Scholtes
2 @ ETH Zürich ECCS 2013 Ingo Scholtes An aggregated perspective ECCS 2013 Ingo Scholtes
3 The fallacy of transitivity ECCS 2013 Ingo Scholtes The time dimension ECCS 2013 Ingo Scholtes
4 Finding Real-world temporal networks are not Markovian! ECCS 2013 Ingo Scholtes 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, , May Finding Aggregate networks are poor representations of dynamic (social) systems! ECCS 2013 Ingo Scholtes 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, , May
5 Effects on dynamical processes Q: How much longer are paths compared to the aggregate network? communities longer paths slower spreading ECCS 2013 Ingo Scholtes 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, , May MIT Reality Mining ECCS 2013 Ingo Scholtes
6 time time Aggregate networks G (1) Does not capture non-markovian dynamics False transitivity No reasonable spectral analysis ECCS 2013 Ingo Scholtes Second-order aggregate networks G (2) State-space expansion Transitivity holds! Spectral analysis of temporal networks ECCS 2013 Ingo Scholtes 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: , July
7 time Second-order aggregate networks G (2) State-space expansion Transitivity holds! Spectral analysis of temporal networks ECCS 2013 Ingo Scholtes 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: , July Spectra of dynamic networks λ 1 = 1 λ 2 = λ 3 = λ 4 = λ 5 = λ 6 = 0 λ 1 = 1 λ 2 = λ 3 = λ 4 = 0 λ 5 = 0 λ 6 = 0 ECCS 2013 Ingo Scholtes 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: , July
8 Spectra of dynamic networks λ 1 = 1 λ 2 = λ 3 = λ 4 = λ 5 = λ 6 = 0 S = Slow-down factor >1 slow-down <1 speed-up λ 1 = 1 λ 2 = λ 3 = λ 4 = 0 λ 5 = 0 λ 6 = 0 ECCS 2013 Ingo Scholtes 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: , July Slow-down of information diffusion maximum slow-down ECCS 2013 Ingo Scholtes 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: , July
9 Speed-up of information diffusion minimum speed-up ECCS 2013 Ingo Scholtes 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: , July Force-based layout of temporal networks 2nd order aggregate network ECCS 2013 Ingo Scholtes I Scholtes, A Garas, R Pfitzner, CJ Tessone: Using Temporal Correlations in the Visualization of Aggregate Representations of Dynamic Networks, working paper, September
10 Force-based layout of temporal networks ECCS 2013 Ingo Scholtes 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
11 A simple example ECCS 2013 Ingo Scholtes A simple example ECCS 2013 Ingo Scholtes
12 MIT RealityMining ECCS 2013 Ingo Scholtes Causality-preserving layout ECCS 2013 Ingo Scholtes
13 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, , May 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: , July I Scholtes, A Garas, R Pfitzner, CJ Tessone: Force-based Layout of Non-Markovian Temporal Networks, working paper, September ischoltes@ethz.ch ECCS 2013 Ingo Scholtes
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