Abstract
Network visualisation techniques are important tools for the exploratory analysis of complex systems. While these methods are regularly applied to visualise data on complex networks, we increasingly have access to time series data that can be modelled as temporal networks or dynamic graphs. In dynamic graphs, the temporal ordering of time-stamped edges determines the causal topology of a system, i.e., which nodes can, directly and indirectly, influence each other via a so-called causal path. This causal topology is crucial to understand dynamical processes, assess the role of nodes, or detect clusters. However, we lack graph drawing techniques that incorporate this information into static visualisations. Addressing this gap, we present a novel dynamic graph visualisation algorithm that utilises higher-order graphical models of causal paths in time series data to compute time-aware static graph visualisations. These visualisations combine the simplicity and interpretability of static graphs with a time-aware layout algorithm that highlights patterns in the causal topology that result from the temporal dynamics of edges .
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Archambault, D., Purchase, H.C.: Mental map preservation helps user orientation in dynamic graphs. In: Didimo, W., Patrignani, M. (eds.) GD 2012. LNCS, vol. 7704, pp. 475–486. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36763-2_42
Beck, F., Burch, M., Diehl, S., Weiskopf, D.: A taxonomy and survey of dynamic graph visualization 36(1), 133–159 (2017)
Brandes, U., Kenis, P., Wagner, D.: Communicating centrality in policy network drawings. IEEE Trans. Visual. Comput. Graph. 9(2), 241–253 (2003)
Burch, M., et al.: Radial edge splatting for visualizing dynamic directed graphs, pp. 603–612 (2012)
De Bruijn, N.G.: A combinatorial problem. Koninklijke Nederlandse Akademie v. Wetenschappen 49(49), 758–764 (1946)
Pathpy developers: pathpy software package (2020). https://github.com/pathpy/pathpy
Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Algorithms for drawing graphs: an annotated bibliography. Comput. Geom. 4(5), 235–282 (1994)
Diehl, S., Görg, C., Kerren, A.: Preserving the mental map using foresighted layout. In: Ebert, D.S., Favre, J.M., Peikert, R. (eds.) Data Visualization 2001, pp. 175–184. Springer, Vienna (2001). https://doi.org/10.1007/978-3-7091-6215-6_19
van den Elzen, S., Holten, D., Blaas, J., van Wijk, J.J.: Dynamic network visualization with extended massive sequence views. IEEE Trans. Visual. Comput. Graph. 20(8), 1087–1099 (2013)
Erten, C., Kobourov, S.G., Le, V., Navabi, A.: Simultaneous graph drawing: layout algorithms and visualization schemes. In: Liotta, G. (ed.) GD 2003. LNCS, vol. 2912, pp. 437–449. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24595-7_41
Friedrich, C., Eades, P.: The marey graph animation tool demo. In: Marks, J. (ed.) GD 2000. LNCS, vol. 1984, pp. 396–406. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44541-2_37
Fruchterman, T.M., Reingold, E.M.: Graph drawing by force-directed placement. Softw. Pract. Exp. 21(11), 1129–1164 (1991)
Génois, M., et al.: Data on face-to-face contacts in an office building suggest a low-cost vaccination strategy based on community linkers. Netw. Sci. 3(3), 326–347 (2015)
Görg, C., Birke, P., Pohl, M., Diehl, S.: Dynamic graph drawing of sequences of orthogonal and hierarchical graphs. In: Pach, J. (ed.) GD 2004. LNCS, vol. 3383, pp. 228–238. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-31843-9_24
Greilich, M., Burch, M., Diehl, S.: Visualizing the evolution of compound digraphs with timearctrees. In: Computer Graphics Forum, vol. 28, pp. 975–982. Wiley Online Library (2009)
Holme, P.: Modern temporal network theory: a colloquium. Eur. Phys. J. B 88(9), 1–30 (2015). https://doi.org/10.1140/epjb/e2015-60657-4
Jacomy, M., Venturini, T., Heymann, S., Bastian, M.: Forceatlas2, a continuous graph layout algorithm for handy network visualization designed for the gephi software. PloS one 9(6), e98679 (2014)
Kaufmann, M., Wagner, D.: Drawing Graphs: Methods and Models, vol. 2025. Springer, Cham (2003)
Kempe, D., Kleinberg, J., Kumar, A.: Connectivity and inference problems for temporal networks. J. Comput. Syst. Sci. 64, 820–842 (2002)
Kumar, G., Garland, M.: Visual exploration of complex time-varying graphs. IEEE Trans. Visual. Comput. Graph. 12(5), 805–812 (2006)
Lambiotte, R., Rosvall, M., Scholtes, I.: From networks to optimal higher-order models of complex systems. Nat. Phys. 15(4), 313–320 (2019)
Loubier, E., Dousset, B.: Temporal and relational data representation by graph morphing. Saf. Reliab. Manag. Risk (ESREL 2008), Hammamet 14(02), 2008–2016 (2008)
Nesbitt, K.V., Friedrich, C.: Applying gestalt principles to animated visualizations of network data. In: Proceedings Sixth International Conference on Information Visualisation, pp. 737–743. IEEE (2002)
Noguchi, C., Kawamoto, T.: Evaluating network partitions through visualization. arXiv e-prints arXiv:1906.00699, June 2019
Perri, V., Scholtes, I.: Hotvis: Higher-order time-aware visualisation of dynamic graphs (2020). https://arxiv.org/abs/1908.05976
Perri, V., Scholtes, I.: Hotvis: Higher-order time-aware visualisation of dynamic graphs (supplementary code and data) (2020). https://doi.org/10.5281/zenodo.3994152
Petrović, L.V., Scholtes, I.: Learning the markov order of paths in a network. arXiv preprint arXiv:2007.02861 (2020)
Pfitzner, R., Scholtes, I., Garas, A., Tessone, C.J., Schweitzer, F.: Betweenness preference: quantifying correlations in the topological dynamics of temporal networks. Phys. Rev. Lett. 110, 198701 (2013)
Purchase, H.C., Hoggan, E., Görg, C.: How important is the “mental map” – an empirical investigation of a dynamic graph layout algorithm. In: Kaufmann, M., Wagner, D. (eds.) GD 2006. LNCS, vol. 4372, pp. 184–195. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-70904-6_19
Scholtes, I.: When is a network a network? Multi-order graphical model selection in pathways and temporal networks, pp. 1037–1046. ACM (2017)
Shewchuk, J.R.: Adaptive precision floating-point arithmetic and fast robust geometric predicates. Discrete Comput. Geom. 18(3), 305–363 (1997)
Simonetto, P., Archambault, D., Kobourov, S.: Drawing dynamic graphs without timeslices. In: Frati, F., Ma, K.-L. (eds.) GD 2017. LNCS, vol. 10692, pp. 394–409. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-73915-1_31
Stehlé, J., Voirin, N., Barrat, A., Cattuto, C., Isella, L., Pinton, J.F., Quaggiotto, M., Van den Broeck, W., Régis, C., Lina, B., et al.: High-resolution measurements of face-to-face contact patterns in a primary school. PloS one 6(8), e23176 (2011)
Tao, J., Xu, J., Wang, C., Chawla, N.V.: Honvis: Visualizing and exploring higher-order networks. In: 2017 IEEE Pacific Visualization Symposium (PacificVis), pp. 1–10. IEEE (2017)
Vanhems, P., et al.: Estimating potential infection transmission routes in hospital wards using wearable proximity sensors. PloS one 8(9), e73970 (2013)
Vehlow, C., Burch, M., Schmauder, H., Weiskopf, D.: Radial layered matrix visualization of dynamic graphs. In: 2013 17th International Conference on Information Visualisation, pp. 51–58. IEEE (2013)
Acknowledgements
Vincenzo Perri and Ingo Scholtes acknowledge support by the Swiss National Science Foundation, grant 176938. Ingo Scholtes acknowledges support by the project bergisch.smart.mobility, funded by the German state of North Rhine-Westphalia.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
1 Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Perri, V., Scholtes, I. (2020). HOTVis: Higher-Order Time-Aware Visualisation of Dynamic Graphs. In: Auber, D., Valtr, P. (eds) Graph Drawing and Network Visualization. GD 2020. Lecture Notes in Computer Science(), vol 12590. Springer, Cham. https://doi.org/10.1007/978-3-030-68766-3_8
Download citation
DOI: https://doi.org/10.1007/978-3-030-68766-3_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-68765-6
Online ISBN: 978-3-030-68766-3
eBook Packages: Computer ScienceComputer Science (R0)