Temporal Scale of Dynamic Networks
Interactions, either of molecules or people, are inherently dynamic, changing with time and context. Interactions have an inherent rhythm, often happening over a range of time scales. Temporal streams of interactions are commonly aggregated into dynamic n
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Abstract Interactions, either of molecules or people, are inherently dynamic, changing with time and context. Interactions have an inherent rhythm, often happening over a range of time scales. Temporal streams of interactions are commonly aggregated into dynamic networks for temporal analysis. Results of this analysis are greatly affected by the resolution at which the original data are aggregated. The mismatch between the inherent temporal scale of the underlying process and that at which the analysis is performed can obscure important insights and lead to wrong conclusions. In this chapter we describe the challenge of identifying the range of inherent temporal scales of a stream of interactions and of finding the dynamic network representation that matches those scales. We describe possible formalizations of the problem of identifying the inherent time scales of interactions and present some initial approaches at solving it, noting the advantages and limitations of these approaches. This is a nascent area of research and our goal is to highlight its importance and to establish a computational foundation for further investigations.
1 Introduction Whether it is on-line communications [11, 33, 34], animal social interactions [15, 19, 48, 55], or gene regulatory processes [25], the dynamic systems they represent have inherent rhythms at which they function. Some of these inherent rhythms come from the system itself, others are imposed by outside circumstances. Circadian patterns of cell regulatory systems, seasonality in mobility patterns of animals, daily and weekly communication patterns of humans are just a few examples of these characteristic temporal scales. Not only do these complex systems have inherent rhythms, different patterns within them form and live at different scales R.S. Caceres () T. Berger-Wolf University of Illinois at Chicago, Chicago, IL 60607, USA e-mail: [email protected]; [email protected] P. Holme and J. Saram¨aki (eds.), Temporal Networks, Understanding Complex Systems, DOI 10.1007/978-3-642-36461-7 4, © Springer-Verlag Berlin Heidelberg 2013
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[32]. For example, when analyzing animal population behavior, three temporal scales are considered to be important for capturing the hierarchical nature of its social structure [21]: the scale of the interactions themselves, the scale of patterns of interactions (relationships), and, finally, the scale of patterns of relationships (network structures). In this context, grooming interactions of baboons usually have a temporal scale ranging from seconds to minutes, mother to infant or peer to peer relationships have a scale extending over years, while an individual troop membership, splitting or formation of new troops extends from years to decades [52]. Similarly, in human social behavior, the patterns of interaction of conversations, friendships, and kinship occupy different temporal scales. Every dynamic complex system exhibits this kind of multi-scalar behavior. We view the system through the filter of data w
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