Temporal Network Analysis
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1) Temporal networks are networks where elements like ties and node properties change over time, unlike static graphs. They require new analysis methods that account for temporal dynamics. 2) Visualization techniques for temporal networks include static aggregated graphs, weighted aggregated graphs, and timelines. Studies of citation patterns between journals show how disciplines evolve over time. 3) Formulating temporal networks involves defining time windows and finding the graph state at random times within or across windows. Metrics are adapted from static graphs to measure temporal aspects like reachability and centrality over time.
![Temporal Networks ο Networks in which Elements Change Over Time
β’ Fluctuation in Tie Weight
β’ [Mainly] Intermittent Tie
β’ Actors Property Values
Time-Evolving | Temporal | Time-Varying | Dynamic Graph β Static Graph
DEFINITION](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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Temporal Network Analysis
- 1. Temporal Networks SemioNet: Semantic Social Network Analysis
- 2. Temporal Networks ο Networks in which Elements Change Over Time β’ Fluctuation in Tie Weight β’ [Mainly] Intermittent Tie β’ Actors Property Values Time-Evolving | Temporal | Time-Varying | Dynamic Graph β Static Graph DEFINITION
- 3. VISUALIZATION β’ Static Graph β’ Aggregated Static Graph: At least one connection during the time span β’ Weighted Aggregated Graph: Weigh the connection persistency by probability or other measurements β’ Timeline
- 4. Studying the citation pattern between about 7000 scientific journals over the past decade Neuroscience from an Interdisciplinary Specialty ο Mature & Stand-alone Discipline Alluvial Diagrams
- 5. FORMULATION Varying Time Window β’ ν‘1, ν‘1 + Ξν‘1 , ν‘2, ν‘2 + Ξν‘2 , β¦ , ν‘ν, ν‘ν + Ξν‘ν = ν΅νννννννννννν β’ ν‘1 = 0, ν‘ν = ν β’ νΊ[0,ν] = νΊ1, νΊ2, β¦ , νΊν = ννννννν νΊνννβ νΏνν ν‘ β’ ν΄ ν‘ν = νννν β ν·νννννννν‘ ν΄νννννννν¦ ννν‘ννν₯ Finding the Graph State at Random Time Frame νΌ, ν½ β ν‘? β’ At least one of β’ ν‘ν β€ νΌ < ν‘ν + Ξν‘ν βΆ β β[ β β β β β β β’ ν‘ν β€ ν½ < ν‘ν + Ξν‘ν βΆ β β β β β β] β β β’ νΌ < ν‘ν β§ ν‘ν + Ξν‘ν β€ ν½ βΆ β β( β β β β β β) Fixed Time Window: Ξν‘ = ννν₯νν ν‘ννν ν νννν β 0 β’ ν‘ν+1 = ν‘ν + Ξν‘ = ν‘1 + i Γ Ξν‘
- 6. Time-Respecting Walks Temporal Walk from Node i to Node j is a Time Increasing Ordered Sequence of L Edges νν0 , νν1 , νν1 , νν2 , β¦ , νννβ1 , ννν νν0 = ν, ννν = ν ν‘ν1 < ν‘ν2 < β¦ < ν‘νν ννννβ1 METRICS Distance ,ννν ν‘νν β 0 Topological: Number of Edges Traversed by the Path Temporal: Time Interval or Duration between the First & the Last Nodes Reachability, Connectedness, Centrality(Betweenness, Closeness, Spectral), β¦
- 7. TEMPORAL SCALE Interval of Time ο A Minute, Day, or A Year β’ kinship relations! Oversampling β’ Affect the Ability to Distinguish the Change β’ Technology ο Very Fine Grained Snapshots β’ Problem under Study ο Determine the Scale β’ Tweeter: Minute β’ Social Tie: Month Aggregation β’ Increase the Time Interval while Preserve Information Heuristics: Persistence is a property that allows us to construct a network with the βcoreβ interactions, discarding the noisy transient interactions. βrightβ temporal scale: the temporal scale that best captures the persistent nature. β’ TWIN: Temporal Window In Networks β’ Graphscope
- 8. The TWIN (Temporal Window In Networks) heuristic uses graph-theoretic measures as proxies of different aspects of network structure. Given a temporal stream of edges and a graph-theoretic measure, the heuristic generates time series of graphs (dynamic graphs) at different levels of aggregation. It then computes the variance and compression ratio for each time series. Finally, the algorithm analyzes the compression ratio and variance as functions of window size and selects the window size for which the variance is relatively small and compression ratio is relatively high. Graphscope uses the notion of compression cost to capture the persistence of network structures (in this case of communities) in time. Similar graph snapshots will incur low compression cost, therefore they can be grouped together in one temporal segment. Whenever the compression cost increases substantially with the addition of a new graph snapshot, Graphscope starts a new temporal segment. A nice feature of the Graphscope heuristic is the fact that it generates a nonuniform partitioning of the timeline. The non-uniform partitioning is a more realistic representation of real-world interaction streams which are commonly characterized by bursty behavior
- 9. Predicting the Temporal Dynamics of Information Diffusion in Social Network β’ Learning Target Function 0 β€ νν₯,ν¦ ν‘ β€ 1by 4-D Feature Space of {User, Topic, Topology, Time} ο {Diffused or Non-Diffused} Spatio-Temporal Dynamics of Online Memes: A Study of Geo-Tagged Tweets β’ Hashtag Adoption Lag β’ Measuring Spatial Impact APPLICATION
- 10. β’ Spatio-Temporal Dynamics of Online Memes: A Study of Geo-Tagged Tweets β’ Peak Analysis of Hashtags & Relation between the Pace to Reach the Peak (fast or slow) to the Spatial Distribution β’ The Peak of Hashtags Propagation in terms of Occurrences
- 11. REFERENCES β’ Caceres, Rajmonda Sulo, and Tanya Berger-Wolf. "Temporal Scale of Dynamic Networks." Temporal Networks. Springer Berlin Heidelberg, 2013. 65-94. β’ Holme, Petter, and Jari SaramΓ€ki. "Temporal networks." Physics reports 519.3 (2012): 97-125. β’ Nicosia, Vincenzo, et al. "Graph metrics for temporal networks." Temporal Networks. Springer Berlin Heidelberg, 2013. 15-40. β’ Kamath, Krishna Y., et al. "Spatio-temporal dynamics of online memes: a study of geo-tagged tweets." Proceedings of the 22nd international conference on World Wide Web. International World Wide Web Conferences Steering Committee, 2013. β’ Guille, Adrien, Hakim Hacid, and CΓ©cile Favre. "Predicting the temporal dynamics of information diffusion in social networks." arXiv preprint arXiv:1302.5235 (2013).