Temporal Networks

SemioNet: Semantic Social Network Analysis

DEFINITION

Temporal Networks Networks in which Elements Change Over Time

• Fluctuation in Tie Weight• [Mainly] Intermittent Tie• Actors Property Values

Time-Evolving | Temporal | Time-Varying | Dynamic Graph ≠ Static Graph

VISUALIZATION

• Static Graph• Aggregated Static Graph: At least one connection during the time span• Weighted Aggregated Graph: Weigh the connection persistency by probability or other measurements

• Timeline

Alluvial Diagrams

Studying the citation pattern between about 7000 scientific journals over the past decadeNeuroscience from an Interdisciplinary Specialty Mature & Stand-alone Discipline

FORMULATION

Varying Time Window

Finding the Graph State at Random Time Frame • At least one of

Fixed Time Window:

METRICS

Distance Topological: Number of Edges Traversed by the PathTemporal: Time Interval or Duration between the First & the Last Nodes

Reachability, Connectedness, Centrality(Betweenness, Closeness, Spectral), … 

Time-Respecting WalksTemporal Walk from Node i to Node j is a Time Increasing Ordered Sequence of L Edges

TEMPORAL SCALE

Interval of Time A Minute, Day, or A Year• kinship relations!

Oversampling• Affect the Ability to Distinguish the Change• Technology Very Fine Grained Snapshots• Problem under Study Determine the Scale

• Tweeter: Minute• Social Tie: Month

Aggregation• Increase the Time Interval while Preserve Information

Heuristics: Persistence is a property that allows us to construct a network with the “core” interactions, discarding the noisy transient interactions. “right” temporal scale: the temporal scale that best captures the persistent nature.

• TWIN: Temporal Window In Networks• Graphscope

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 morerealistic representation of real-world interaction streams which are commonly characterized by bursty behavior

Predicting the Temporal Dynamics of Information Diffusion in Social Network• Learning Target Function by 4-D Feature Space of {User, Topic, Topology, Time} {Diffused or Non-Diffused}

Spatio-Temporal Dynamics of Online Memes: A Study of Geo-Tagged Tweets• Hashtag Adoption Lag

• Measuring Spatial Impact

APPLICATION

• Spatio-Temporal Dynamics of Online Memes: A Study of Geo-Tagged Tweets• Peak Analysis of Hashtags & Relation between the Pace to Reach the Peak (fast or slow) to the Spatial

Distribution• The Peak of Hashtags Propagation in terms of Occurrences

REFERENCES

• Caceres, Rajmonda Sulo, and Tanya Berger-Wolf. "Temporal Scale of Dynamic Networks." Temporal Networks. Springer Berlin Heidelberg, 2013. 65-94.

• Holme, Petter, and Jari Saramäki. "Temporal networks." Physics reports 519.3 (2012): 97-125.

• Nicosia, Vincenzo, et al. "Graph metrics for temporal networks." Temporal Networks. Springer Berlin Heidelberg, 2013. 15-40.

• 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.

• Guille, Adrien, Hakim Hacid, and Cécile Favre. "Predicting the temporal dynamics of information diffusion in social networks." arXiv preprint arXiv:1302.5235 (2013).