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.

1. Temporal
Networks
SemioNet: Semantic Social Network Analysis

2. 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
DEFINITION

3. 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

4. Studying the citation pattern between about 7000 scientific journals over the past decade
Neuroscience from an Interdisciplinary Specialty  Mature & Stand-alone Discipline
Alluvial Diagrams

5. FORMULATION
Varying Time Window
• 푡1, 푡1 + Δ푡1 , 푡2, 푡2 + Δ푡2 , … , 푡푚, 푡푚 + Δ푡푚 = 푵풐풏풐풗풆풓풍풂풑풊풏품
• 푡1 = 0, 푡푚 = 푇
• 퐺[0,푚] = 퐺1, 퐺2, … , 퐺푚 = 푂푟푑푒푟푒푑 퐺푟푎푝ℎ 퐿푖푠푡
• 퐴 푡푖 = 푇푖푚푒 − 퐷푒푝푒푛푑푎푛푡 퐴푑푗푎푐푒푛푐푦 푀푎푡푟푖푥
Finding the Graph State at Random Time Frame 훼, 훽 → 푡?
• At least one of
• 푡푖 ≤ 훼 < 푡푖 + Δ푡푖 ∶ − −[ − − − − − −
• 푡푖 ≤ 훽 < 푡푖 + Δ푡푖 ∶ − − − − − −] − −
• 훼 < 푡푖 ∧ 푡푖 + Δ푡푖 ≤ 훽 ∶ − −( − − − − − −)
Fixed Time Window: Δ푡 = 푓푖푥푒푑 푡푖푚푒 푠푐푎푙푒 → 0
• 푡푖+1 = 푡푖 + Δ푡 = 푡1 + i × Δ푡

6. Time-Respecting Walks
Temporal Walk from Node i to Node j is a Time Increasing Ordered Sequence of L Edges
푛푟0 , 푛푟1 , 푛푟1 , 푛푟2 , … , 푛푟푙−1 , 푛푟푙
푛푟0 = 푖, 푛푟푙 = 푗
푡푟1 < 푡푟2 < … < 푡푟푙
푎푛푟푙−1
METRICS
Distance
,푛푟푙
푡푟푙 ≠ 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), …

7. 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

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
• Learning Target Function 0 ≤ 푓푥,푦 푡 ≤ 1by 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

10. • 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

11. 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).