English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Triangle counting is a fundamental technique in network analysis, that hasreceived much attention in various input models. The vast majority of trianglecounting algorithms are targeted to static graphs. Yet, many real-world graphsare directed and temporal, where edges come with timestamps. Temporal trianglesyield much more information, since they account for both the graph topology andthe timestamps.  Temporal triangle counting has seen a few recent results, but there arevarying definitions of temporal triangles. In all cases, temporal trianglepatterns enforce constraints on the time interval between edges (in thetriangle). We define a general notion $(\delta_{1,3}, \delta_{1,2},\delta_{2,3})$-temporal triangles that allows for separate time constraints forall pairs of edges.  Our main result is a new algorithm, DOTTT (Degeneracy Oriented TemporalTriangle Totaler), that exactly counts all directed variants of $(\delta_{1,3},\delta_{1,2}, \delta_{2,3})$-temporal triangles. Using the classic idea ofdegeneracy ordering with careful combinatorial arguments, we can prove thatDOTTT runs in $O(m\kappa\log m)$ time, where $m$ is the number of (temporal)edges and $\kappa$ is the graph degeneracy (max core number). Up to logfactors, this matches the running time of the best static triangle counters.Moreover, this running time is better than existing.  DOTTT has excellent practical behavior and runs twice as fast as existingstate-of-the-art temporal triangle counters (and is also more general). Forexample, DOTTT computes all types of temporal queries in Bitcoin temporalnetwork with half a billion edges in less than an hour on a commodity machine.

Faster and Generalized Temporal Triangle Counting, via Degeneracy Ordering