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

The degree distribution is one of the most fundamental graph properties ofinterest for real-world graphs. It has been widely observed in numerous domainsthat graphs typically have a tailed or scale-free degree distribution. Whilethe average degree is usually quite small, the variance is quite high and thereare vertices with degrees at all scales. We focus on the problem ofapproximating the degree distribution of a large streaming graph, with smallstorage. We design an algorithm headtail, whose main novelty is a new estimatorof infrequent degrees using truncated geometric random variables. We give amathematical analysis of headtail and show that it has excellent behavior inpractice. We can process streams will millions of edges with storage less than1% and get extremely accurate approximations for all scales in the degreedistribution.  We also introduce a new notion of Relative Hausdorff distance between tailedhistograms. Existing notions of distances between distributions are notsuitable, since they ignore infrequent degrees in the tail. The RelativeHausdorff distance measures deviations at all scales, and is a more suitabledistance for comparing degree distributions. By tracking this new measure, weare able to give strong empirical evidence of the convergence of headtail.

Catching the head, tail, and everything in between: a streaming algorithm for the degree distribution