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 Erd\"os Renyi graph is a popular choice to model network data as it isparsimoniously parametrized, straightforward to interprete and easy toestimate. However, it has limited suitability in practice, since it often failsto capture crucial characteristics of real-world networks. To check theadequacy of this model, we propose a novel class of goodness-of-fit tests forhomogeneous Erd\"os Renyi models against heterogeneous alternatives that allowfor nonconstant edge probabilities. We allow for asymptotically dense andsparse networks. The tests are based on graph functionals that cover a broadclass of network statistics for which we derive limiting distributions in aunified manner. The resulting class of asymptotic tests includes severalexisting tests as special cases. Further, we propose a parametric bootstrap andprove its consistency, which allows for performance improvements particularlyfor small network sizes and avoids the often tedious variance estimation forasymptotic tests. Moreover, we analyse the sensitivity of differentgoodness-of-fit test statistics that rely on popular choices of subgraphs. Weevaluate the proposed class of tests and illustrate our theoretical findings byextensive simulations.

Goodness of fit testing based on graph functionals for homogenous Erd\"os Renyi graphs