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 problem of betweenness centrality remains a fundamental unsolved problemin complex networks. After a pioneering work by Barthelemy, it has beenwell-accepted that the maximal betweenness-degree ($b$-$k$) exponent forscale-free (SF) networks is $\eta_{\text{max}}=2$, belonging to scale-freetrees (SFTs), based on which one concludes $\delta\ge\frac{\gamma+1}{2}$, where$\gamma$ and $\delta$ are the scaling exponents of the distribution functionsof the degree and betweenness centrality, respectively. Here we presentevidence for violation of this conjecture for SF visibility graphs (VGs). Tothis end, we consider the VG of three models: two-dimensional (2D)Bak-Tang-Weisenfeld (BTW) sandpile model, 1D fractional Brownian motion (FBM)and, 1D Levy walks, the two later cases are controlled by the Hurst exponent$H$ and step-index $\alpha$, respectively. Specifically, for the BTW model andFBM with $H\lesssim 0.5$, $\eta$ is greater than $2$, and also$\delta<\frac{\gamma+1}{2}$ for the BTW model, while Barthelemy's conjectureremains valid for the Levy process. We argue that this failure of Barthelemy'sconjecture is due to large fluctuations in the scaling $b$-$k$ relationresulting in the violation of hyperscaling relation$\eta=\frac{\gamma-1}{\delta-1}$ and emergent anomalous behaviors for the BTWmodel and FBM. A super-universal behavior is found for the distributionfunction for a generalized degree function identical to the Barabasi-Albertnetwork model.

The Visibility Graphs of Correlated Time Series Violate the Barthelemy's Conjecture for Degree and Betweenness Centralities