Benford Networks
1
Land Consult, landConsult.de Öhinghaltweg 3 D, 77815 Bühl, Germany
2
Department of Statistical Sciences, Sapienza University of Rome, Piazzale Aldo Moro 5, 00185 Roma, Italy
*
Author to whom correspondence should be addressed.
Academic Editors: Claudio Lupi, Roy Cerqueti and Marcel Ausloos
Stats 2022, 5(4), 934-947; https://doi.org/10.3390/stats5040054
Received: 28 July 2022
/
Revised: 10 September 2022
/
Accepted: 20 September 2022
/
Published: 30 September 2022
(This article belongs to the Special Issue Benford's Law(s) and Applications)
The Benford law applied within complex networks is an interesting area of research. This paper proposes a new algorithm for the generation of a Benford network based on priority rank, and further specifies the formal definition. The condition to be taken into account is the probability density of the node degree. In addition to this first algorithm, an iterative algorithm is proposed based on rewiring. Its development requires the introduction of an ad hoc measure for understanding how far an arbitrary network is from a Benford network. The definition is a semi-distance and does not lead to a distance in mathematical terms, instead serving to identify the Benford network as a class. The semi-distance is a function of the network; it is computationally less expensive than the degree of conformity and serves to set a descent condition for the rewiring. The algorithm stops when it meets the condition that either the network is Benford or the maximum number of iterations is reached. The second condition is needed because only a limited set of densities allow for a Benford network. Another important topic is assortativity and the extremes which can be achieved by constraining the network topology; for this reason, we ran simulations on artificial networks and explored further theoretical settings as preliminary work on models of preferential attachment. Based on our extensive analysis, the first proposed algorithm remains the best one from a computational point of view.
View Full-Text
Keywords:
Benford law; complex networks; semi-distance
▼
Show Figures
Figure 1
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
MDPI and ACS Style
de Kok, R.; Rotundo, G. Benford Networks. Stats 2022, 5, 934-947. https://doi.org/10.3390/stats5040054
AMA Style
de Kok R, Rotundo G. Benford Networks. Stats. 2022; 5(4):934-947. https://doi.org/10.3390/stats5040054
Chicago/Turabian Stylede Kok, Roeland, and Giulia Rotundo. 2022. "Benford Networks" Stats 5, no. 4: 934-947. https://doi.org/10.3390/stats5040054
Find Other Styles
