Eur. Phys. J. B (2015) 88: 12
https://doi.org/10.1140/epjb/e2014-50220-4

Regular Article

Directed triadic closure and edge deletion mechanism induce asymmetry in directed edge properties^*

¹ Gonda Brain Research Center, Bar-Ilan University, 52900 Ramat Gan, Israel
² Northwestern Institute on Complex Systems, Northwestern University, Evanston, Illinois 60208, USA
³ School of Business Administration, Hebrew University, Jerusalem, Israel
⁴ Department of Mathematics, Bar-Ilan University, 52900 Ramat Gan, Israel

^a e-mail: hillay@gmail.com
^b e-mail: louzouy@math.biu.ac.il

Received: 31 March 2014
Received in final form: 11 September 2014
Published online: 12 January 2015

Abstract

Many directed real world networks, such as the WWW, genetic regulation networks and economic networks exhibit significant differences between the properties of the incoming and outgoing edges, while the differences exhibited by other networks, such as Social Netw. are far more limited. This phenomenon is most evident in the differences between the distributions of incoming and outgoing degrees and direct clustering coefficients. There is currently no generic network generation model that would reproduce and tune these observed dissimilarities. We propose and empirically validate a simple and realistic model that can explain the emergence of the dissimilarities between the incoming and outgoing network degrees and clustering coefficients by combining directed triadic closure, random edge addition and directed edge removal. Surprisingly, we find that the difference between in and out degree distributions is attributed to asymmetries in the edge removal, highlighting the neglected yet crucial importance of edge removal mechanisms to the static and dynamic properties of real world networks. The model is governed by only two parameters: the first tunes the randomness of the edge addition mechanism, while the second controls the difference between the in and out degrees. The combination of these parameters reproduces the observed variety of directed degree distributions and clustering coefficients. Further comparisons of the model’s microscopic dynamics against the empirically observed evolution of real world social network confirms that while quite simple, the model properly describes both the edge addition and deletion processes in directed networks.