Multiplex congruence network of natural numbers

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalNot applicablepeer-review

5 Scopus Citations
View graph of relations

Author(s)

Related Research Unit(s)

Detail(s)

Original languageEnglish
Article number23714
Journal / PublicationScientific Reports
Volume6
Publication statusPublished - 31 Mar 2016

Link(s)

Abstract

Congruence theory has many applications in physical, social, biological and technological systems. Congruence arithmetic has been a fundamental tool for data security and computer algebra. However, much less attention was devoted to the topological features of congruence relations among natural numbers. Here, we explore the congruence relations in the setting of a multiplex network and unveil some unique and outstanding properties of the multiplex congruence network. Analytical results show that every layer therein is a sparse and heterogeneous subnetwork with a scale-free topology. Counterintuitively, every layer has an extremely strong controllability in spite of its scale-free structure that is usually difficult to control. Another amazing feature is that the controllability is robust against targeted attacks to critical nodes but vulnerable to random failures, which also differs from ordinary scale-free networks. The multi-chain structure with a small number of chain roots arising from each layer accounts for the strong controllability and the abnormal feature. The multiplex congruence network offers a graphical solution to the simultaneous congruences problem, which may have implication in cryptography based on simultaneous congruences. Our work also gains insight into the design of networks integrating advantages of both heterogeneous and homogeneous networks without inheriting their limitations.

Research Area(s)

Citation Format(s)

Multiplex congruence network of natural numbers. / Yan, Xiao-Yong; Wang, Wen-Xu; Chen, Guan-Rong; Shi, Ding-Hua.

In: Scientific Reports, Vol. 6, 23714, 31.03.2016.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalNot applicablepeer-review

Download Statistics

No data available