Abstract
The rich club organization (the presence of highly connected hub core in a network) influences many structural and functional characteristics of networks including topology, the efficiency of paths and distribution of load. Despite its major role, the literature contains only a very limited set of models capable of generating networks with realistic rich club structure. One possible reason is that the rich club organization is a divisive property among complex networks which exhibit great diversity, in contrast to other metrics (e.g. diameter, clustering or degree distribution) which seem to behave very similarly across many networks. Here we propose a simple yet powerful geometry-based growing model which can generate realistic complex networks with high rich club diversity by controlling a single geometric parameter. The growing model is validated against the Internet, protein-protein interaction, airport and power grid networks.
Highlights
The rich club organization plays a central role in the structure and function of networks[1,2,3,4,5,6,7,8]
We propose a simple geometry-based growing model which can explain the emergence of the rich club variability in real networks by adjusting a single spatial parameter
An intriguing question could be whether our model captures something fundamental from the growth processes of real networks, or exhibit similar rich-club diversity by chance
Summary
The rich club organization plays a central role in the structure and function of networks[1,2,3,4,5,6,7,8]. The state-of-the-art models targeting the rich club organization are based on heavy randomization techniques[10,11,12,13], which shuffle network connections until a given organization structure is artificially imitated. In certain social networks, middlemen as intermediate nodes may play crucial role in enhancing cooperation between the individuals or groups[17] Such networks seem to implement an “artificial” threshold above which no direct connections are allowed. In this paper we confine these observations into a simple geometric growing model, in which we introduce a length threshold for creating edges We show that such a growing model can naturally reproduce and account for the experienced diversity in the rich-club organization of networks, while keeping other network statistics www.nature.com/scientificreports/.
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