One-max constant-probability models for complex networks

Abstract

This paper presents a number of the tree-like networks that grow according to the following newly studied principles: i) each new vertex can be connected to at most one existing vertex; ii) any connection event is realized with the same probability p; iii) the probability Π that a new vertex will be connected to vertex i depends not directly on its degree d i but on the place of d i in the sorted list of vertex degrees. The paper proposes a number of models for such networks, which are called one-max constant-probability models. In the frame of these models, structure and behavior of the corresponding tree-like networks are studied both analytically, and by using computer simulations. © 2014 Springer International Publishing Switzerland.