One-max constant-probability networks: Results and future work

Abstract

In a number of our works we present and use the tree-like network models, so called one-max constant-probability models characterized by the following newly studied principles: (i) each new vertex may be connected to at most one existing vertex; (ii) any connection event is realized with the same probability p due to external factors; (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. In this announcement we describe features and applications of these models and discuss possible ways of their generalization.