Poor–rich demarcation of Matthew effect on scale-free systems and its application

In a scale-free network, only a minority of nodes are connected very often, while the majority of nodes are connected rarely. However, what is the ratio of minority nodes to majority nodes resulting from the Matthew effect? In this paper, based on a simple preferential random model, the poor-rich demarcation points are found to vary in a limited range, and form a poor-rich demarcation interval that approximates to k/m ∈ 3,4. As a result, the (cumulative) degree distribution of a scale-free network can be divided into three intervals: the poor interval, the demarcation interval and the rich interval. The inequality of the degree distribution in each interval is measured. Finally, the Matthew effect is applied to the ABC analysis of project management.