Additional Closeness and Networks Growth

Abstract

Creation and growth are very important in network analysis. In this article we propose one possible model for networks generation. The probabilities of new links are proportional to the expected closeness of the added node. We also propose a new characteristic of graphs - additional closeness, which measures the maximal closeness of a graph after adding a new link. Some properties of the additional closeness are explored. Three different ways of joining two networks are investigated.