Abstract Closeness is one of the most studied characteristics of networks. Residual closeness is a very sensitive measure of graphs robustness. Additional closeness is a measure of growth potentials of networks. In this article, we calculate the closeness, vertex residual closeness, link residual closeness and additional closeness of lollipop graphs.

The study of networks characteristics is an important subject in different fields, like math, chemistry, transportation, social network analysis etc. The residual closeness is one of the most sensitive measure of graphs’ vulnerability. In this article we calculate the link residual closeness of Harary graphs.

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.

One of the most sensitive characteristics of network vulnerability is residual closeness. Calculating the closeness and the residual closeness of larger graphs is a time consuming and operations heavy process. In this article, we try to mitigate the process for thorn graphs - we present the thorn g raphs residual closeness as a function of the closeness and the residual closeness of the original graphs.