arXiv subjects
Publications and source records attributed to Chavdar Dangalchev.
In this article we consider networks, which for a given time period can have one link broken. Which new link should we build so the closeness of the resulting network satisfies some optimal criteria? We consider different criteria for optimization and different graphs: cycle, paths, lollipop graphs, and two complete graphs, connected by a link.
Closeness is an important measure of network centrality. In this article we will calculate the closeness of graphs, created by using operations on graphs. We will prove a formula for the closeness of shadow graphs. We will calculate the closeness of line graphs of some wellknown graphs (like path, star, cycle, and complete graphs) and the closeness of line graphs of two of these graphs, connected by a bridge (like lollipop, tadpole, broom, and bistar graphs).
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.