This paper proposes two important mathematical models related to network topology
which helps in computing some of the efficiency or reliability factors of communication
network as well as design purposes. Each of these models represents a topology
property. The first (second) of these models is used to compute the number of
appearances of any link (node) in the geodesics between nodes in a given network
topology, and so can be used to help in uniformly distributing the data flow through
links (nodes), as well as helping in measuring the degree of survivability of the network
in case of failure of some of its links (nodes). The two models have been developed
using “Graph Theory”, and so, giving the advantage of using the very wide range of
ideas, tools, and theorems of this field in case of developing other network topology
formulas based on the two models proposed in this paper.