Connectivity is one of the most important parameters related to networks such as internet routing, transport network flow, and so on, which can be used to measure the stability of a network. This concept has particular importance in fuzzy graphs. A cubic fuzzy graph is a fuzzy graph that supports both fuzzy membership and interval-valued fuzzy membership. Simultaneity of two different memberships leads to better flexibility in modeling problems than uncertain variables.The limitations of previous definitions in this area led to the description of connectivity indices in a cubic fuzzy graph. In this research work, the parameters of connectivity index and average connectivity index are described as the main parameters related to the network. Some of their properties and boundaries have been studied. The results of removing a vertex and its effect on the connectivity index are discussed. Finally, an application of connectivity index in an interconnected network of journals is presented.
