Connectivity index
CI
has a vital role in real-world problems especially in Internet routing and transport network flow. Intuitionistic fuzzy graphs
IFGs
allow to describe two aspects of information using membership and nonmembership degrees under uncertainties. Keeping in view the importance of
CI
s
in real life problems and comprehension of
IFGs
, we aim to develop some
CI
s
in the environment of
IFGs
. We introduce two types of
CI
s
, namely,
CI
and average
CI
, in the frame of
IFGs
. In spite of that, certain kinds of nodes called
IF
connectivity enhancing node
IFCEN
,
IF
connectivity reducing node
IFCRN
, and
IF
neutral node are introduced for
IFGs
. We have introduced strongest strong cycles,
θ
-evaluation of vertices, cycle connectivity, and
CI
of strong cycle. Applications of the
CI
s
in two different types of networks are done, Internet routing and transport network flow, followed by examples to show the applicability of the proposed work.