In this paper, we will investigate the concept of the torsion-graph of an R-module M, in which the set

makes up the vertices of the corresponding torsion graph,

, with any two distinct vertices forming an edge if

. We prove that, if

contains a cycle, then

and

has a connected induced subgraph

with vertex set

and diam

. Moreover, if M is a multiplication R-module, then

is a maximal connected subgraph of

. Also

and

are isomorphic graphs, where

. Furthermore, we show that, if

is uniquely complemented, then

is a von Neumann regular module or

is a star graph.