  One of the most prominent properties in real-world networks is the presence
of a community structure, i.e. dense and loosely interconnected groups of nodes
called communities. In an attempt to better understand this concept, we study
the relationship between the strength of the community structure and the
network transitivity (or clustering coefficient). Although intuitively
appealing, this analysis was not performed before. We adopt an approach based
on random models to empirically study how one property varies depending on the
other. It turns out the transitivity increases with the community structure
strength, and is also affected by the distribution of the community sizes.
Furthermore, increasing the transitivity also results in a stronger community
structure. More surprisingly, if a very weak community structure causes almost
zero transitivity, the opposite is not true and a network with a close to zero
transitivity can still have a clearly defined community structure. Further
analytical work is necessary to characterize the exact nature of the identified
relationship.
