  Relay transmission can enhance coverage and throughput, while it can be
vulnerable to eavesdropping attacks due to the additional transmission of the
source message at the relay. Thus, whether or not one should use relay
transmission for secure communication is an interesting and important problem.
In this paper, we consider the transmission of a confidential message from a
source to a destination in a decentralized wireless network in the presence of
randomly distributed eavesdroppers. The source-destination pair can be
potentially assisted by randomly distributed relays. For an arbitrary relay, we
derive exact expressions of secure connection probability for both colluding
and non-colluding eavesdroppers. We further obtain lower bound expressions on
the secure connection probability, which are accurate when the eavesdropper
density is small. By utilizing these lower bound expressions, we propose a
relay selection strategy to improve the secure connection probability. By
analytically comparing the secure connection probability for direct
transmission and relay transmission, we address the important problem of
whether or not to relay and discuss the condition for relay transmission in
terms of the relay density and source-destination distance. These analytical
results are accurate in the small eavesdropper density regime.
