Given the high uncertainty in the dynamics of Wireless Sensor Networks (WSN), it is essential to monitor the Quality-of-Service metrics in order to find the links with poor characteristics. This would allow to implement fault-tolerant protocols to reroute the control packets and avoid zones with untrusted links. However, network monitoring is not used as a permanent analysis tool. This is due both to the conventional use of highly-complex inference algorithms and active approaches such as injection of probing packets. In this paper, we introduce a tree-graph representation for WSN with a general topology, and also suitable for link parameters inference problems. Factor Graphs and the Sum-Product algorithm are considered to develop low complexity schemes for permanent and passive monitoring of multiple link parameters such as Link Loss Rate, Link Error Rate and Link Delay.