This brief reviews concepts of inter-relationship in modern industrial processes, biological and social systems. Specifically ideas of connectivity and causality within and between elements of a complex system are treated; these ideas are of great importance in analysing and influencing mechanisms, structural properties and their dynamic behaviour, especially for fault diagnosis and hazard analysis. Fault detection and isolation for industrial processes being concerned with root causes and fault propagation, the brief shows that, process connectivity and causality information can be...