A new methodology is given for describing the effectiveness of communicating networks of processing subsystems which are subject to communication and processing failures or losses. The network attributes are described as a graph of nodes and edges. A class of performance measures called the “survival index” is defined axiomatically on a connectivity state for the network graph and its reductions. This definition is based on the idea of a team of members cooperating or sharing resources by use of communication links, and on the existence of synergism or a “team effect,” where a group of connected members are more effective than isolated members. The present work is restricted to homogeneous teams — where members have equal capability.