The influence of secrecy on the communication structure of covert networks

In order to be able to devise successful strategies for destabilizing covert organizations it is vital to recognize and understand their structural properties. Every covert organization faces the constant dilemma of staying secret and ensuring the necessary coordination between its members. Using elements from multi-objective optimization and bargaining game theory we analyze which communication structures are optimal in the sense of providing a balanced tradeoff between secrecy and operational efficiency. For several different secrecy and information scenarios this tradeoff is analyzed considering the set of connected graphs of given order as possible communication structures. Assuming uniform exposure probability of individuals in the network we show that the optimal communication structure corresponds to either a network with a central individual (the star graph) or an all-to-all network (the complete graph) depending on the link detection probability, which is the probability that communication between individuals will be detected. If the probability that an individual is exposed as member of the network depends on the information hierarchy determined by the structure of the graph, the optimal communication structure corresponds to a reinforced ring or wheel graph in case of an information measure based on average performance. In worst case performance with respect to information it can be seen that windmill wing graphs approximate optimal structures. Finally we give an example how optimal structures change when considering a non-balanced tradeoff between secrecy and operational efficiency.