Corruption and its detection: a graph-theoretic approach

We consider a corruption network where agents, both internal or external to the network, use connections and bribes to obtain goods or services outside the formal procedures. We develop a graph-theoretic model for the system and present sufficient conditions for detectability of the corruption status of at least one agent. Where detectability is not possible, we determine the topology of the network and all the possible corruption statuses of the agents. Further we provide, if we have information on the corruption status of a single agent, an algorithm that identifies the corruption status of every other agent in the network. Our results provide tools for detecting corrupt agents in organizations such as revenue authorities, municipalities, police, vehicle inspection departments, financial institutions and firms, while allowing the system to operate in normal mode.