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Percolation in an information-theoretically secure graph is considered whereboth the legitimate and the eavesdropper nodes are distributed as Poisson pointprocesses. For both the path-loss and the path-loss plus fading model, upperand lower bounds on the minimum density of the legitimate nodes (as a functionof the density of the eavesdropper nodes) required for non-zero probability ofhaving an unbounded cluster are derived. The lower bound is universal innature, i.e. the constant does not depend on the density of the eavesdroppernodes.

Super Critical and Sub Critical Regimes of Percolation with Secure Communication