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To defend against reconnaissance activity in ad hoc wireless networks, we propose transmission power control as an effective mechanism for minimizing the eavesdropping risk. Our main contributions are given as follows. First, we cast the wth-order eavesdropping risk as the maximum probability of packets being eavesdropped when there are w adversarial nodes in the network. Second, we derive the closed-form solution of the first-order eavesdropping risk as a polynomial function of the normalized transmission radius. This derivation assumes a uniform distribution of user nodes. Then, we generalize the model to allow arbitrary user nodes distribution and prove that the uniform user distribution minimizes the first-order eavesdropping risk. This result plays an essential role in deriving analytical bounds for the eavesdropping risk given arbitrary user distributions. Our simulation results show that, for a wide range of nonuniform traffic patterns, the difference in their eavesdropping risk values from the corresponding lower bounds is 3 dB or less.