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The geodetic problem was introduced by Harary et al. In order to model some social network problems, a similar problem is introduced in this paper and named the strong geodetic problem. The problem is solved for complete Apollonian networks. It is also proved that in general the strong geodetic problem is NP-complete.arXiv:1708.03868v1 fatcat:3dz6zcra4bcffi47zqfaplosgm