Lobachevskii Journal of Mathematics

, Volume 40, Issue 1, pp 106–113 | Cite as

On Optimization of Complete Social Networks

  • A. T. WeldegebrielEmail author
  • B. Y. StodolskyEmail author


A balanced social network is a social network where, for any member of the social network, the following two statements are true; a friend of my friend is my friend and an enemy of my enemy is my friend. In this paper we demonstrate a polynomial time greedy algorithm that balances any complete social network with n members by changing at most ⌈n2/4 − n/2⌉ of the initial relationships between the members of the network. We also demonstrate that the problem of determining the minimum number of relationships that needs to change so that a complete social network, where each member has at least as many friends as enemies, becomes balanced is still NP-Complete.

Keywords and phrases

Balanced signed graphs Graph algorithms 


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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Istanbul Technical University, Fen-Edebiyat Faculty, Department of Mathematics B1-303Maslak, IstanbulTurkey

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