Monotonicity in undirected networks

Abstract Is it always beneficial to create a new relationship (have follower/friend) in social network? This question can be formally stated as property of the centrality measure that defines importance actors network. Score monotonicity means adding an arc increases score target arc; rank improves relatively remaining nodes. It is known most centralities are both and monotone on directed, strongly connected graphs. In this paper, we study problem for classical measures case undirected networks: case, require score, or relative importance, at endpoints edge. We show that, surprisingly, situation very different, particular closeness, harmonic centrality, betweenness, eigenvector Seeley’s index, Katz’s PageRank not monotone; betweenness even monotone. other words, while good thing get follower, friend.