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<http://schema.org/description>
"Is it always beneficial to create a new relationship (have a new\nfollower/friend) in a social network? This question can be formally stated as a\nproperty of the centrality measure that defines the importance of the actors of\nthe network. Score monotonicity means that adding an arc increases the\ncentrality score of the target of the arc; rank monotonicity means that adding\nan arc improves the importance of the target of the arc relatively to the\nremaining nodes. It is known that most centralities are both score and rank\nmonotone on directed, strongly connected graphs. In this paper, we study the\nproblem of score and rank monotonicity for classical centrality measures in the\ncase of undirected networks: in this case, we require that score, or relative\nimportance, improve at both endpoints of the new edge. We show that,\nsurprisingly, the situation in the undirected case is very different, and in\nparticular that closeness, harmonic centrality, betweenness, eigenvector\ncentrality, Seeley's index, Katz's index, and PageRank are not rank monotone;\nbetweenness and PageRank are not even score monotone. In other words, while it\nis always a good thing to get a new follower, it is not always beneficial to\nget a new friend."
<http://api.deepai.org/profile/sebastiano-vigna>