Monotonicity in undirected networks

IF 1.4 Q2 SOCIAL SCIENCES, INTERDISCIPLINARY

Network Science Pub Date : 2023-02-02 DOI:10.1017/nws.2022.42

Paolo Boldi, Flavio Furia, Sebastiano Vigna

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引用次数: 0

Abstract

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

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无向网络的单调性

在社交网络中建立一个新的关系(有一个新的追随者/朋友)总是有益的吗?这个问题可以正式表述为定义网络参与者重要性的中心性度量的属性。分数单调性是指增加一条弧，使该弧目标的中心性分数增加;秩单调性是指增加一个弧，相对于剩余的节点，该弧的目标的重要性得到提高。已知大多数中心性在有向强连通图上都是分数单调和秩单调。在本文中，我们研究了无向网络中经典中心度量的分数和秩单调性问题:在这种情况下，我们要求分数或相对重要性在新边的两个端点上都有所提高。令人惊讶的是，我们证明了无向情况下的情况是非常不同的，特别是接近度、调和中心性、中间性、特征向量中心性、Seeley指数、Katz指数和PageRank不是秩单调的;between和PageRank甚至不是得分单调的。换句话说，虽然得到一个新的追随者总是一件好事，但得到一个新朋友并不总是有益的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Network Science SOCIAL SCIENCES, INTERDISCIPLINARY-

CiteScore

3.50

自引率

5.90%

发文量

期刊介绍： Network Science is an important journal for an important discipline - one using the network paradigm, focusing on actors and relational linkages, to inform research, methodology, and applications from many fields across the natural, social, engineering and informational sciences. Given growing understanding of the interconnectedness and globalization of the world, network methods are an increasingly recognized way to research aspects of modern society along with the individuals, organizations, and other actors within it. The discipline is ready for a comprehensive journal, open to papers from all relevant areas. Network Science is a defining work, shaping this discipline. The journal welcomes contributions from researchers in all areas working on network theory, methods, and data.