《Distinctiveness centrality in social networks》

Abstract

The determination of node centrality is a fundamental topic in social network studies. As an addition to established metrics, which identify central nodes based on their brokerage power, the number and weight of their connections, and the ability to quickly reach all other nodes, we introduce five new measures of Distinctiveness Centrality. These new metrics attribute a higher score to nodes keeping a connection with the network periphery. They penalize links to highly-connected nodes and serve the identification of social actors with more distinctive network ties. We discuss some possible applications and properties of these newly introduced metrics, such as their upper and lower bounds. Distinctiveness centrality provides a viewpoint of centrality alternative to that of established metrics.

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中心性指标可以确定图中的最重要的节点

在复杂网络学习中，有着几种经典的度量指标，如：degree centrality度中心性，closeness centrality近性中心性， betweenness介性中心性，eigenvector centrality特征向量中心性

本文作者提出了Distinctiveness centrality 独特中心性

Distinctiveness Centrality (DC)—that attribute more importance to nodes which have links to loosely connected others

在introduction中，作者认为 the majority of centrality metrics tend to attribute stronger influence to nodes that are highly connected, or which are connected to other important nodes. Connections to the network periphery（边缘、外围、次要部分）, on the other hand, are often regarded as less relevant.

与网络外围的连接很少被认为是相关的，故最重要的节点有可能是那些将网络外围连接在一起的节点

虽然传统的度量指标很有代表性，但某些情况下，与外围节点的连接也应该被重视

作者进行了举例说明：For example, it might be the case that nodes with more peripheral connections keep the network together, avoiding fragmentation. In other applications, for example when analysing word co-occurrence networks [1] to evaluate brand importance [2], brands with connections to distinctive words may be more important, as they show unique traits that distinguish them from competitors.

该指标还存在的优势：Distinctiveness centrality is also relatively fast to compute, as it does not require the calculation of shortest network paths

五个指标：

• Weighted distinctiveness centrality
• Distinctiveness centrality
• Global weight distinctiveness centrality
• Weighted proportional distinctiveness centrality
• Proportional distinctiveness centrality

作者进行了举例说明，demo和data如下：

红色为最高值，即越重要；蓝色为最低值，即不重要。α≥1 is used to allow a stronger penalization of connections with highly connected nodes（增加α的值会惩罚高度连接的节点）.

可以看出：

• 随着α增大，D1、D2和D3变化趋势很大，不稳定；而D4和D5却比较稳定

在有向网络中，作者也进行了推广

• Weighted Distinctiveness Centrality IN and OUT
• Distinctiveness Centrality IN and OUT
• Global Weight Distinctiveness Centrality IN and OUT
• Weighted Proportional Distinctiveness Centrality IN and OUT
• Proportional Distinctiveness Centrality IN and OUT

同样，demo和data如下：

可以看出：

• 对于出度来说，B节点具有更多的出度，因此惩罚其out-distinctiveness，则重要性略低于A节点；α越大，效果越明显

对于实际应用，作者提到了the identification of prominent nodes in criminal organizations

对比之前做的分析网络黑灰产的项目，我们是直接在gephi软件中运用已存在且广泛运用的一些指标进行分析，偶然看到了这篇论文，确实为分析问题打开了新思路和新见解。

还举了 relationships between Florentine families in the 15th century （unweighted network）来验证：

参考文献：

1. Evert S. The statistics of word cooccurrences: word pairs and collocations. Universita¨t Stuttgart; 2005.

2. Fronzetti Colladon A. The semantic brand score. Journal of Business Research. 2018; 88:150–160. https://doi.org/10.1016/j.jbusres.2018.03.026