A centrality measure for communication ability in weighted network

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Highlights

  • We proposed a new node centrality measurement in weighted network.

  • We investigated the properties of the communication centrality.

  • It is superior to other centrality measures in the use of information.

  • It contains a well-balanced mix of other centrality measures.

Abstract

This paper proposes a new node centrality measurement in a weighted network, the communication centrality, which is inspired by Hirsch’s h-index. We investigated the properties of the communication centrality, and proved that the distribution of the communication centrality has the power-law upper tail in weighted scale-free networks. Relevant measures for node and network are discussed as extensions. A case study of a scientific collaboration network indicates that the communication centrality is different from other common centrality measures and other h-type indexes. Communication centrality displays moderate correlation with other indexes, and contains a well-balanced mix of other centrality measures and cannot be replaced by any of them.

Introduction

Efficient communication means high impact (wide access or high reach) and low cost, whether in communication networks, or in social and biological networks  [1]. In a complex network, the roles, positions, influence and centrality of nodes is usually expressed by node degree centrality  [2], [3], [4], node strength  [5], closeness centrality  [6], [7], betweenness centrality  [2] and eigenvector centrality  [8] etc. Nonetheless, none of these indexes can accurately capture the communication ability of the nodes  [1].

This paper brings forth a new concept of communication centrality in the weighted network to measure the communication ability of the node. We principally considered three major influencing factors. First, node degree, namely the number of neighbor nodes, is the most direct perceived factor exerting effects on the communication ability of the node. Clearly, more neighbor nodes indicate more effective communication of a node since it can pass on and receive information through more channels. Second, the stronger communication ability of the neighbor nodes of a node demonstrates the greater influence of its communication since the neighbor nodes boast a tremendous capacity to communicate. For instance in the network of lobbyists (or diplomats), the persuasion of a lobbyist who is stronger in lobby ability can produce better results than that of a weaker lobbyist. Third, the edge weight of a node has a remarkable influence on the communication ability of this node. Without loss of generality, we suppose that greater edge weight represents faster arrival or lower communication costs or higher trust. Therefore greater edge weight means the stronger ability of this node to communicate with its neighbor nodes. For example, in a collaboration network, greater edge weight indicates more frequent collaboration, and then the bilateral communication is obviously highly efficient. For another example, in the network of friends, if the edge weight represents the intimacy degree or the trust, then the edge weight will exert influence on the communication between friends and further influence the communication ability of a person.

Hirsch  [9] proposed the h-index, which integrates the amount of papers and citation times of papers to measure the academic achievements or influence of scholars. “A scientist has h-index h if h of his or her Np papers have at least h citations each and the other (Nph) papers have h citations each”  [9]. The H-index simply and effectively measures the key part of a dataset in a relatively natural way  [10]. Since its introduction, the h-index and some related bibliometric indices have received a lot of attention from the scientific community in the last few years  [11].

Scholars have applied the h-index and some other indexes in the network to measure the centrality of the nodes. Zhao et al.  [10] stated that the h-degree in the weighted network can be used as the centrality measure of nodes. “The h-degree of node x in a weighted network is equal to k if k is the largest natural number such that x has at least k links each with strength at least equal to k”  [10]. Furthermore, Zhao et al.  [12] promoted the concept of h-degree to the directional weighted network and introduced the directed h-degree  [12]. But h-degree does not consider the influence of neighbor nodes upon the centrality of this node. Schubert [13] proposed the partnership ability index φ   [13], where φ is a special case of the h-degree  [14]. In 2009, Korn et al. put forward the lobby index for the non-weighted network to describe communication ability  [1]. “The lobby index of a node x is the largest integer k such that x has at least k neighbors with a degree of at least k”  [1]. Zhao et al. [10] promoted the lobby index to be the w-lobby index in the weighted network, stating that “the w-lobby index of a node x is the largest integer k such that x has at least k neighbors with node strength at least k”  [10]. Consistent with  [5], [10], in this paper we define the node strength of a node in a weighted network as the sum of weights of all its edges. Campiteli et al. studied the nature of lobby index combining a actual non-weighted biological network and a linguistic network  [15]. The lobby index and w-lobby index integrate node degree and degree (strength) of neighbor nodes. They are superior to indexes measuring node centrality without using information of neighbor nodes for communication ability, such as node degree, node strength and h-degree. However, lobby index and w-lobby index neglect an important factor: different edge weights of this node mean different communication ability. Additionally, the lobby index displays strong correlation with degree centrality   [1].

Based on the idea of h-index, this paper proposes a communication centrality to measure node centrality reflecting a communication ability which is suitable for the analysis of weighted undirected networks. The structure of the paper is as follows: Section  2 gives the definition of communication centrality and discusses its theoretical properties. Section  3 documents a case study conducted to comprehensively evaluate the communication centrality in a large co-author network, along with other well-known centrality indexes. Section  4 concludes the paper.

Section snippets

The communication centrality

In this section, we will define communication centrality and discuss its property. As mentioned, the communication ability of a node’s neighbor nodes in the weighted network stands as the important factor influencing its communication ability. Then, how is the communication ability of the neighbor nodes reflected? For a given node, larger degree means more neighbor nodes and higher communication ability in the network, and greater edge weight with neighbor nodes indicates more frequent contact

Data

We choose eight top academic journals in the field of information systems (see Table 2) as the data source to construct a co-author network. We retrieved data from the Web of Science databases on September 1, 2012. 3457 articles with 4322 authors recorded by “Article” are downloaded from the nine journals for the period of January 1, 1981–September 1, 2012. The co-author network takes the scholar as the node, constructs the edge according to the collaboration relationship and makes

Conclusions

Built upon well-known scientific measurement index h-index and h-degree in network, this paper proposes the communication centrality to measure the communication ability of a node in a weighted undirected network. Communication centrality overcomes the strong correlation of lobby index and w-lobby index with node degree, adds the information of edge weight of the node that influences communication ability in the calculation and effectuates more accurate measurement. Nevertheless, the lobby

Acknowledgments

This work is partly supported by the National Natural Science Foundation of PRC (No. 71171067, 71328103, 71171068) and Postdoctoral Science-research Developmental Foundation of Heilongjiang province (No. LBH-Q11114).

References (19)

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