Closeness centrality is one way of measuring how central a node is in the given network. The closeness centrality measure assigns a centrality value to each node based on its accessibility to the whole network. In real life applications, we are mainly interested in ranking nodes based on their centrality values. The classical method to compute the rank of a node first computes the closeness centrality of all nodes and then compares them to get its rank. Its time complexity is @math , where @math represents total number of nodes, and @math represents total number of edges in the network. In the present work, we propose a heuristic method to fast estimate the closeness rank of a node in @math time complexity, where @math . We also propose an extended improved method using uniform sampling technique. This method better estimates the rank and it has the time complexity @math , where @math . This is an excellent improvement over the classical centrality ranking method. The efficiency of the proposed methods is verified on real world scale-free social networks using absolute and weighted error functions.
studied the correlation of closeness centrality with the local neighborhood volume of the node @cite_25 . The ranking based on local neighborhood volume is named as DACCER (Distributed Assessment of the Closeness CEntrality Ranking) and is highly correlated with closeness centrality ranking in both real world and synthetic networks.
@cite_25
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We propose a method for the Distributed Assessment of the Closeness CEntrality Ranking (DACCER) in complex networks. DACCER computes centrality based only on localized information restricted to a limited neighborhood around each node, thus not requiring full knowledge of the network topology. We indicate that the node centrality ranking computed by DACCER is highly correlated with the node ranking based on the traditional closeness centrality, which requires high computational costs and full knowledge of the network topology by the entity responsible for calculating the centrality. This outcome is quite useful given the vast potential applicability of closeness centrality, which is seldom applied to large-scale networks due to its high computational costs. Results indicate that DACCER is simple, yet efficient, in assessing node centrality while allowing a distributed implementation that contributes to its performance. This also contributes to the practical applicability of DACCER to the analysis of large complex networks, as indicated in our experimental evaluation using both synthetically generated networks and real-world network traces of different kinds and scales. Centrality metrics have shown to be highly correlated with the importance and loads of the nodes within the network traffic. In this work, we provide fast incremental algorithms for closeness centrality computation. Our algorithms efficiently compute the closeness centrality values upon changes in network topology, i.e., edge insertions and deletions. We show that the proposed techniques are efficient on many real-life networks, especially on small-world networks, which have a small diameter and spike-shaped shortest distance distribution. We experimentally validate the efficiency of our algorithms on large-scale networks and show that they can update the closeness centrality values of 1.2 million authors in the temporal DBLP-coauthorship network 460 times faster than it would take to recompute them from scratch. Abstract As network analysis methods prevail, more metrics are applied to co-word networks to reveal hot topics in a field. However, few studies have examined the relationships among these metrics. To bridge this gap, this study explores the relationships among different ranking metrics, including one frequency-based and six network-based metrics, in order to understand the impact of network structural features on ranking themes on co-word networks. We collected bibliographic data from three disciplines from Web of Science (WoS), and generated 40 simulation networks following the preferential attachment assumption. Correlation analysis on the empirical and simulated networks shows strong relationships among the metrics. Their relationships are consistent across disciplines. The metrics can be categorized into three groups according to the strength of their correlations, where Degree Centrality, H-index, and Coreness are in one group, Betweenness Centrality, Clustering Coefficient, and frequency in another, and Weighted PageRank by itself. Regression analysis on the simulation networks reveals that network topology properties, such as connectivity, sparsity, and aggregation, influence the relationships among selected metrics. In addition, when comparing the top keywords ranked by the metrics in the three disciplines, we found the metrics exhibit different discriminative capacity. Coreness and H-index may be better suited for categorizing keywords rather than ranking keywords. Findings from this study contribute to a better understanding of the relationships among different metrics and provide guidance for using them effectively in different contexts. Centrality has revealed crucial for understanding the structural properties of complex relational networks. Centrality is also relevant for various spatial factors affecting human life and behaviors in cities. Here, we present a comprehensive study of centrality distributions over geographic networks of urban streets. Five different measures of centrality, namely degree, closeness, betweenness, straightness and information, are compared over 18 1-square-mile samples of different world cities. Samples are represented by primal geographic graphs, i.e., valued graphs defined by metric rather than topologic distance where intersections are turned into nodes and streets into edges. The spatial behavior of centrality indices over the networks is investigated graphically by means of color-coded maps. The results indicate that a spatial analysis, that we term multiple centrality assessment, grounded not on a single but on a set of different centrality indices, allows an extended comprehension of the city structur...