Abstract :

Nowadays, it is imperative to identify the role of key players within product networks mainly for business growth applications. Data exploration for such a broad-spectrum network requires sophisticated tools for their analysis and meaningful inferences. The most commonly used metric are the centrality metrics that are easy and fast in computation. These include Degree Centrality (DC), Closeness Centrality (CC), Betweenness Centrality (BC), Eigenvector Centrality (EVC), Katz Centrality (KC) and the local clustering coefficient-dependent degree centrality (LCCDC or LD). In this study, these metrics have been evaluated and discussed for product datasets of Amazon website. Additionally, novel centrality metrics, the global clustering coefficient-dependent degree centrality (GCCDC or GD) and Dangling centrality have been introduced. LCCDC or LD is pretty easy to compute as compared to BC but it cannot deal with uncertainties in big data or networks that contain nodes with DC equal to unity or nodes that have no links between their connected neighbors. On the other hand, GCCDC or GD showed positive association with BC and in this study, it has been evaluated through three correlation coefficients; "Pearson's correlation coefficient (PCC), Spearman's correlation coefficient (SCC) and Kendall's correlation coefficient (KCC)". The acquired results proved that GD is preferable over LD. Moreover, "Dangling centrality (Øc)" algorithm also showed robust relation with all centrality metrics and provided quite useful information about essentiality of nodes. Another computation method of network analysis, that is maximal clique size (MC), was also modified to decrease uncertainty and complexity in computations. In addition to this, modified MC helped to investigate influential actors (nodes) in a network. Previous studies focused on centrality metrics like "Degree Centrality (DC)", "Closeness Centrality (CC)", "Betweenness Centrality (BC)" and "Eigenvector centrality (EVC)" and compare them with MC, while in this study "Katz centrality (KC)" and "Dangling centrality(b.)" measures were evaluated against MC and showed positive robust relation with maximal clique size (MC). Moreover, association between MC and six centrality metrics has been evaluated through recognized methods (PCC, SCC and KCC). The strong strength of association (positive correlation) between them has been observed through all three correlation coefficients measure (≥ 0.4) for different datasets.

In network analysis, another important problem was to determine useful configuration of communities in large network datasets. Current available techniques were limited to the
network topology and size of data. To tackle the identification of community structures in real-life big datasets, another important contribution was the development of "fuzzy community detection technique" that was able to deal with uncertainties ( due to continuous growth in data with respect to time t) in configuration of communities.

Keywords: Centrality Measures, Network Analysis, Global clustering coefficient-dependent degree centrality