Shapley-Based Analysis of the Leadership Formation in Social Networks

Shapley-Based Analysis of the Leadership Formation in Social Networks

Ivan Belik (Norwegian School of Economics, Norway)
DOI: 10.4018/978-1-5225-7591-7.ch016

Abstract

The dynamic nature of networks formation requires the development of multidisciplinary methods for the effective social network analysis. The research presented in this chapter is motivated by the necessity to overcome the limitation of using analytical methods from the originally disconnected research domains. Hence, the authors present an approach based on techniques from different areas, such as graph theory, theory of algorithms, and game theory. Specifically, this chapter is based on the analysis of how an agent can move towards leadership in real-life socioeconomic networks. For the agent's importance measure, the authors employed a Shapley value concept from the area of cooperative games. Shapley value is interpreted as the node centrality that corresponds to the significance of the agent within a socioeconomic network. Employing game theoretic concept, the authors introduced an algorithmic approach that detects the potential connectivity modifications required to increase an agent's leadership position.
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Introduction

Social network analysis (SNA) is a powerful tool for analyzing the interpersonal relations and different types of cooperation between a variety of social groups such as research or business communities, governmental or private institutions. The uniqueness of SNA is its interdisciplinary approach that combines sociology, graph theory, mathematics, psychology, etc. (Knoke & Yang, 2008). In contrast to pure network analysis, SNA is not concentrated on the structural analysis only, but also takes into consideration the multi-factorial social aspects of relations (Carrington, Scott, & Wasserman, 2005). Nowadays the practical use of SNA is growing fast. The analysis of large-scale networks, pattern recognition, and big data processing within networks is important in many aspects such as decision-making, management and control. SNA techniques are applicable in the analysis of criminal, money-laundering and terrorist networks where the detection of leaders, hidden substructures and influential members is critically important. Social network services, web search engines, web crawlers, and network marketing companies use SNA in symbiosis with big data processing not only to explore and predict customers’ preferences, but also to form them (Bonchi, Castillo, Gionis, & Jaimes, 2011; Catanese, De Meo, Ferrara, Fiumara, & Provetti, 2011; Verbeke, Martens, & Baesens, 2014). Another broad direction of modern SNA is organizational network analysis that covers different quantitative techniques for leadership diagnostics, collaboration boosting and network design based on the organizational interactions (Merrill, Bakken, Rockoff, Gebbie, & Carley, 2007).

Quantitative analysis of leadership formation in social networks is motivated by the following challenging problem. SNA employs methods and techniques from the originally disconnected research domains, such as graph theory, mathematical optimization, and game theory. By bridging different fragmented approaches, it becomes possible to get a comprehensive understanding about various concepts and greater flexibility in their usage. In the given chapter, the authors present an integrated approach of the strategic network analysis in terms of the leadership formation in real-life networks. Specifically, they focus on the domain of network’s centralities.

The variety of approaches for the analysis of network centralities has a purpose to understand and formalize a relative importance of nodes on graphs (i.e., networks). The classical approaches are based on the structural measurements which are derived from graph theory. Centralities based on degree (Freeman, 1978), closeness (Beauchamp, 1965; Sabidussi, 1966), betweenness (Anthonisse, 1971; Freeman, 1977), and information (Wasserman & Faust, 1994) are the most common (conventional) measures. More specifically, degree centrality is a number of direct links incident upon a node. Closeness is an average shortest path from the given node to all other nodes in the network. Betweenness measures how frequently the analyzed node is present in the shortest paths between any two other nodes. In addition, there exist centrality measures for the analysis of node’s importance in complex networks: percolation centrality (Piraveenan, Prokopenko, & Hossain, 2013), cross-clique centrality (Faghani & Nguyen, 2013), and others. Details about each of these network centralities can be found in the corresponding literature. However, it is important to note that the majority of the mentioned topological measures are based on two main concepts: (a) the analysis of different types of flows transferred across a network (Borgatti, 2005), and (b) the analysis of cohesiveness of a network (Borgatti & Everett, 2006).

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