# Distributed Centrality Analysis of Social Network Data Using MapReduce
## 1 Introduction  
Ongoing advances in information technology (IT), and particularly the exponential growth of social networks, are main drivers for the growing global connections of businesses and individuals [1]. Identifying key network nodes (or influencing nodes) is an important problem in network information theory [2] that helps in the analysis of complex multi-agent systems such as social networks. The main feature of social networks is that their structure develops via mutual connections between network members. The way the users are interconnected and integrated into the network defines their communication and interaction behavior. Social network analysis (SNA) helps in the mapping relationships between network entities and identifying the patterns of behavior in a network [3], in understanding the dynamic evolution or relationships within the user community over time, which may provide a solution for non-standard analytical problems. Regularities, or patterns in relationships between social entities, can be used to characterize the social environment and even predict its further evolution [4], especially for rapidly evolving social commerce networks (e.g., Alibaba, Sina Weibo) and traditional ones [5] (e.g., Facebook, Twitter). Centrality measures can be used to discover an influential member, such as recognizing a critical node in a network [6] or an influencer in a social network [7]. For example, a person actively involved in social networks can exert significant influence on consumer behavior of other users; therefore,understanding the structure of relations in a social network can be leveraged to predict the categories of products the consumers will buy [8]. Centrality measures can also be used to find the most reputable users in a network, which is important for many web-based platforms such as e-shopping sites, product review websites, and Q & A systems [9]. Different techniques have been applied for complete network analysis, for example, centrality analysis, equivalence analysis, motif analysis, subgroup analysis, clustering analysis [10], clique analysis [11], friend entropy and communication frequency entropy [12], community-level influence analysis [13; 14], social centrality [15], and centrality-based network decomposition [16], and Word2 Vector [17]. We focused on a centrality analysis of streaming data of social network users, in which the structure of the network changes continuously over time. Centrality identifies the most important vertices, or nodes, in a network, which have a big influence on the dissemination of information over the web [18], identifying key concepts in complex networks [19], analyzing and predicting factors influencing consumer purchase behavior such as trust and word-of-mouth, evaluating the stability of a social network with regard to malicious users [20], identifying potential for communication activity [21], influencing users on social media [22], or providing recommendations [23]. Identifying the main influencers in a social network using centrality measures can help in trying to increase the speed of information spreading over the network, which could be used, for example, to decrease it in case of a cyber attack by a hostile entity using misinformation or fake news [24]. The MapReduce-based approach has been employed previously for SNA of a cricket community in order to implement a ranking system based on social network metrics [25], to discover communities in social networking data by calculating k-path edge centrality [26], and to assess the closeness and betweenness centrality for comparing and merging large datasets [27]. [PERSON] et al. [28] deconstructed the A* algorithm into Map and Reduce tasks for performing path computation on Hadoop MapReduce, and demonstrated the application of parallel computation for real road networks. [PERSON] et al.