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Getting Social: Graph Theory and Social Network Analysis
Published in Jesús Rogel-Salazar, Advanced Data Science and Analytics with Python, 2020
In some cases, instead of asking how efficient the communication between nodes may be, we may be interested in finding out how well-connected the actors in our network are. This can be seen as an extension to the degree centrality we discussed earlier on. The indegree centrality scores a point for every link a node receives; however, in a more general case, not all nodes are equivalent and there may be some that are more relevant / powerful / important than others. This is effectively a case of being endorsed by influential nodes. This can be measured by the eigenvector centrality which tells us that a node is important if it is linked to other important nodes. This is the equivalent of “having friends in high places”.Eigenvector centrality tells us that a node is important if it is connected to other important nodes.
Big Graph Analytics: Techniques, Tools, Challenges, and Applications
Published in Mohiuddin Ahmed, Al-Sakib Khan Pathan, Data Analytics, 2018
Dhananjay Kumar Singh, Pijush Kanti Dutta Pramanik, Prasenjit Choudhury
By incorporating the importance of the neighbors, eigenvector centrality tries to generalize degree centrality. Eigenvector centrality is defined for both the directed graphs as well as the undirected graphs. To keep track of neighbors, we can use the adjacency matrix A of a graph. The eigenvector centrality is defined as ce(vi)=1λ∑j=1nAj,ice(vi)
Competitive Adaptation in Militant Networks: Preliminary Findings from an Islamist Case Study
Published in Alex Stedmon, Glyn Lawson, Hostile Intent and Counter-Terrorism, 2017
Michael Kenney, John Horgan, Cale Horne, Peter Vining, Kathleen M. Carley, Mia Bloom, Kurt Braddock
Well-connected agents connected to other well-connected agents score high on this metric, while the formula discounts nodes possessing many connections, as well as accounting for the fact that most nodes will have some connections. The eigenvector centrality measure is calculated using the largest positive eigenvalue of the adjacency matrix representation. Notably, Omar Bakri’s eigenvector centrality ranking actually improves in networks B and C, after he leaves Britain for Lebanon. While Bakri’s direct connections to the network rank-and-file suffer while in exile, his continued association with the AM leadership (i.e. other well-connected nodes) maintains his high scores on this measure. This is consistent with the first author’s interviews and ethnographic data, which found that AM leaders in Britain maintained regular contact with Bakri through various communications technologies. Moreover, several current AM leaders even visited Lebanon, where they sought to meet with their religious leader (source: author interviews with AM members, November–December 2010 and June 2011, field notes November–December 2010, June 2011).
Resilience metrics and measurement methods for transportation infrastructure: the state of the art
Published in Sustainable and Resilient Infrastructure, 2020
Wenjuan Sun, Paolo Bocchini, Brian D. Davison
Connectivity-based centrality measures include degree centrality (Cheng et al., 2015; Pinnaka et al., 2015; Wang et al., 2011; Zhang et al., 2013), eigenvector centrality (Kim & Anderson, 2013), and commuter flow centrality (Cheng et al., 2015). Degree centrality is a first centrality measure, defined as the number of links incident upon a node. Eigenvector centrality is also called Gould’s index, widely used for air traffic network analysis (Cook et al., 2015; Spizziri, 2011). The eigenvector centrality of a node is proportional to the sum of the centralities of the nodes that it connects to (Bonacich, 2007). Commuter flow centrality is the total number of commuters through the node per hour (Cheng et al., 2015). These three measures allow one to quantify the functionality related to connectivity and to identify important nodes in disaster resilience analyses.
Centrality and connectivity analysis of the European airports: a weighted complex network approach
Published in Transportation Planning and Technology, 2023
Similarly, cumulative degree distribution P(k) which defines the probability that a randomly selected vertex has k or more degrees is found by: Eigenvector centrality is another vertex centrality measure that builds up on the degree centrality. In degree centrality, all links are assumed to have the same value; however, eigenvector centrality gives higher value to connections to nodes which are already well-connected (Newman 2008). This measure is calculated as follows: where λ is the eigenvalue of the eigenvector of the adjacency matrix.
NATO Human View Executable Architectures for Critical Infrastructure Analysis
Published in Engineering Management Journal, 2019
Johnathon Huff, William B. Leonard, Brian K. Smith, Kelly Griendling, Hugh Medal
Eigenvector centrality refers to the “relative importance in terms of influence of a node to its neighboring nodes in the network” (Choudhary & Singh, 2015, p. 26). The normalized eigenvector centrality values spanned approximately 0.26% to 9.55%. Eigenvector centrality can help to detect nodes (positions) that have great influence over other nodes (positions), by pinpointing which individuals are “well connected to other well-connected persons” (Choudhary & Singh, 2015, p. 26). Since the Director, EMS Operations Manager, and Grid Control Manager are well-connected to many others in the organization, it follows that they are connected to other well-connected individuals.