Degree Centrality in Complex Networks
Explore the concepts of degree centrality in complex networks, including the importance of nodes, mathematical descriptions, and practical applications. Learn about interpreting degree centrality values and distinguishing between degree and degree centrality for effective network analysis.
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Prof. Ralucca Gera, rgera@nps.edu Applied Mathematics Department, Excellence Through Knowledge Naval Postgraduate School MA4404 Complex Networks Degree Centrality
Compute degree centrality. Interpret the meaning of the values of degree centrality. Distinguish between the degree and degree centrality. Learning Outcomes
Degree Centrality Quality: what makes a node important (central) Mathematical Description Appropriate Usage Identification Lots of one-hop connections from ? The number of vertices that ? influences directly The proportion of the vertices that ? influences directly Local influence matters Small diameter Local influence matters Small diameter Degree deg(?) Lots of one-hop connections from ? relative to the size of the graph Degree centrality deg(?) |V(G)|
Degree per vertex as a vector 4 7 2 4 2 1 1 1 3 1 1 3 1 1 1 1 1 1 1 1 4
Degree Centrality per vertex 4/20 7 20 2/20 4/20 2/20 1/20 1/20 1/20 3/20 1/20 1/20 3/20 1/20 1/20 1/20 1/20 1/20 1/20 1/20 1/20 Divide by ? 1 not counting the vertex at which centrality is computed. Or divide by (?) to normalize it since we only care for the relative centrality. 5
Degree distribution And you can also compute Degree centrality distribution 6
7 MA4404: Centralities categories Adjacencies Distances Degree Closeness Eigenvector Betweenness Katz HITS PageRank
