"uuid","repository link","title","author","contributor","publication year","abstract","subject topic","language","publication type","publisher","isbn","issn","patent","patent status","bibliographic note","access restriction","embargo date","faculty","department","research group","programme","project","coordinates"
"uuid:055f7afd-22bf-4bc5-b841-dddf31b66217","http://resolver.tudelft.nl/uuid:055f7afd-22bf-4bc5-b841-dddf31b66217","Degree and Principal Eigenvectors in Complex Networks","Li, C.; Wang, H.; Van Mieghem, P.","","","The largest eigenvalue ? 1 of the adjacency matrix powerfully characterizes dynamic processes on networks, such as virus spread and synchronization. The minimization of the spectral radius by removing a set of links (or nodes) has been shown to be an NP-complete problem. So far, the best heuristic strategy is to remove links/nodes based on the principal eigenvector corresponding to the largest eigenvalue ? 1. This motivates us to investigate properties of the principal eigenvector x 1 and its relation with the degree vector. (a) We illustrate and explain why the average E[x 1] decreases with the linear degree correlation coefficient ? D in a network with a given degree vector; (b) The difference between the principal eigenvector and the scaled degree vector is proved to be the smallest, when ?1=N2N1 , where N k is the total number walks in the network with k hops; (c) The correlation between the principal eigenvector and the degree vector decreases when the degree correlation ? D is decreased.","networks; spectral radius; principal eigenvector; degree; as-sortativity","en","conference paper","Springer","","","","","","","","Electrical Engineering, Mathematics and Computer Science","Network Architectures and Services Group (NAS)","","","",""