Projects per year
Abstract
The heterogeneity of the sum of all distances from one node to the rest of nodes in a graph (distancesum or status of the node) is analyzed. We start here by analyzing the cumulative statistical distributions of the distancesum of nodes in random and realworld networks. From this analysis we conclude that statistical distributions do not reveal the distancesumheterogeneity in networks. Thus, we motivate an index of distancesumheterogeneity based on a hypothetical consensus model in which the nodes of the network try to reach an agreement on their distancesum values. This index is expressed as a quadratic form of the combinatorial Laplacian matrix of the network. The distancesumheterogeneity index φ(G) gives a natural interpretation of the Balaban index for any kind of graph/network. We conjecture here that among graphs with a given number of nodes φ(G) is maximized for a graph with a structure resembling the agave plant. We also found the graphs that maximize φ(G) for a given number of nodes and links. Using this index and a normalized version of it we studied random graphs as well as 57 realworld networks. Our findings indicate that the distancesumheterogeneity index reveals important structural characteristics of networks which can be important for understanding the functional and dynamical processes in complex systems.
Original language  English 

Pages (fromto)  1039310405 
Number of pages  13 
Journal  Applied Mathematics and Computation 
Volume  218 
Issue number  21 
DOIs  
Publication status  Published  1 Jul 2012 
Keywords
 distance distributions
 distancesum
 complex networks
 Balaban index
 graph distances
Fingerprint Dive into the research topics of 'Distancesum heterogeneity in graphs and complex networks'. Together they form a unique fingerprint.
Projects
 1 Finished

Mathematics of Large Technological Evolving Networks (MOLTEN)
Higham, D. & Estrada, E.
EPSRC (Engineering and Physical Sciences Research Council)
24/01/11 → 31/03/13
Project: Research