Uncovering the Role of Elementary Processes in Network Evolution
OPEN Uncovering the role of elementary SUBJECT AREAS: processes in network evolution PHASE TRANSITIONS Gourab Ghoshal1,2*, Liping Chi1,3 & Albert-La´szlo´ Baraba´si1,2 AND CRITICAL PHENOMENA APPLIED PHYSICS 1Department of Physics, Biology and Computer Science, Center for Complex Network Research, Northeastern University, Boston, MA 02115, USA, 2Department of Medicine, Harvard Medical School and Center for Cancer Systems Biology, Dana-Farber Cancer STATISTICAL PHYSICS Institute, Boston, MA 02115, USA, 3Complexity Science Research Center, Institute of Particle Physics, Central China Normal COMPLEX NETWORKS University, Wuhan 430079, China. Received The growth and evolution of networks has elicited considerable interest from the scientific community and a 8 July 2013 number of mechanistic models have been proposed to explain their observed degree distributions. Various microscopic processes have been incorporated in these models, among them, node and edge addition, vertex Accepted fitness and the deletion of nodes and edges. The existing models, however, focus on specific combinations of 25 September 2013 these processes and parameterize them in a way that makes it difficult to elucidate the role of the individual elementary mechanisms. We therefore formulated and solved a model that incorporates the minimal Published processes governing network evolution. Some contribute to growth such as the formation of connections 10 October 2013 between existing pair of vertices, while others capture deletion; the removal of a node with its corresponding edges, or the removal of an edge between a pair of vertices. We distinguish between these elementary mechanisms, identifying their specific role on network evolution. Correspondence and requests for materials he study of networks has received significant attention from the scientific community, thanks to its utility as should be addressed to a useful representation of many complex systems found in the real world, ranging from social to technolo- G.G.
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