Adaptive networks: theory, models and applications by Thilo Gross, Hiroki Sayama

By Thilo Gross, Hiroki Sayama

With adaptive, complicated networks, the evolution of the community topology and the dynamical strategies at the community are both vital and infrequently essentially entangled.

Recent examine has proven that such networks can convey a plethora of latest phenomena that are eventually required to explain many real-world networks. a few of these phenomena comprise powerful self-organization in the direction of dynamical criticality, formation of complicated international topologies in response to basic, neighborhood ideas, and the spontaneous department of "labor" during which an at the start homogenous inhabitants of community nodes self-organizes into functionally exact sessions. those are only a couple of.

This ebook is a cutting-edge survey of these distinct networks. In it, best researchers got down to outline the long run scope and course of a few of the main complex advancements within the huge box of complicated community technology and its applications.

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E 68, 056110 (2003) 50. : Structure and tie strengths in mobile communication networks. Proc. Natl. Acad. Sci. USA 104, 7332–7336 (2007) 51. : Analysis of a large-scale weighted network of one-to-one human communication. New J. Phys. 9, 179 (2007) 52. : Quantifying social group evolution. Nature 446, 664–667 (2007) 53. : Uncovering the overlapping community structure of complex networks in nature and society. Nature 435, 814–818 (2005) 54. : Directed network modules. New J. Phys. 9, 186 (2007) 55.

9 Possible events in the community evolution. When new members are introduced, the community grows, whereas leaving members cause decay in the size. Communities can merge and split, new groups may emerge and old ones can disappear. 5) where |A ∩ B| is the number of common nodes in A and B, and |A ∪ B| is the number of nodes in the union of the two communities. 5) between At+1 and Bt can be larger than the relative overlap between At+1 and At . To overcome this difficulty, we refine the identification of communities as shown in Fig.

When the ratio r of the group of unclassified nodes compared to the total number of nodes N exceeds a certain limit r ∗ , a number of q vertices from the group establish a new community. (Obviously, q must be smaller than Nr even in the initial state). To be able to compare the results of the model with the community structure of the co-authorship network, the runs were stopped when the number of nodes in the model reached the size of the co-authorship network. Our experience showed that the model is quite insensitive to changes in r or q, and μ is the only important parameter.

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