Network where the ties among nodes have weights assigned to them
A weighted network is a network where the ties among nodes have weights assigned to them. A network is a system whose elements are somehow connected.[1] The elements of a system are represented as nodes (also known as actors or vertices) and the connections among interacting elements are known as ties, edges, arcs, or links. The nodes might be neurons, individuals, groups, organisations, airports, or even countries, whereas ties can take the form of friendship, communication, collaboration, alliance, flow, or trade, to name a few.
In a number of real-world networks, not all ties in a network have the same capacity. In fact, ties are often associated with weights that differentiate them in terms of their strength, intensity, or capacity[2][3] On the one hand, Mark Granovetter (1973)[4] argued that the strength of social relationships in social networks is a function of their duration, emotional intensity, intimacy, and exchange of services. On the other, for non-social networks, weights often refer to the function performed by ties, e.g., the carbon flow (mg/m2/day) between species in food webs,[5] the number of synapses and gap junctions in neural networks,[6] or the amount of traffic flowing along connections in transportation networks.[7]
Example of a weighted network (weights can also be visualized by giving edges different widths)
By recording the strength of ties,[8] a weighted network can be created (also known as a valued network).
Weighted networks are also widely used in genomic and systems biologic applications.[3] For example, weighted gene co-expression network analysis (WGCNA) is often used for constructing a weighted network among genes (or gene products) based on gene expression (e.g. microarray) data.[9] More generally, weighted correlation networks can be defined by soft-thresholding the pairwise correlations among variables (e.g. gene measurements).[10]
^Wasserman, S., Faust, K., 1994. Social Network Analysis: Methods and Applications. Cambridge University Press, New York, NY.
^A. Barrat and M. Barthelemy and R. Pastor-Satorras and A. Vespignani (2004). "The architecture of complex weighted networks". Proceedings of the National Academy of Sciences. 101 (11): 3747–3752. arXiv:cond-mat/0311416. Bibcode:2004PNAS..101.3747B. doi:10.1073/pnas.0400087101. PMC 374315. PMID 15007165.
^ abHorvath, S., 2011. Weighted Network Analysis. Applications in Genomics and Systems Biology. Springer Book. ISBN 978-1-4419-8818-8.
^Granovetter, M (1973). "The strength of weak ties". American Journal of Sociology. 78 (6): 1360–1380. doi:10.1086/225469. S2CID 59578641.
^Luczkowich, J.J.; Borgatti, S.P.; Johnson, J.C.; Everett, M.G. (2003). "Defining and measuring trophic role similarity in food webs using regular equivalence". Journal of Theoretical Biology. 220 (3): 303–321. Bibcode:2003JThBi.220..303L. CiteSeerX 10.1.1.118.3862. doi:10.1006/jtbi.2003.3147. PMID 12468282.
^D. J. Watts and Steven Strogatz (June 1998). "Collective dynamics of 'small-world' networks" (PDF). Nature. 393 (6684): 440–442. Bibcode:1998Natur.393..440W. doi:10.1038/30918. PMID 9623998. S2CID 4429113. Archived from the original (PDF) on 2007-02-21.
^Tore Opsahl and Vittoria Colizza and Pietro Panzarasa and Jose J. Ramasco (2008). "Prominence and control: The weighted rich-club effect". Physical Review Letters. 101 (16): 168702. arXiv:0804.0417. Bibcode:2008PhRvL.101p8702O. doi:10.1103/PhysRevLett.101.168702. PMID 18999722. S2CID 29349737. Archived from the original on 2009-11-27. Retrieved 2009-09-17.
^"Operationalisation of tie strength in social networks". 2009-02-06. Archived from the original on 2009-08-24. Retrieved 2009-09-17.
^Zhang, Bin; Horvath, Steve (2005). "A general framework for weighted gene co-expression network analysis". Statistical Applications in Genetics and Molecular Biology. 4: Article17. doi:10.2202/1544-6115.1128. PMID 16646834. S2CID 7756201.
^Cite error: The named reference Langfelder2008 was invoked but never defined (see the help page).
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