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Correlation in Complex Networks

dc.contributor.authorCantwell, George Tsering
dc.date.accessioned2020-10-04T23:38:09Z
dc.date.availableNO_RESTRICTION
dc.date.available2020-10-04T23:38:09Z
dc.date.issued2020
dc.identifier.urihttps://hdl.handle.net/2027.42/163269
dc.description.abstractNetwork representations are now ubiquitous across science. Indeed, they are the natural representation for complex systems—systems composed of large numbers of interacting components. Occasionally systems can be well represented by simple, regular networks, such as lattices. Usually, however, the networks themselves are complex—highly structured but with no obvious repeating pattern. In this thesis I examine the effects of correlation and interdependence on network phenomena, from three different perspectives. First, I consider patterns of mixing within networks. Nodes within a network frequently have more connections to others that are similar to themselves than to those that are dissimilar. However, nodes can (and do) display significant heterogeneity in mixing behavior—not all nodes behave identically. This heterogeneity manifests as correlations between individuals' connections. I show how to identify and characterize such patterns, and how this correlation can be used for practical tasks such as imputation. Second, I look at the effects of correlation on the structure of networks. If edges within a relational data set are correlated with each other, and if we construct a network from this data, then several of the properties commonly associated with real-world complex networks naturally emerge, namely heavy-tailed degree distributions, large numbers of triangles, short path lengths, and large connected components. Third, I develop a family of technical tools for calculations about networks. If you are using a network representation, there's a good chance you wish to calculate something about the network—for example, what will happen when a disease spreads across it. An important family of techniques for network calculations assume that the networks are free of short loops, which means that the neighbors of any given node are conditionally independent. However, real-world networks are clustered and clumpy, and this structure undermines the assumption of conditional independence. I consider a prescription to deal with this issue, opening up the possibility for many more analyses of realistic and real-world data.
dc.language.isoen_US
dc.subjectnetworks
dc.subjectcomplex systems
dc.titleCorrelation in Complex Networks
dc.typeThesis
dc.description.thesisdegreenamePhDen_US
dc.description.thesisdegreedisciplinePhysics
dc.description.thesisdegreegrantorUniversity of Michigan, Horace H. Rackham School of Graduate Studies
dc.contributor.committeememberNewman, Mark E
dc.contributor.committeememberJacobs, Abigail Zoe
dc.contributor.committeememberDoering, Charles R
dc.contributor.committeememberHorowitz, Jordan Michael
dc.contributor.committeememberMao, Xiaoming
dc.subject.hlbsecondlevelMathematics
dc.subject.hlbsecondlevelPhysics
dc.subject.hlbsecondlevelStatistics and Numeric Data
dc.subject.hlbtoplevelScience
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/163269/1/gcant_1.pdfen_US
dc.identifier.orcid0000-0002-4205-3691
dc.identifier.name-orcidCantwell, George; 0000-0002-4205-3691en_US
dc.owningcollnameDissertations and Theses (Ph.D. and Master's)


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