LEADER 05219nam 22006855 450 001 9910254586303321 005 20201223092515.0 010 $a3-319-69438-3 024 7 $a10.1007/978-3-319-69438-2 035 $a(CKB)4340000000223490 035 $a(DE-He213)978-3-319-69438-2 035 $a(MiAaPQ)EBC5153635 035 $a(PPN)221253009 035 $a(EXLCZ)994340000000223490 100 $a20171121d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMaximum-Entropy Networks $ePattern Detection, Network Reconstruction and Graph Combinatorics /$fby Tiziano Squartini, Diego Garlaschelli 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XII, 116 p. 34 illus., 31 illus. in color.) 225 1 $aUnderstanding Complex Systems,$x2191-5326 311 $a3-319-69436-7 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $aIntroduction -- Maximum-entropy ensembles of graphs -- Constructing constrained graph ensembles: why and how? -- Comparing models obtained from different constraints -- Pattern detection -- Detecting assortativity and clustering -- Detecting dyadic motifs -- Detecting triadic motifs -- Some extensions to weighted networks -- Network reconstruction -- Reconstructing network properties from partial information -- The Enhanced Configuration Model -- Further reducing the observational requirements -- Graph combinatorics -- A dual route to combinatorics? -- ?Soft? combinatorial enumeration -- Quantifying ensemble (non)equivalence -- Breaking of equivalence between ensembles -- Implications of (non)equivalence for combinatorics -- ?What then shall we choose?? Hardness or softness? -- Concluding remarks. 330 $aThis book is an introduction to maximum-entropy models of random graphs with given topological properties and their applications. Its original contribution is the reformulation of many seemingly different problems in the study of both real networks and graph theory within the unified framework of maximum entropy. Particular emphasis is put on the detection of structural patterns in real networks, on the reconstruction of the properties of networks from partial information, and on the enumeration and sampling of graphs with given properties.  After a first introductory chapter explaining the motivation, focus, aim and message of the book, chapter 2 introduces the formal construction of maximum-entropy ensembles of graphs with local topological constraints. Chapter 3 focuses on the problem of pattern detection in real networks and provides a powerful way to disentangle nontrivial higher-order structural features from those that can be traced back to simpler local constraints. Chapter 4 focuses on the problem of network reconstruction and introduces various advanced techniques to reliably infer the topology of a network from partial local information. Chapter 5 is devoted to the reformulation of certain ?hard? combinatorial operations, such as the enumeration and unbiased sampling of graphs with given constraints, within a ?softened? maximum-entropy framework. A final chapter offers various overarching remarks and take-home messages. By requiring no prior knowledge of network theory, the book targets a broad audience ranging from PhD students approaching these topics for the first time to senior researchers interested in the application of advanced network techniques to their field. 410 0$aUnderstanding Complex Systems,$x2191-5326 606 $aPhysics 606 $aStatistical physics 606 $aSystem theory 606 $aGraph theory 606 $aComputational complexity 606 $aApplications of Graph Theory and Complex Networks$3https://scigraph.springernature.com/ontologies/product-market-codes/P33010 606 $aStatistical Physics and Dynamical Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P19090 606 $aComplex Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/M13090 606 $aGraph Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M29020 606 $aComplexity$3https://scigraph.springernature.com/ontologies/product-market-codes/T11022 615 0$aPhysics. 615 0$aStatistical physics. 615 0$aSystem theory. 615 0$aGraph theory. 615 0$aComputational complexity. 615 14$aApplications of Graph Theory and Complex Networks. 615 24$aStatistical Physics and Dynamical Systems. 615 24$aComplex Systems. 615 24$aGraph Theory. 615 24$aComplexity. 676 $a003.54 700 $aSquartini$b Tiziano$4aut$4http://id.loc.gov/vocabulary/relators/aut$0823091 702 $aGarlaschelli$b Diego$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254586303321 996 $aMaximum-Entropy Networks$91984712 997 $aUNINA