Closeness Centralization Measure for Two-mode Data of Prescribed Sizes
Identifieur interne : 000174 ( Main/Exploration ); précédent : 000173; suivant : 000175Closeness Centralization Measure for Two-mode Data of Prescribed Sizes
Auteurs : Matjaž Krnc [Slovénie] ; Jean-Sébastien Sereni [France] ; Rist Skrekovski [Slovénie] ; Zelealem Yilma [Qatar, États-Unis]Source :
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Abstract
We confirm a conjecture by Everett, Sinclair, and Dankelmann [Some Centrality results new and old, J. Math. Sociology 28 (2004), 215–227] regarding the problem of maximizing closeness centralization in two-mode data, where the number of data of each type is fixed. Intuitively, our result states that among all networks obtainable via two-mode data, the largest closeness is achieved by simply locally maximizing the closeness of a node. Mathematically, our study concerns bipartite graphs with fixed size bipartitions, and we show that the extremal configuration is a rooted tree of depth 2, where neighbors of the root have an equal or almost equal number of children.
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Box 24866 Doha, Qatar</addrLine><country key="QA"></country></address><ref type="url">http://www.qatar.cmu.edu/</ref></desc><listRelation><relation active="#struct-300719" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-300719" type="direct"><org type="institution" xml:id="struct-300719" status="VALID"><orgName>Carnegie Mellon University</orgName><desc><address><country key="US"></country></address></desc></org></tutelle></tutelles></hal:affiliation><country>Qatar</country><placeName><settlement type="city">Pittsburgh</settlement><region type="state">Pennsylvanie</region></placeName><country>États-Unis</country><orgName type="university">Université Carnegie-Mellon</orgName></affiliation></author></analytic></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="mix" xml:lang="en"><term>centrality</term><term>closeness centrality</term><term>complex network</term><term>graph</term><term>network</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">We confirm a conjecture by Everett, Sinclair, and Dankelmann [Some Centrality results new and old, J. Math. Sociology 28 (2004), 215–227] regarding the problem of maximizing closeness centralization in two-mode data, where the number of data of each type is fixed. Intuitively, our result states that among all networks obtainable via two-mode data, the largest closeness is achieved by simply locally maximizing the closeness of a node. Mathematically, our study concerns bipartite graphs with fixed size bipartitions, and we show that the extremal configuration is a rooted tree of depth 2, where neighbors of the root have an equal or almost equal number of children.</div></front></TEI><affiliations><list><country><li>France</li><li>Qatar</li><li>Slovénie</li><li>États-Unis</li></country><region><li>Pennsylvanie</li></region><settlement><li>Pittsburgh</li></settlement><orgName><li>Université Carnegie-Mellon</li></orgName></list><tree><country name="Slovénie"><noRegion><name sortKey="Krnc, Matjaz" sort="Krnc, Matjaz" uniqKey="Krnc M" first="Matjaž" last="Krnc">Matjaž Krnc</name></noRegion><name sortKey="Skrekovski, Rist" sort="Skrekovski, Rist" uniqKey="Skrekovski R" first="Rist" last="Skrekovski">Rist Skrekovski</name></country><country name="France"><noRegion><name sortKey="Sereni, Jean Sebastien" sort="Sereni, Jean Sebastien" uniqKey="Sereni J" first="Jean-Sébastien" last="Sereni">Jean-Sébastien Sereni</name></noRegion></country><country name="Qatar"><region name="Pennsylvanie"><name sortKey="Yilma, Zelealem" sort="Yilma, Zelealem" uniqKey="Yilma Z" first="Zelealem" last="Yilma">Zelealem Yilma</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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