Graph Contraction on Attribute-Based Coloring

Graphstructuresnowadays pervasiveBigData.It is oftenusefulto regroupsuchclustersdata incanclusters,accordingdistinctivenodefeatures,and use area representativeelementinforeachcluster.In manyreal-worldcases,be identifiedby toa setof connectedfeatures,and shareuse a representativeelementfor eachfunction,cluster. Ini.e.manyreal-worldcases,clustersbe identifiedbyrepresentationa set of connectedvertices thatthe result of somecategoricala mappingof theverticesintocansomecategoricalthatverticesthat insharethe setresultof somecategoricalfunction,a mappingterrainsof the withverticesinto somecategoricalthattakes valuesa finiteC. Asan example,we canidentifyi.e.contiguousthe samediscretepropertyrepresentationon a geographicaltakesvaluesinafinitesetC.Asanexample,wecanidentifycontiguousterrainswiththesamediscretepropertyonageographicalmap, leveraging Space Syntax. In this case, thematic areas within cities are labelled with different colors and color zones aremap,leveragingSpaceSyntax.In thisareas withinContractedcities are labelledwithdifferentzones areanalysedby meansof theirstructureandcase,theirthematicmutual interactions.graphs canhelpidentifycolorsissuesandandcolorcharacteristicsanalysedbymeansoftheirstructureandtheirmutualinteractions.Contractedgraphscanhelpidentifyissuesandcharacteristicsof the original structures that were not visible before.of Thisthe originalstructures andthatdiscusseswere not visiblebefore.paper introducesthe problemof contracting possibly large colored graphs into much smaller representatives.Thisprovidespaper introducesand discussesthe problemof contractinggraphs into muchrepresentatives.It alsoa novel serialbut parallelizablealgorithmto tackle possiblythis task.largeSomecoloredinitial performanceplots smallerare givenand discussedItalsoprovidesanovelserialbutparallelizablealgorithmtotacklethistask.Someinitialperformanceplotsaregivenand discussedtogether with hints for future development.together with hints for future development.