?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Feprints.imtlucca.it%2F2685%2F&rft.title=Hyperbolicity+Measures+%22Democracy%22+in+Real-World+Networks&rft.creator=Borassi%2C+Michele&rft.creator=Chessa%2C+Alessandro&rft.creator=Caldarelli%2C+Guido&rft.subject=HA+Statistics&rft.subject=HM+Sociology&rft.subject=QC+Physics&rft.description=We+analyze+the+hyperbolicity+of+real-world+networks%2C+a+geometric+quantity+that+measures+if+a+space+is+negatively+curved.+In+our+interpretation%2C+a+network+with+small+hyperbolicity+is+%22aristocratic%22%2C+because+it+contains+a+small+set+of+vertices+involved+in+many+shortest+paths%2C+so+that+few+elements+%22connect%22+the+systems%2C+while+a+network+with+large+hyperbolicity+has+a+more+%22democratic%22+structure+with+a+larger+number+of+crucial+elements.%0D%0AWe+prove+mathematically+the+soundness+of+this+interpretation%2C+and+we+derive+its+consequences+by+analyzing+a+large+dataset+of+real-world+networks.+We+confirm+and+improve+previous+results+on+hyperbolicity%2C+and+we+analyze+them+in+the+light+of+our+interpretation.%0D%0AMoreover%2C+we+study+(for+the+first+time+in+our+knowledge)+the+hyperbolicity+of+the+neighborhood+of+a+given+vertex.+This+allows+to+define+an+%22influence+area%22+for+the+vertices+in+the+graph.+We+show+that+the+influence+area+of+the+highest+degree+vertex+is+small+in+what+we+define+%22local%22+networks%2C+like+most+social+or+peer-to-peer+networks.+On+the+other+hand%2C+if+the+network+is+built+in+order+to+reach+a+%22global%22+goal%2C+as+in+metabolic+networks+or+autonomous+system+networks%2C+the+influence+area+is+much+larger%2C+and+it+can+contain+up+to+half+the+vertices+in+the+graph.+In+conclusion%2C+our+newly+introduced+approach+allows+to+distinguish+the+topology+and+the+structure+of+various+complex+networks.&rft.publisher=ArXiv&rft.date=2015-03&rft.type=Working+Paper&rft.type=NonPeerReviewed&rft.identifier=++Borassi%2C+Michele+and+Chessa%2C+Alessandro+and+Caldarelli%2C+Guido++Hyperbolicity+Measures+%22Democracy%22+in+Real-World+Networks.++Working+Paper+++ArXiv+++++++(Submitted)+++&rft.relation=http%3A%2F%2Farxiv.org%2Fabs%2F1503.03061