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Table 4 Network concepts in the simulated block-diagonal network.

From: Understanding network concepts in modules

Concept Fundamental CF-based Approx CF-based
Connectivity i ( n 1 1 ) b 1 I n d i n 1 + ( n 2 1 ) b 2 I n d i > n 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqGGOaakcqWGUbGBdaWgaaWcbaGaeGymaedabeaakiabgkHiTiabigdaXiabcMcaPiabdkgaInaaBaaaleaacqaIXaqmaeqaaOGaemysaKKaemOBa4Maemizaq2aaSbaaSqaaiabdMgaPjabgsMiJkabd6gaUnaaBaaameaacqaIXaqmaeqaaaWcbeaakiabgUcaRiabcIcaOiabd6gaUnaaBaaaleaacqaIYaGmaeqaaOGaeyOeI0IaeGymaeJaeiykaKIaemOyai2aaSbaaSqaaiabikdaYaqabaGccqWGjbqscqWGUbGBcqWGKbazdaWgaaWcbaGaemyAaKMaeyOpa4JaemOBa42aaSbaaWqaaiabigdaXaqabaaaleqaaaaa@513D@ ( n 1 1 ) b 1 I n d i n 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqGGOaakcqWGUbGBdaWgaaWcbaGaeGymaedabeaakiabgkHiTiabigdaXiabcMcaPiabdkgaInaaBaaaleaacqaIXaqmaeqaaOGaemysaKKaemOBa4Maemizaq2aaSbaaSqaaiabdMgaPjabgsMiJkabd6gaUnaaBaaameaacqaIXaqmaeqaaaWcbeaaaaa@3ED3@ n 1 b 1 I n d i n 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGUbGBdaWgaaWcbaGaeGymaedabeaakiabdkgaInaaBaaaleaacqaIXaqmaeqaaOGaemysaKKaemOBa4Maemizaq2aaSbaaSqaaiabdMgaPjabgsMiJkabd6gaUnaaBaaameaacqaIXaqmaeqaaaWcbeaaaaa@3B44@
Density n 1 ( n 1 1 ) b 1 + n 2 ( n 2 1 ) b 2 ( n 1 + n 2 ) ( n 1 + n 2 1 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@5509@ n 1 2 b 1 ( n 1 + n 2 ) ( n 1 + n 2 1 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaWcaaqaaiabd6gaUnaaDaaaleaacqaIXaqmaeaacqaIYaGmaaGccqWGIbGydaWgaaWcbaGaeGymaedabeaaaOqaaiabcIcaOiabd6gaUnaaBaaaleaacqaIXaqmaeqaaOGaey4kaSIaemOBa42aaSbaaSqaaiabikdaYaqabaGccqGGPaqkcqGGOaakcqWGUbGBdaWgaaWcbaGaeGymaedabeaakiabgUcaRiabd6gaUnaaBaaaleaacqaIYaGmaeqaaOGaeyOeI0IaeGymaeJaeiykaKcaaaaa@43E2@
Centralization n 2 ( ( n 1 1 ) b 1 + ( n 2 1 ) b 2 ) ( n 1 + n 2 1 ) ( n 1 + n 2 2 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@560F@ ( n 1 1 ) n 2 b 1 ( n 1 + n 2 1 ) ( n 1 + n 2 2 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaWcaaqaaiabcIcaOiabd6gaUnaaBaaaleaacqaIXaqmaeqaaOGaeyOeI0IaeGymaeJaeiykaKIaemOBa42aaSbaaSqaaiabikdaYaqabaGccqWGIbGydaWgaaWcbaGaeGymaedabeaaaOqaaiabcIcaOiabd6gaUnaaBaaaleaacqaIXaqmaeqaaOGaey4kaSIaemOBa42aaSbaaSqaaiabikdaYaqabaGccqGHsislcqaIXaqmcqGGPaqkcqGGOaakcqWGUbGBdaWgaaWcbaGaeGymaedabeaakiabgUcaRiabd6gaUnaaBaaaleaacqaIYaGmaeqaaOGaeyOeI0IaeGOmaiJaeiykaKcaaaaa@4AEA@ n 1 n 2 b 1 ( n 1 + n 2 1 ) ( n 1 + n 2 2 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaWcaaqaaiabd6gaUnaaBaaaleaacqaIXaqmaeqaaOGaemOBa42aaSbaaSqaaiabikdaYaqabaGccqWGIbGydaWgaaWcbaGaeGymaedabeaaaOqaaiabcIcaOiabd6gaUnaaBaaaleaacqaIXaqmaeqaaOGaey4kaSIaemOBa42aaSbaaSqaaiabikdaYaqabaGccqGHsislcqaIXaqmcqGGPaqkcqGGOaakcqWGUbGBdaWgaaWcbaGaeGymaedabeaakiabgUcaRiabd6gaUnaaBaaaleaacqaIYaGmaeqaaOGaeyOeI0IaeGOmaiJaeiykaKcaaaaa@475B@
Heterogeneity ( n 1 + n 2 ) [ n 1 ( n 1 1 ) 2 b 1 2 + n 2 ( n 2 1 ) 2 b 2 2 ] [ n 1 ( n 1 1 ) b 1 + n 2 ( n 2 1 ) b 2 ] 2 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@6EF1@ n 2 n 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaGcaaqaamaalaaabaGaemOBa42aaSbaaSqaaiabikdaYaqabaaakeaacqWGUbGBdaWgaaWcbaGaeGymaedabeaaaaaabeaaaaa@31DA@ n 2 n 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaGcaaqaamaalaaabaGaemOBa42aaSbaaSqaaiabikdaYaqabaaakeaacqWGUbGBdaWgaaWcbaGaeGymaedabeaaaaaabeaaaaa@31DA@
TopOverlap ij b 1 I n d i , j n 1 + b 2 I n d i , j > n 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGIbGydaWgaaWcbaGaeGymaedabeaakiabdMeajjabd6gaUjabdsgaKnaaBaaaleaacqWGPbqAcqGGSaalcqWGQbGAcqGHKjYOcqWGUbGBdaWgaaadbaGaeGymaedabeaaaSqabaGccqGHRaWkcqWGIbGydaWgaaWcbaGaeGOmaidabeaakiabdMeajjabd6gaUjabdsgaKnaaBaaaleaacqWGPbqAcqGGSaalcqWGQbGAcqGH+aGpcqWGUbGBdaWgaaadbaGaeGymaedabeaaaSqabaaaaa@4981@ b 1 I n d i , j n 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGIbGydaWgaaWcbaGaeGymaedabeaakiabdMeajjabd6gaUjabdsgaKnaaBaaaleaacqWGPbqAcqGGSaalcqWGQbGAcqGHKjYOcqWGUbGBdaWgaaadbaGaeGymaedabeaaaSqabaaaaa@3AF6@ b 1 n 1 b 1 + 1 ( n 1 1 ) b 1 + 1 I n d i , j n 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGIbGydaWgaaWcbaGaeGymaedabeaakmaalaaabaGaemOBa42aaSbaaSqaaiabigdaXaqabaGccqWGIbGydaWgaaWcbaGaeGymaedabeaakiabgUcaRiabigdaXaqaaiabcIcaOiabd6gaUnaaBaaaleaacqaIXaqmaeqaaOGaeyOeI0IaeGymaeJaeiykaKIaemOyai2aaSbaaSqaaiabigdaXaqabaGccqGHRaWkcqaIXaqmaaGaemysaKKaemOBa4Maemizaq2aaSbaaSqaaiabdMgaPjabcYcaSiabdQgaQjabgsMiJkabd6gaUnaaBaaameaacqaIXaqmaeqaaaWcbeaaaaa@4C35@
ClusterCoef i b 1 I n d i n 1 + b 2 I n d i > n 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGIbGydaWgaaWcbaGaeGymaedabeaakiabdMeajjabd6gaUjabdsgaKnaaBaaaleaacqWGPbqAcqGHKjYOcqWGUbGBdaWgaaadbaGaeGymaedabeaaaSqabaGccqGHRaWkcqWGIbGydaWgaaWcbaGaeGOmaidabeaakiabdMeajjabd6gaUjabdsgaKnaaBaaaleaacqWGPbqAcqGH+aGpcqWGUbGBdaWgaaadbaGaeGymaedabeaaaSqabaaaaa@4507@ b 1 I n d i n 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGIbGydaWgaaWcbaGaeGymaedabeaakiabdMeajjabd6gaUjabdsgaKnaaBaaaleaacqWGPbqAcqGHKjYOcqWGUbGBdaWgaaadbaGaeGymaedabeaaaSqabaaaaa@38B9@ b 1 I n d i n 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGIbGydaWgaaWcbaGaeGymaedabeaakiabdMeajjabd6gaUjabdsgaKnaaBaaaleaacqWGPbqAcqGHKjYOcqWGUbGBdaWgaaadbaGaeGymaedabeaaaSqabaaaaa@38B9@
  1. The indicator function Ind(·) takes on the value 1 if the condition is satisfied and 0 otherwise.