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Table 1 Multiplex network size of the 36 largest German cities with valid GTFS data as described in the "Data" section. Nodes correspond to stops and layers correspond to public transport lines, i.e. e.g., the public transport network of Augsburg consists of 5 tram lines, 63 bus lines, and a total of 68 public transport lines. Each line only serves a subset of all stops of the city, which is typically small compared to the full network. This entails that most node-layer pairs in the individual layers and consequently in the full networks are isolated, i.e, possess no incident edge. Hence, the number of non-isolated node-layer pairs and the number of intra-layer edges is similar for all considered networks

From: Orientations and matrix function-based centralities in multiplex network analysis of urban public transport

City Nodes Layers Node-layer pairs Non-isolated node-layer pairs Intra-layer edges Inter-layer edges
Tram Subway Bus Other Total
Aachen \(1\,113\) 0 0 108 0 108 \(120\,204\) \(4\,872\) \(4\,887\) \(19\,025\)
Augsburg 901 5 0 63 0 68 \(61\,268\) \(1\,381\) \(1\,340\) 942
Berlin \(7\,565\) 23 9 242 5 279 \(2\,110\,635\) \(13\,845\) \(14\,062\) \(11\,812\)
Bielefeld \(1\,561\) 8 0 101 0 109 \(170\,149\) \(4\,668\) \(4\,645\) \(8\,171\)
Bonn \(1\,264\) 9 0 61 0 70 \(88\,480\) \(3\,864\) \(3\,824\) \(6\,995\)
Braunschweig 954 7 0 45 0 52 \(49\,608\) \(2\,029\) \(2\,008\) \(2\,188\)
Bremen \(1\,602\) 22 0 82 0 104 \(166\,608\) \(4\,256\) \(4\,186\) \(6\,707\)
Chemnitz \(1\,168\) 9 0 70 0 79 \(92\,272\) \(2\,521\) \(2\,481\) \(2\,920\)
Cologne \(2\,084\) 13 0 92 0 105 \(218\,820\) \(3\,456\) \(3\,336\) \(2\,217\)
Dortmund \(2\,232\) 0 8 129 2 139 \(310\,248\) \(5\,399\) \(5\,408\) \(7\,123\)
Dresden \(1\,865\) 13 0 93 4 110 \(205\,150\) \(4\,198\) \(4\,246\) \(5\,212\)
Duisburg \(1\,639\) 2 1 47 0 50 \(81\,950\) \(2\,186\) \(2\,140\) 841
Düsseldorf \(1\,878\) 7 11 86 0 104 \(195\,312\) \(3\,850\) \(3\,782\) \(4\,067\)
Erfurt 675 8 0 36 0 44 \(29\,700\) \(1\,246\) \(1\,315\) \(1\,136\)
Essen \(1\,724\) 8 3 80 0 91 \(156\,884\) \(2\,814\) \(2\,702\) \(1\,529\)
Frankfurt am Main \(2\,118\) 8 9 96 0 113 \(239\,334\) \(3\,530\) \(3\,450\) \(2\,203\)
Freiburg 608 5 0 33 0 38 \(23\,104\) 954 993 569
Halle (Saale) 824 19 0 43 0 62 \(51\,088\) \(2\,397\) \(2\,468\) \(5\,892\)
Hamburg \(4\,630\) 0 4 241 8 253 \(1\,171\,390\) \(10\,193\) \(10\,011\) \(13\,544\)
Hanover \(1\,188\) 0 12 52 0 64 \(76\,032\) \(1\,881\) \(1\,823\) 984
Karlsruhe 793 9 0 44 0 53 \(42\,029\) \(1\,526\) \(1\,567\) \(1\,130\)
Kiel 996 0 0 64 2 66 \(65\,736\) \(2\,511\) \(2\,463\) \(3\,279\)
Krefeld 799 4 2 31 0 37 \(29\,563\) \(1\,565\) \(1\,576\) \(1\,401\)
Leipzig \(1\,748\) 16 0 64 0 80 \(139\,840\) \(3\,385\) \(3\,430\) \(4\,193\)
Lübeck 886 0 0 35 0 35 \(31\,010\) \(1\,619\) \(1\,600\) \(1\,754\)
Mainz 515 5 0 34 0 39 \(20\,085\) \(1\,753\) \(1\,891\) \(4\,274\)
Mannheim 805 14 0 42 2 58 \(46\,690\) \(1\,562\) \(1\,639\) \(1\,612\)
Munich \(2\,850\) 24 8 126 0 158 \(450\,300\) \(5\,258\) \(5\,165\) \(4\,070\)
Mönchengladbach \(1\,196\) 0 0 39 0 39 \(46\,644\) \(2\,254\) \(2\,307\) \(1\,917\)
Münster 479 0 0 42 0 42 \(20\,118\) \(1\,187\) \(1\,160\) \(1\,960\)
Nuremberg \(1\,430\) 6 3 67 0 76 \(108\,680\) \(2\,359\) \(2\,315\) \(1\,487\)
Oberhausen \(1\,060\) 2 0 86 0 88 \(93\,280\) \(3\,065\) \(2\,996\) \(8\,478\)
Rostock 336 6 0 39 2 47 \(15\,792\) 793 817 915
Stuttgart \(1\,333\) 1 17 70 2 90 \(119\,970\) \(2\,154\) \(2\,121\) \(1\,423\)
Wiesbaden \(1\,042\) 0 0 68 0 68 \(70\,856\) \(2\,814\) \(2\,857\) \(4\,920\)
Wuppertal \(1\,688\) 0 0 175 1 176 \(297\,088\) \(4\,815\) \(4\,708\) \(10\,929\)