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
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 | \(297\,088\) | \(4\,815\) | \(4\,708\) | \(10\,929\) |