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Cycling is a promising solution to unsustainable car-centric urban transport systems. However, prevailing bicycle network development follows a slow and piecewise process, without taking into account the structural complexity of transportation networks. Here we explore systematically the topological limitations of urban bicycle network development. For 62 cities we study different variations of growing a synthetic bicycle network between an arbitrary set of points routed on the urban street network. We find initially decreasing returns on investment until a critical threshold, posing fundamental consequences to sustainable urban planning: Cities must invest into bicycle networks with the right growth strategy, and persistently, to surpass a critical mass. We also find pronounced overlaps of synthetically grown networks in cities with well-developed existing bicycle networks, showing that our model reflects reality. Growing networks from scratch makes our approach a generally applicable starting point for sustainable urban bicycle network planning with minimal data requirements.
The use of public transportation or simply moving about in streets are gendered issues. Women and girls often engage in multi-purpose, multi-stop trips in order to do household chores, work, and study (trip chaining). Women-headed households are ofte
We study the Krapivsky-Redner (KR) network growth model but where new nodes can connect to any number of existing nodes, $m$, picked from a power-law distribution $p(m)sim m^{-alpha}$. Each of the $m$ new connections is still carried out as in the KR
We introduce and analyze a model of a multi-directed Eulerian network, that is a directed and weighted network where a path exists that passes through all the edges of the network once and only once. Networks of this type can be used to describe info
During the last decades, the study of cities has been transformed by new approaches combining engineering and complexity sciences. Network theory is playing a central role, facilitating the quantitative analysis of crucial urban dynamics, such as mob
Popularity is attractive -- this is the formula underlying preferential attachment, a popular explanation for the emergence of scaling in growing networks. If new connections are made preferentially to more popular nodes, then the resulting distribut