The overarching motivation in the development of
cityseer has been the quantification of urban characteristics in a manner that is as sensitive as possible to local particularities and variations.
cityseer is designed for localised urban analysis at the pedestrian scale, meaning that observations are tailored towards pedestrian walking tolerances, commonly in the range of 400m to 800m, and infrequently exceeding 1,600m. In the case of certain land-use and mixed-use measures, it can be beneficial to work with weighted measures at distance thresholds as small as 100m or even 50m so that metrics are sufficiently precise to be pertinent to the day-to-day decisions made by architects and urban designers. These use-cases require information anchored to particular locations and measures must be adequately sensitive to reflect varying outcomes in response to different planned scenarios.
cityseer is developed from the ground-up to address a particular range of issues that are prevalent in pedestrian-scale urban analysis:
- It uses localised forms of network analysis (as opposed to global forms of analysis) based on network methods applied over the graph through means of a ‘moving-window’ methodology: the graph is isolated at a specified distance threshold for the currently selected node, and the process subsequently repeats for every other node in the network. These thresholds are conventionally based on either crow-flies euclidean distances or true network distances1:
cityseertakes the position that true network distances are more representative when working at smaller pedestrian distance thresholds, particularly when applied to land-use accessibilities and mixed-use calculations;
- It is common to use either shortest-distance or simplest-path (shortest angular ‘distance’) impedance heuristics. When using simplest-path heuristics, it is necessary to modify the underlying shortest-path algorithms to prevent side-stepping of sharp angular turns2, otherwise two smaller side-steps can be combined to ‘short-cut’ sharp corners. It is also common for methods to be applied to either primal graph representations (generally used with shortest-path methods such as those applied by multiple centrality assessment3 analysis) or dual graph representations (typically used with simplest-path methods in the tradition of space syntax4);
- There are a range of possible centrality and mixed-use methods, many of which can be weighted by distances or street lengths. These methods and their implications are explored in detail in the localised land-use diversity and localised land-use diversity methods papers. Some conventional methods, even if widely used, have not necessarily proved suitable for localised urban analysis;
- Centrality methods are susceptible to topological distortions arising from ‘messy’ graph representations as well as due to the conflation of topological and geometrical properties of street networks.
cityseeraddresses these through the inclusion of graph cleaning functions; procedures for splitting geometrical properties from topological representations; and the inclusion of segmentised centrality measures, which are less susceptible to distortions introduced by varying intensities of nodes;
- Hyperlocal analysis requires approaches facilitating the evaluation of respective measures at finely-spaced intervals along streetfronts. Further, granular evaluation of land-use accessibilities and mixed-uses requires that landuses be assigned to the street network in a contextually precise manner. These are addressed in
cityseerthrough application of network decomposition combined with algorithms incorporating bidirectional assignment of data points to network nodes based on the closest adjacent street edge.
The broader emphasis on localised methods and the manner in which
cityseer addresses these is broached in the accompanying paper (link forthcoming).
cityseer includes a variety of convenience methods for the general preparation of networks and for their conversion into (and out of) the lower-level data structures used by the underlying algorithms. These graph utility methods are designed to work with
NetworkX to facilitate ease-of-use. A complement of code tests has been developed for maintaining the integrity of the code-base through general package maintenance and upgrade cycles. Shortest-path algorithms, harmonic closeness, and betweenness algorithms are tested against
NetworkX. Mock data and test plots have been used to visually confirm the intended behaviour for divergent simplest and shortest-path heuristics, and for testing data assignment to network nodes given a variety of scenarios.
A notebook of this guide can be found at google colaboratory.
Good sources of street network data, such as the Ordnance Survey’s OS Open Roads, typically have two distinguishing characteristics:
- The network has been simplified to its essential structure: i.e. unnecessarily complex representations of intersections; on-ramps; split roadways; etc. have been reduced to a simpler representation concurring more readily with the core topological structure of street networks. This is in contrast to network representations focusing on completeness (e.g. for route way-finding, see OS ITN Layer): these introduce unnecessary complexity serving to hinder rather than help shortest-path algorithms in the sense used by pedestrian centrality measures.
- The topology of the network is kept distinct from the geometry of the streets. Often-times, as can be seen with Open Street Map, additional nodes are added to streets for the purpose of representing geometric twists and turns along a roadway. These additional nodes cause topological distortions that impact network centrality measures.
When a high-quality source is available, it may be best not to attempt additional clean-up unless there is a particular reason to do so. On the other-hand, many indispensable sources of network information, particularly Open Street Map data, can be messy for the purposes of network analysis. This section describes how such sources can be cleaned and prepared for subsequent analysis.
cityseer uses methods attempting to clean the topology of the graph in such a manner as to reduce topological artefacts that might otherwise confound centrality measures e.g. by attempting to remove dual carriageways and by deriving topologies and geometrical forms of edge consolidation that are as ‘tidy’ as possible so as not to complicate simplest-path (angular) methods.
This example will make use of OSM data downloaded from the OSM API. To keep things interesting, let’s pick London Soho, which will be buffered and cleaned for a 1,250m radius.
from shapely import geometry import utm from cityseer.tools import graphs, plot, mock # Let's download data within a 1,250m buffer around London Soho: lng, lat = -0.13396079424572427, 51.51371088849723 G_utm = mock.make_buffered_osm_graph(lng, lat, 1250) # As an alternative, you can use OSMnx to download data. Set simplify to False: # e.g.: OSMnx_multi_di_graph = ox.graph_from_point((lat, lng), dist=1250, simplify=False) # Then convert to a cityseer compatible MultiGraph: # e.g.: G_utm = graphs.nX_from_OSMnx(OSMnx_multi_di_graph, tolerance=10) # select extents for plotting easting, northing = utm.from_latlon(lat, lng)[:2] # buffer buff = geometry.Point(easting, northing).buffer(1000) # extract extents min_x, min_y, max_x, max_y = buff.bounds # reusable plot function def simple_plot(_G, plot_geoms=True): # plot using the selected extents plot.plot_nX(_G, labels=False, plot_geoms=plot_geoms, node_size=15, edge_width=2, x_lim=(min_x, max_x), y_lim=(min_y, max_y), figsize=(20, 20), dpi=200) simple_plot(G_utm, plot_geoms=False)
The pre-consolidation OSM street network for Soho, London. © OpenStreetMap contributors.
Deducing the network topology
Once OSM data has been converted to a
tools.graphs module can be used to clean the network.
The convenience method used for this demonstration has already converted the graph from a geographic WGS to projected UTM coordinate system; however, if working with a graph which is otherwise in a WGS coordinate system then it must be converted to a projected coordinate system prior to further processing. This can be done with
Now that raw OSM data has been loaded into a NetworkX graph, the
cityseer.tools.graph methods can be used to further clean and prepare the network prior to analysis.
At this stage, the raw OSM graph is going to look a bit messy. Note how that nodes have been used to represent the roadway geometry. These nodes need to be removed and will be abstracted into
LineString geometries assigned to the respective street edges. So doing, the geometric representation will be kept distinct from the network topology.
# the raw osm nodes denote the road geometries by the placement of nodes # the first step generates explicit LineStrings geometries for each street edge G = graphs.nX_simple_geoms(G_utm) # We'll now strip the "filler-nodes" from the graph # the associated geometries will be welded into continuous LineStrings # the new LineStrings will be assigned to the newly consolidated topological links G = graphs.nX_remove_filler_nodes(G) # and remove dangling nodes: short dead-end stubs # these are often found at entrances to buildings or parking lots # The removed_disconnected flag will removed isolated network components # i.e. disconnected portions of network that are not joined to the main street network G = graphs.nX_remove_dangling_nodes(G, despine=20, remove_disconnected=True) # removing danglers can cause newly orphaned filler nodes, which we'll remove for good measure G = graphs.nX_remove_filler_nodes(G) simple_plot(G)
After removal of filler nodes, dangling nodes, and disconnected components.
Refining the network
Things are already looked much better, but we still have areas with large concentrations of nodes at complex intersections and many parallel roadways, which will confound centrality methods. We’ll now try to remove as much of this as possible. These steps involve the consolidation of nodes to clean-up extraneous nodes, which may otherwise exaggerate the intensity or complexity of the network in certain situations.
In this case, we’re trying to get rid of parallel road segments so we’ll do this in three steps, though it should be noted that, depending on your use-case, Step 1 may already be sufficient:
Step 1: An initial pass to cleanup complex intersections will be performed with the
graphs.nX_consolidate_nodes function. The arguments passed to the parameters allow for a number of different strategies, such as whether to ‘crawl’; minimum and maximum numbers of nodes to consider for consolidation; and to set the policies according to which nodes and edges are consolidated. These are explained more fully in the documentation. In this case, we’re accepting the defaults except for explicitly setting the buffer distance and bumping the minimum size of node groups to be considered for consolidation from 2 to 3.
G1 = graphs.nX_consolidate_nodes(G, buffer_dist=10, min_node_group=3) simple_plot(G1)
After an initial pass of node consolidation.
Complex intersections have now been simplified, for example, the intersection of Oxford and Regent has gone from 17 nodes to a single node.
In Step 2, we’ll use
graphs.nX_split_opposing_geoms to intentionally split edges in near proximity to nodes located on an adjacent roadway. This is going to help with the final pass of consolidation in Step 3.
G2 = graphs.nX_split_opposing_geoms(G1, buffer_dist=15) simple_plot(G2)
After “splitting opposing geoms” on longer parallel segments.
In the final step, we can now rerun the consolidation to clean up any remaining clusters of nodes. In this case, we’re setting the
crawl parameter to
min_node_degree down to 2, and prioritising nodes of
degree=4 for determination of the newly consolidated centroids:
G3 = graphs.nX_consolidate_nodes(G2, buffer_dist=15, crawl=False, min_node_degree=2, cent_min_degree=4) simple_plot(G3)
After the final step of node consolidation.
When using shortest-path methods, automated graph simplification and consolidation can arguably eliminate the need for manual checks; however, it is worth plotting the graph and performing a quick look-through to be sure there aren’t any unexpectedly odd situations.
When using simplest-path (angular) centralities, manual checks become more important because automated simplification and consolidation can result in small twists and turns where nodes and edges have been merged.
cityseer uses particular methods that attempt to keep these issues to a minimum, though there may still be some situations necessitating manual checks. From this perspective, it may be preferable to use a cleaner source of network topology (e.g. OS Open Roads) if working with simplest-path centralities; else, if only OSM data is available, to instead consider the use of shortest-path methods if the graph has too many unresolvable situations to clean-up manually.
The above recipe should be enough to get you started, but there are innumerable other strategies that may also work for any variety of scenarios.
Relation to other packages
OSMnx connects the Open Street Map (
OSM) API to
networkX graphs and the wider ecosystem of python-based geospatial tools through which it provides access to a range of graph-analysis, conversion, and visualisation methods. In the first-instance,
cityseer is not about
networkX, nor is it about
OSM. Earlier versions of
cityseer emerged around graphs in a more abstract sense — raw
numpy arrays and
numba data structures that scale relatively well to larger graphs — and the associated data structures were manually created from data stored on
postgres) databases. To ease the repeated use of these methods, and to lower the barrier to entry, these workflows were gradually abstracted to
networkX based approaches to make it simpler to create the graphs and to apply methods such as “decomposition”; casting a graph to its “dual”; and subsequent conversion into
cityseer data structures with the correct format of attributes for use by downstream
cityseer algorithms. Nevertheless, it bears emphasis that
networkX primarily as an in-out and graph preparation tool, not as its primary representation; similarly, it is not tailored for ingestion of
OSM data-sources but is rather intended to be data-source agnostic.
Other differences stem accordingly:
cityseer does not use the
networkX package for graph analysis, but implements its own algorithms that have developed around experimental exploration of niche methods intended only for pedestrian-scale analysis on street-networks as opposed to the more general-purpose and much wider variety of algorithms available in
networkX. The algorithms employed in
cityseer are accordingly intended only for localised (windowed) graph analysis: they use explicit distance thresholds; employ unique variants of centrality measures; handle cases such as simplest-path heuristics and segmentised forms of analysis; and extend these algorithms to handle the derivation of land-use accessibilities, mixed-uses, and statistical aggregations using similarly windowed and network-distance-weighted methods.
Taking the following into account, it is possible to use
cityseer together, and an example is provided in the code snippet which follows below:
- Whereas some basic
OSMingestion and conversion functions are included in the
tools.mockmodule, these are primarily intended for internal code development. If used directly, these assume that the end-user will have some direct knowledge of how these APIs work and how the recipes and conversion functions can be manipulated for specific situations. i.e. unless you want to roll-your-own OSM queries, it is best to stick with
OSMnxfor purposes of ingesting
OSMnxprepared graphs can be converted to
cityseercompatible graphs by using the
tools.graphs.nX_from_OSMnxmethod. In doing so, keep the following in mind:
multiDiGraphgraph structures which use directional edges. As such, it can be used for understanding vehicular routing, i.e. where one-way routes can have a major impact on the available shortest-routes.
cityseer— and intentionally so — is only concerned with pedestrian networks and therefore makes use of
MultiGraphson the premise that pedestrian networks are not ordinarily directional. When using the
tools.graphs.nX_from_OSMnxmethod, be cognisant that all directional information will consequently be discarded.
cityseergraph simplification and consolidation workflows will give subtly different results to those employed in
OSMnx. If you’re using
OSMnxto ingest networks from
OSMbut wish to simplify and consolidate the network as part of a
cityseerworkflow, then set the
Falseso that the network is not automatically simplified.
cityseeruses internal graph validation workflows to check that the geometries associated with an edge remain connected to the coordinates of the nodes on either side. If performing any graph manipulation outside of
cityseerthen the conversion function may complain of disconnected geometries. If so, you may need to relax the tolerance parameter which is used for error checking upon conversion to a
MultiGraph. Geometries that are disconnected from their end-nodes (within the tolerance parameter) will be “snapped” to meet their endpoints as part of the conversion process.
- For graph cleaning and simplificaton:
cityseeris oriented less towards automation and ease-of-use and more towards explicit and intentional use of potentially varied steps of processing. This involves a tradeoff, whereas some recipes are provided as a starting point (see
Graph Cleaning), you may find yourself needing to do more up-front experimentation and fine-tuning, but with the benefit of a degree of flexibility in how these methods are applied for a given network topology: e.g. steps can be included or omitted, used in different sequences, or repeated. Some of these methods, particularly
tools.graphs.nX_consolidate_nodes, may have severable tunable parameters which can have markedly different outcomes. This philosophy is by design, and if you want a simplified method that you can easily repeat, then you’ll need to wrap your own sequence of steps in a simplified utility function.
from cityseer import tools import osmnx as ox from shapely import geometry import utm # centre-point lng, lat = -0.13396079424572427, 51.51371088849723 # select extents for plotting easting, northing = utm.from_latlon(lat, lng)[:2] buff = geometry.Point(easting, northing).buffer(1000) min_x, min_y, max_x, max_y = buff.bounds # reusable plot function def simple_plot(_G): # plot using the selected extents tools.plot.plot_nX(_G, labels=False, plot_geoms=True, node_size=15, edge_width=2, x_lim=(min_x, max_x), y_lim=(min_y, max_y), figsize=(20, 20), dpi=200) # Let's use OSMnx to fetch an OSM graph # We'll use the same raw network for both workflows (hence simplify=False) multi_di_graph_raw = ox.graph_from_point((lat, lng), dist=1250, simplify=False) # Workflow 1: Using OSMnx to prepare the graph # ============================================ # explicit simplification and consolidation via OSMnx multi_di_graph_utm = ox.project_graph(multi_di_graph_raw) multi_di_graph_simpl = ox.simplify_graph(multi_di_graph_utm) multi_di_graph_cons = ox.consolidate_intersections(multi_di_graph_simpl, tolerance=10, dead_ends=True) # let's use the same plotting function for both scenarios to aid visual comparisons multi_graph_cons = tools.graphs.nX_from_OSMnx(multi_di_graph_cons, tolerance=50) simple_plot(multi_graph_cons) # WORKFLOW 2: Using cityseer to prepare the graph # =============================================== # let's convert the OSMnx graph to a cityseer compatible `multiGraph` G_raw = tools.graphs.nX_from_OSMnx(multi_di_graph_raw) # convert to UTM G = tools.graphs.nX_wgs_to_utm(G_raw) # infer geoms G = tools.graphs.nX_simple_geoms(G) # remove degree=2 nodes G = tools.graphs.nX_remove_filler_nodes(G) # remove dangling nodes G = tools.graphs.nX_remove_dangling_nodes(G, despine=10) # repeat degree=2 removal to remove orphaned nodes due to despining G = tools.graphs.nX_remove_filler_nodes(G) # let's consolidate the nodes G1 = tools.graphs.nX_consolidate_nodes(G, buffer_dist=10, min_node_group=3) # and we'll try to remove as many parallel roadways as possible G2 = tools.graphs.nX_split_opposing_geoms(G1, buffer_dist=15) G3 = tools.graphs.nX_consolidate_nodes(G2, buffer_dist=15, crawl=False, min_node_degree=2, cent_min_degree=4) simple_plot(G3)
OSMnx simplification and consolidation workflow.
cityseer conversion followed by simplification and consolidation workflow in
Computational methods for network-based centrality and land-use analysis make extensive use of shortest-path algorithms: these present substantial computational complexity due to nested-loops. Centrality methods implemented in pure
python, such as those contained in
NetworkX, can be particularly slow and may hinder timely application to large urban street networks (though, for the record,
NetworkX is an exquisitely designed package). Speed improvements are offered by running intensive algorithms against packages such as
igraph, which wrap underlying optimised code libraries implemented in more performant languages such as
C++. This is the approach that was adopted by the author prior to the development of
cityseer, but whereas these performant packages offer tremendous utility for general-purpose network analysis they can remain cumbersome to piggy-back for more esoteric use-cases, some of which are briefly alluded to in the discussion on motivation. Doing so can lead to a degree of code complexity presenting a bottleneck to further experimentation and development, and heavily overloading such packages from
python can cause any speed-advantages to rapidly dissipate. It was this conundrum that kickstarted the development of the current codebase which became formalised as the
cityseer does not explicitly implement globalised forms of network analysis, and currently has no intention of doing so because these make it tricky to compare metrics across locations. Therefore, if the aim is conventional forms of global centralities applied to the network as a global entity, then it may be worth sticking with a package such as
Graph-Tool which wraps heavily optimised code designed for exactly these types of purposes. On the other-hand, if using localised forms of analysis that take into account factors such as localised distance thresholds, specialised centralities, shortest vs. simplest-path heuristics, or land-use accessibilities and mixed-uses, then
cityseer offers methods that are not available through other off-the-shelf network analysis packages.
The present approach leveraged by
cityseer consists of pure
numpy, but with computationally intensive algorithms implemented in
numba for the sake of performant JIT compilation. The use of python has provided the necessary flexibility to easily experiment with different implementations of underlying methodologies and algorithms, thereby facilitating the development of measures specific to analytics from an urbanist’s perspective. The use of
numba has made it feasible to scale these methods to large and, optionally, decomposed networks. Further,
numba permits a style of programming more in-keeping with lower-level languages, i.e. it is possible to use loops explicitly, which can in many cases be easier to reason-with than nested array indices more typical of
numpy. Note that
cityseer algorithms, at present, are not necessarily heavily optimised for performance or designed explicitly for a performance-first paradigm: they have instead been implemented from a practical perspective that happens to be ‘fast-enough’ for day-to-day usage. There may well be opportunities for further efficiencies, however, these have not been deemed a priority at present and will only be implemented if they do not unnecessarily complicate the package.
- 1. Cooper CHV. Spatial localization of closeness and betweenness measures: a self-contradictory but useful form of network analysis. International Journal of Geographical Information Science [Internet]. 2015;29(8):1293–309. Available from: https://www.tandfonline.com/doi/pdf/10.1080/13658816.2015.1018834?needAccess=true↩
- 2. Turner A. From axial to road-centre lines: a new representation for space syntax and a new model of route choice for transport network analysis. Environment and Planning B: Planning and Design [Internet]. 2007;34:539–55. Available from: http://journals.sagepub.com/doi/pdf/10.1068/b32067↩
- 3. Porta S, Crucitti P, Latora V. The Network Analysis of Urban Streets: A Primal Approach. Environment and Planning B: Planning and Design [Internet]. 2006;33:705–25. Available from: http://journals.sagepub.com/doi/pdf/10.1068/b32045↩
- 4. Hillier B, Hanson J. The Social Logic of Space. Cambridge: Cambridge University Press; 1984. ↩