# SVG <path> elementGuide

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 a ‘moving-window’ methodology. The graph is isolated at the specified distance thresholds for a 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 actual network distances (Cooper (2015)): cityseer takes the position that network distances are more representative when working at smaller pedestrian distance thresholds, especially 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 turns (Turner (2007)); 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 assessment (Porta et al. (2006)) analysis) or dual graph representations (typically used with simplest-path methods in the tradition of space syntax(Hillier & Hanson (1984)));
• There is 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 centrality methods 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. cityseer addresses 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;
• Micro-morphological analysis requires approaches facilitating the evaluation of respective measures at finely-spaced intervals along street fronts. Further, granular evaluation of land-use accessibilities and mixed-uses requires that land uses be assigned to the street network in a contextually precise manner. These are addressed in cityseer by applying 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 how cityseer addresses these is broached in the accompanying paper. cityseer includes a variety of convenience methods for the general preparation of networks and 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 to maintain the codebase’s integrity 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 testing data assignment to network nodes given various scenarios.

## SVG <path> elementCRS

x and y node attributes determine the spatial coordinates of the node, and should be in a suitable projected (“flat”) coordinate reference system (CRS) in metres. For convenience, nx_wgs_to_utm can be used for converting a networkX graph from WGS84 lng, lat geographic CRS to the local UTM x, y projected CRS. geopandas data points should likewise be in a projected CRS and the CRS should match that used by the node attributes.

## SVG <path> elementEdge Rolloff

When calculating network or layer metrics, the network has to be buffered by a distance equal to the maximum distance threshold being considered by the algorithms. This prevents problematic results arising due to edge roll-off effects. For example, if running centrality and/or land-use analysis using distances of 500, 1000, 2000m, then the network must be buffered by 2000m. When using data layers, the data points should — for the same reasons — cover these buffered extents as well.

The live=True node attribute is used for identifying nodes falling within the original non-buffered graph extents as opposed to the live=False nodes that fall within the surrounding buffered area. The underlying shortest-path algorithms will have access to both live=True and live=False nodes (thus preventing edge rolloff), but metrics are only computed for live=True nodes. This eliminates edge roll-off effects, reduces unnecessary computation, and cleanly identifies which nodes are or are not in the buffered roll-off area. If some other process will be used for filtering the nodes, or if boundary roll-off is not being considered, then set all nodes to live=True.

## SVG <path> elementGraph Cleaning

You can find a notebook of this guide on the examples page.

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, divided roadways, etc., have been reduced to a simpler representation concurring more readily with the core topological structure of street networks. Simplified forms of network representation contrast those 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 to represent 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 is best not to attempt additional clean-up unless there is a particular reason. On the other hand, many indispensable sources of network information, particularly Open Street Map data, can be particularly messy for network analysis purposes.

cityseer uses customisable graph cleaning methods that reduce topological idiosyncrasies which may otherwise confound centrality measures. It can, for example, remove dual carriageways while merging nodes and roadways in a manner that is as ‘tidy’ as possible.

### SVG <path> elementDownloading data

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, io

lng, lat = -0.13396079424572427, 51.51371088849723
buffer = 1250
# creates a WGS shapely polygon
poly_wgs, _poly_utm, _utm_zone_number, _utm_zone_letter = io.buffered_point_poly(
lng, lat, buffer
)
# this version will not simplify
G_raw = io.osm_graph_from_poly(poly_wgs, simplify=False)
# whereas this version does simplify
G_utm = io.osm_graph_from_poly(poly_wgs)

# select extents for clipping the plotting extents
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_geoms=True):
# plot using the selected extents
plot.plot_nx(
_G,
labels=False,
plot_geoms=plot_geoms,
node_size=3,
edge_width=1,
x_lim=(min_x, max_x),
y_lim=(min_y, max_y),
figsize=(6, 6),
dpi=150,
)

The pre-consolidation OSM street network for Soho, London. © OpenStreetMap contributors.

The automatically cleaned OSM street network for Soho, London. © OpenStreetMap contributors.

The automated graph cleaning provided by osm_graph_from_poly may give satisfactory results depending on the intended end-use. See the steps following beneath for an example of how to manually clean the graph where additional control is preferred.

### SVG <path> elementDeducing the network topology

Once OSM data has been converted to a NetworkX MultiGraph, the 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 graphs.nx_wgs_to_utm.

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 shapely 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_raw)
# 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)
simple_plot(G)

After removal of filler nodes, dangling nodes, and disconnected components.

### SVG <path> elementRefining 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=15, crawl=True, min_node_group=4, cent_min_degree=4, cent_min_names=4
)
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 next 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 False, setting 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, cent_min_names=4
)
simple_plot(G3)

After the final step of node consolidation.

Finally, we can optionally “iron” the edges to straighten out artefacts introduced by automated cleaning, which will sometimes bend the ends of edge segments to the locations of new centroids.

G4 = graphs.nx_iron_edges(G3)
simple_plot(G4)

After edge straightening.

#### Manual Cleaning

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.

## SVG <path> elementOSM and NetworkX

cityseer is intended to be data-source agnostic, and is predominately used in concert with Postgres/PostGIS databases or with OSM data. OSM queries can be used to populate cityseer graphs directly, else OSMnx can be used to gather OSM data which can then be converted into cityseer graphs, an example of which is provided in the code snippet beneath.

cityseer uses networkX primarily as an in-out and graph preparation tool for end-user ease of use, not as a means for algorithmic analysis. It avoids networkX for algorithmic analysis for two reasons. First, the algorithms employed in cityseer are intended for localised (windowed) graph analysis specifically within an urban analysis context: they use explicit distance thresholds; engage 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. Second, networkX scales very poorly to larger graphs, and can become unusable for large cities or large distance thresholds.

The following points may be helpful when using OSMnx and cityseer together:

• OSMnx prepared graphs can be converted to cityseer compatible graphs by using the tools.io.nx_from_osm_nx method. In doing so, keep the following in mind:
• OSMnx uses networkX multiDiGraph graph structures that 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 is only concerned with pedestrian networks and therefore uses networkX MultiGraphs on the premise that pedestrian networks are not ordinarily directional. When using the tools.io.nx_from_osm_nx method, be cognisant that all directional information will be discarded.
• cityseer graph simplification and consolidation workflows will give different results to those employed in OSMnx. If you’re using OSMnx to ingest networks from OSM but wish to simplify and consolidate the network as part of a cityseer workflow, set the OSMnx simplify argument to False so that the network is not automatically simplified.
• cityseer uses internal validation workflows to check that the geometries associated with an edge remain connected to the coordinates of the nodes on either side. If performing graph manipulation outside of cityseer before conversion, the conversion function may complain of disconnected geometries. In these cases, you may need to relax the tolerance parameter used for error checking upon conversion to a cityseer MultiGraph, in which case geometries disconnected from their end-nodes (within the tolerance parameter) will be “snapped” to meet their endpoints as part of the conversion process.

The below example is available as a Jupyter Notebook on the Examples page.

import osmnx as ox
from shapely import geometry
import utm

from cityseer.tools import graphs, plot, io

# centrepoint
lng, lat = -0.13396079424572427, 51.51371088849723

# select extents for plotting
easting, northing = utm.from_latlon(lat, lng)[:2]
buffer_dist = 1250
buffer_poly = geometry.Point(easting, northing).buffer(1000)
min_x, min_y, max_x, max_y = buffer_poly.bounds

# reusable plot function
def simple_plot(_G):
# plot using the selected extents
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=(10, 10),
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=buffer_dist, 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)
# let's use the same plotting function for both scenarios to aid visual comparisons
multi_graph_cons = io.nx_from_osm_nx(multi_di_graph_cons, tolerance=50)
simple_plot(multi_graph_cons)

# WORKFLOW 2: Using cityseer to manually clean an OSMnx graph
# ===========================================================
G_raw = io.nx_from_osm_nx(multi_di_graph_raw)
G = graphs.nx_wgs_to_utm(G_raw)
G = graphs.nx_simple_geoms(G)
G = graphs.nx_remove_filler_nodes(G)
G = graphs.nx_remove_dangling_nodes(G, despine=20, remove_disconnected=True)
G1 = graphs.nx_consolidate_nodes(
G, buffer_dist=15, crawl=True, min_node_group=4, cent_min_degree=4, cent_min_names=4
)
G2 = graphs.nx_split_opposing_geoms(G1, buffer_dist=15)
G3 = graphs.nx_consolidate_nodes(
G2, buffer_dist=15, crawl=False, min_node_degree=2, cent_min_degree=4, cent_min_names=4
)
G4 = graphs.nx_iron_edges(G3)
simple_plot(G4)

# WORKFLOW 3: Using cityseer to download and automatically simplify the graph
# ===========================================================================
poly_wgs, _poly_utm, _utm_zone_number, _utm_zone_letter = io.buffered_point_poly(lng, lat, buffer_dist)
G_utm = io.osm_graph_from_poly(poly_wgs, simplify=True, remove_parallel=True, iron_edges=True)
simple_plot(G_utm)

An example OSMnx simplification and consolidation workflow.

An example OSMnx to cityseer conversion followed by simplification and consolidation workflow in cityseer.

An example where OSM data is retrieved with cityseer with automatic simplification.

## SVG <path> elementOptimised packages

Computational methods for network-based analysis rely extensively on shortest-path algorithms: these present substantial computational complexity due to nested-loops. For this reason, methods implemented in pure Python, i.e. NetworkX, can be prohibitively slow. Speed improvements can be found by running intensive algorithms against packages implemented in lower-level languages such as Graph-Tool or igraph, which wrap underlying optimised code libraries implemented in more performant languages such as C++. However, off-the-shelf network analysis packages are not ideal for application to urbanism; for example, these do not typically cater for localised distance thresholds, specialised centrality methods, shortest vs simplest-path heuristics, or calculation of land-use accessibilities and mixed-uses.

Another difficulty in working with packages wrapping C++ is that these present a barrier to experimentation with customised forms of analysis. Overloading these forms of packages with functionality such as land-use or statistical analysis from within the Python ecosystem can therefor entail a dramatic slow-down in performance, whereas modifying these directly in C/C++ presents a steep learning curve.

cityseer evolved as a WIP package over the span of years, initially used for experimentation and comparative tests of centrality methods and landuse methods. For which purposes it has opted for pure python and numpy, but with computationally intensive algorithms wrapped in numba for the sake of performant JIT compilation. The use of numba has made it feasible to scale these methods to large and, optionally, decomposed networks. Further, when convenient to do so, 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 simpler to reason-with than nested array indices more typical of numpy. The more recent additions of networkX (for friendlier graph manipulation) and GeoDataFrame (for managing data state) are intended to provide an easier interface.

## SVG <path> elementGeoPandas

GeoPandas adds support for spatial features and related operations to Pandas dataframes. However, dataframes can be slow for purposes of iteratively adding and removing rows, for which reason it is preferable to use networkX graphs for the graph cleaning and preparation stage of analysis. After graph preparation steps, cityseer then uses a combination of GeoDataFrame structures (for downstream data state) and numpy arrays (wrapped in structures.NetworkStructure, which is accessed by numba optimised functions). It is relatively straight-forward to convert GeoPandas network and data representations — such as those used by momepy — to and from cityseer compatible graphs or data structures. Efforts are ongoing to automate these forms of workflows. Stay tuned!

Cooper, C.H.V., 2015. Spatial localization of closeness and betweenness measures: a self-contradictory but useful form of network analysis. International Journal of Geographical Information Science, 29(8), pp.1293–1309. Available at: https://www.tandfonline.com/doi/pdf/10.1080/13658816.2015.1018834?needAccess=true.
Hillier, B. & Hanson, J., 1984. The Social Logic of Space, Cambridge: Cambridge University Press.
Porta, S., Crucitti, P. & Latora, V., 2006. The Network Analysis of Urban Streets: A Primal Approach. Environment and Planning B: Planning and Design, 33, pp.705–725. Available at: http://journals.sagepub.com/doi/pdf/10.1068/b32045.
Turner, A., 2007. 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, 34, pp.539–555. Available at: http://journals.sagepub.com/doi/pdf/10.1068/b32067.