Morphological Graph from Overture Maps & OpenStreetMap with City2Graph¶

This notebook demonstrates how to create morphological graph using City2Graph and data from Overture Maps. Morphological graph provide a comprehensive graph representation of urban form that captures the relationships between public and private spaces in cities.

What are Morphological Graphs?¶

Morphological graphs are heterogeneous graphs where:

• Nodes represent both public spaces (street segments) and private spaces (enclosed areas/tessellations)
• Edges capture three types of spatial relationships:
  • 🔴 Private-to-private: Adjacency between neighboring private spaces
  • 🔵 Public-to-public: Connectivity along street networks (dual graph representation)
  • 🟣 Private-to-public: Interface between private spaces and adjacent streets

Workflow Overview¶

1. Data Loading: Import building footprints and street segments from Overture Maps
2. Data Processing: Clean and prepare spatial data for network creation
3. Morphological Graph Generation: Create tessellations and extract spatial relationships
4. Graph Conversion: Convert to PyTorch Geometric for machine learning applications
5. Visualization: Explore the resulting morphological graph

This approach enables advanced urban analytics including connectivity analysis, accessibility studies, and graph-based machine learning for urban form analysis.

1. Setup and Dependencies¶

In [1]:

# Core libraries
import numpy as np
import geopandas as gpd
import matplotlib.pyplot as plt
import contextily as cx
from shapely import Point

# city2graph for morphological graph analysis
import city2graph as c2g

# Configure matplotlib for high-quality visualizations
plt.rcParams['figure.figsize'] = (14, 10)
plt.rcParams['figure.dpi'] = 100
plt.rcParams['font.size'] = 11
plt.style.use('ggplot')

print("✅ Dependencies loaded successfully")
print(f"city2graph version: {c2g.__version__}")
print(f"geopandas version: {gpd.__version__}")

# Core libraries import numpy as np import geopandas as gpd import matplotlib.pyplot as plt import contextily as cx from shapely import Point # city2graph for morphological graph analysis import city2graph as c2g # Configure matplotlib for high-quality visualizations plt.rcParams['figure.figsize'] = (14, 10) plt.rcParams['figure.dpi'] = 100 plt.rcParams['font.size'] = 11 plt.style.use('ggplot') print("✅ Dependencies loaded successfully") print(f"city2graph version: {c2g.__version__}") print(f"geopandas version: {gpd.__version__}")

✅ Dependencies loaded successfully
city2graph version: 0.1.7
geopandas version: 1.1.1

2. Loading Data from Overture Maps¶

We'll work with real urban data from Liverpool, UK, using Overture Maps which provides high-quality, open geospatial data including:

• Building footprints: Representing private/built spaces
• Road segments: Representing the street network
• Connectors: Intersection points in the road network

The data covers Liverpool city centre and demonstrates how City2Graph can process real-world urban environments.

In [ ]:

# Download data from Overture Maps (uncomment to download fresh data)
# This downloads building footprints, road segments, and connectors for Liverpool city centre

bbox = [-3.090173, 53.355487, -2.917138, 53.465587]  # Liverpool city centre bounding box

c2g.load_overture_data(
    area=bbox,
    types=["segment", "building", "connector"],
    output_dir="./data/overturemaps",
    prefix="liverpool_",
    save_to_file=True,
    return_data=False,
)

print("Data loading configuration complete")
print("To download fresh data, uncomment the city2graph.load_overture_data() call above")

# Download data from Overture Maps (uncomment to download fresh data) # This downloads building footprints, road segments, and connectors for Liverpool city centre bbox = [-3.090173, 53.355487, -2.917138, 53.465587] # Liverpool city centre bounding box c2g.load_overture_data( area=bbox, types=["segment", "building", "connector"], output_dir="./data/overturemaps", prefix="liverpool_", save_to_file=True, return_data=False, ) print("Data loading configuration complete") print("To download fresh data, uncomment the city2graph.load_overture_data() call above")

Data loading configuration complete
To download fresh data, uncomment the city2graph.load_overture_data() call above

In [3]:

# Load the downloaded GeoJSON files
buildings_gdf = gpd.read_file("./data/overturemaps/liverpool_building.geojson")
segments_gdf = gpd.read_file("./data/overturemaps/liverpool_segment.geojson") 
connectors_gdf = gpd.read_file("./data/overturemaps/liverpool_connector.geojson")

# Convert to British National Grid (EPSG:27700) for accurate distance calculations
buildings_gdf = buildings_gdf.to_crs(epsg=27700)
segments_gdf = segments_gdf.to_crs(epsg=27700)
connectors_gdf = connectors_gdf.to_crs(epsg=27700)

print("✅ Data loaded successfully!")
print(f"📊 Dataset summary:")
print(f"   • Buildings: {len(buildings_gdf):,}")
print(f"   • Road segments: {len(segments_gdf):,}")
print(f"   • Connectors: {len(connectors_gdf):,}")
print(f"   • CRS: {buildings_gdf.crs}")

# Load the downloaded GeoJSON files buildings_gdf = gpd.read_file("./data/overturemaps/liverpool_building.geojson") segments_gdf = gpd.read_file("./data/overturemaps/liverpool_segment.geojson") connectors_gdf = gpd.read_file("./data/overturemaps/liverpool_connector.geojson") # Convert to British National Grid (EPSG:27700) for accurate distance calculations buildings_gdf = buildings_gdf.to_crs(epsg=27700) segments_gdf = segments_gdf.to_crs(epsg=27700) connectors_gdf = connectors_gdf.to_crs(epsg=27700) print("✅ Data loaded successfully!") print(f"📊 Dataset summary:") print(f" • Buildings: {len(buildings_gdf):,}") print(f" • Road segments: {len(segments_gdf):,}") print(f" • Connectors: {len(connectors_gdf):,}") print(f" • CRS: {buildings_gdf.crs}")

✅ Data loaded successfully!
📊 Dataset summary:
   • Buildings: 132,549
   • Road segments: 38,523
   • Connectors: 48,758
   • CRS: EPSG:27700

3. Street Network Processing¶

Before creating morphological graphs, we need to process the raw street data. This involves:

1. Filtering: Keep only road segments (exclude pedestrian paths, railways, etc.)
2. Barrier Processing: Handle bridges and tunnels to create accurate spatial barriers
3. Network Cleanup: Ensure proper connectivity for graph operations

The barrier_geometry column will contain the processed geometries that act as spatial barriers for tessellation.

In [4]:

# Filter to keep only road segments (excluding pedestrian paths, railways, etc.)
segments_gdf = segments_gdf[segments_gdf["subtype"] == "road"].copy()

# Process segments to handle bridges/tunnels and create proper spatial barriers
segments_gdf = c2g.process_overture_segments(
    segments_gdf=segments_gdf,
    get_barriers=True,
    connectors_gdf=connectors_gdf
)

print(f"✅ Processed {len(segments_gdf)} road segments")
print(f"📈 Barrier geometries created for tessellation")

# Check the geometry types in the barrier_geometry column
geometry_types = segments_gdf["barrier_geometry"].geom_type.value_counts()
print(f"\n🔍 Barrier geometry types:")
for geom_type, count in geometry_types.items():
    print(f"   • {geom_type}: {count:,}")

# Filter to keep only road segments (excluding pedestrian paths, railways, etc.) segments_gdf = segments_gdf[segments_gdf["subtype"] == "road"].copy() # Process segments to handle bridges/tunnels and create proper spatial barriers segments_gdf = c2g.process_overture_segments( segments_gdf=segments_gdf, get_barriers=True, connectors_gdf=connectors_gdf ) print(f"✅ Processed {len(segments_gdf)} road segments") print(f"📈 Barrier geometries created for tessellation") # Check the geometry types in the barrier_geometry column geometry_types = segments_gdf["barrier_geometry"].geom_type.value_counts() print(f"\n🔍 Barrier geometry types:") for geom_type, count in geometry_types.items(): print(f" • {geom_type}: {count:,}")

✅ Processed 63819 road segments
📈 Barrier geometries created for tessellation

🔍 Barrier geometry types:
   • LineString: 62,869
   • MultiLineString: 531

You can convert these segments to a (homogeneous) graph using the segments_to_graph function. Note that this function can be applied for any segments GeoDataFrame, not only for segments derived from OvertureMaps.

In [5]:

segments_G = c2g.segments_to_graph(segments_gdf, as_nx=True)

segments_G = c2g.segments_to_graph(segments_gdf, as_nx=True)

Removed 9 invalid geometries

In [6]:

c2g.plot_graph(segments_G)

c2g.plot_graph(segments_G)

Out[6]:

<Axes: >

4. Creating Morphological Graphs¶

Now we'll create the morphological graph - the core contribution of City2Graph. This process:

The Process:¶

1. Tessellation Creation: Divide space into private areas using street segments as barriers
2. Network Extraction: Identify three types of spatial relationships:
   • Private-to-private (red): Adjacency between neighboring private spaces
   • Public-to-public (blue): Connectivity along street networks
   • Private-to-public (purple): Interface between private spaces and streets

Why Morphological Graphs?¶

Unlike traditional approaches that analyze street networks and buildings separately, morphological graphs provide a unified representation of urban space that:

• Captures the complete topology of public and private spaces
• Enables holistic urban analysis combining street accessibility and land use
• Provides a foundation for spatially-explicit graph machine learning
• Supports integration of diverse urban attributes (POIs, demographics, functions)

In [7]:

# Define center point for the analysis area (Liverpool city centre)
center_point = gpd.GeoSeries([Point(-2.9879004, 53.4062724)], crs='EPSG:4326').to_crs(epsg=27700)

# Create the morphological graph
morpho_nodes, morpho_edges = c2g.morphological_graph(
    buildings_gdf=buildings_gdf,
    segments_gdf=segments_gdf,
    center_point=center_point,
    distance=500,                    # Analysis radius in meters
    clipping_buffer=300,            # Buffer for edge effects
    primary_barrier_col='barrier_geometry',
    contiguity="queen",             # Adjacency rule for tessellation
    keep_buildings=True,            # Preserve building geometries
)

# Define center point for the analysis area (Liverpool city centre) center_point = gpd.GeoSeries([Point(-2.9879004, 53.4062724)], crs='EPSG:4326').to_crs(epsg=27700) # Create the morphological graph morpho_nodes, morpho_edges = c2g.morphological_graph( buildings_gdf=buildings_gdf, segments_gdf=segments_gdf, center_point=center_point, distance=500, # Analysis radius in meters clipping_buffer=300, # Buffer for edge effects primary_barrier_col='barrier_geometry', contiguity="queen", # Adjacency rule for tessellation keep_buildings=True, # Preserve building geometries )

Removed 9 invalid geometries
/Users/yutasato/Projects/Liverpool/city2graph/.venv/lib/python3.13/site-packages/libpysal/weights/contiguity.py:347: UserWarning: The weights matrix is not fully connected: 
 There are 3 disconnected components.
 There are 2 islands with ids: 32_107405, 32_107413.
  W.__init__(self, neighbors, ids=ids, **kw)

In [8]:

print(f"Node types: {list(morpho_nodes.keys())}")
print(f"Edge types: {list(morpho_edges.keys())}")
print(f"Private spaces: {len(morpho_nodes['private']):,}")
print(f"Public spaces: {len(morpho_nodes['public']):,}")

for edge_type, edge_gdf in morpho_edges.items():
    print(f"   • {edge_type}: {len(edge_gdf):,} connections")

print(f"Node types: {list(morpho_nodes.keys())}") print(f"Edge types: {list(morpho_edges.keys())}") print(f"Private spaces: {len(morpho_nodes['private']):,}") print(f"Public spaces: {len(morpho_nodes['public']):,}") for edge_type, edge_gdf in morpho_edges.items(): print(f" • {edge_type}: {len(edge_gdf):,} connections")

Node types: ['private', 'public']
Edge types: [('private', 'touched_to', 'private'), ('public', 'connected_to', 'public'), ('private', 'faced_to', 'public')]
Private spaces: 1,342
Public spaces: 801
   • ('private', 'touched_to', 'private'): 615 connections
   • ('public', 'connected_to', 'public'): 1,475 connections
   • ('private', 'faced_to', 'public'): 2,503 connections

In [9]:

morpho_nodes["private"].head()

morpho_nodes["private"].head()

Out[9]:

	geometry	enclosure_index	id	version	sources	level	subtype	class	height	names	...	facade_color	facade_material	roof_material	roof_shape	roof_direction	roof_orientation	roof_color	roof_height	building_geometry	tessellation_geometry
private_id
12_31956	POINT (334727.903 390226.444)	12	c904b7f1-c8dc-4892-bc1d-c40589a14df2	2.0	[{'property': '', 'dataset': 'OpenStreetMap', ...	NaN	commercial	retail	22.054096	{'primary': 'Primark', 'common': None, 'rules'...	...	None	None	None	None	NaN	None	None	NaN	POLYGON ((334741.448 390215.167, 334756.666 39...	POLYGON ((334755.579 390206.699, 334741.754 39...
12_31956	POINT (334727.903 390226.444)	12	dc8bce71-dc2c-4f77-aef2-38d97e5587ad	1.0	[{'property': '', 'dataset': 'OpenStreetMap', ...	NaN	None	None	NaN	None	...	None	None	None	None	NaN	None	None	NaN	POLYGON ((334765.068 390239.944, 334756.666 39...	POLYGON ((334755.579 390206.699, 334741.754 39...
12_31957	POINT (334783.221 390224.611)	12	6e125793-4950-4b77-a574-98bf89e02f7a	1.0	[{'property': '', 'dataset': 'OpenStreetMap', ...	NaN	None	None	NaN	{'primary': 'Pauline Books & Media', 'common':...	...	None	None	None	None	NaN	None	None	NaN	POLYGON ((334808.007 390196.826, 334817.382 39...	POLYGON ((334768.613 390253.5, 334803.709 3902...
12_31957	POINT (334783.221 390224.611)	12	c904b7f1-c8dc-4892-bc1d-c40589a14df2	2.0	[{'property': '', 'dataset': 'OpenStreetMap', ...	NaN	commercial	retail	22.054096	{'primary': 'Primark', 'common': None, 'rules'...	...	None	None	None	None	NaN	None	None	NaN	POLYGON ((334741.448 390215.167, 334756.666 39...	POLYGON ((334768.613 390253.5, 334803.709 3902...
12_31957	POINT (334783.221 390224.611)	12	dc8bce71-dc2c-4f77-aef2-38d97e5587ad	1.0	[{'property': '', 'dataset': 'OpenStreetMap', ...	NaN	None	None	NaN	None	...	None	None	None	None	NaN	None	None	NaN	POLYGON ((334765.068 390239.944, 334756.666 39...	POLYGON ((334768.613 390253.5, 334803.709 3902...

5 rows × 25 columns

In [10]:

morpho_nodes["public"].head()

morpho_nodes["public"].head()

Out[10]:

	id	version	sources	subtype	class	names	connectors	routes	subclass_rules	access_restrictions	...	road_flags	speed_limits	width_rules	subclass	geometry	split_from	split_to	length	barrier_geometry	segment_geometry
public_id
56159	a5e01c9b-5290-4eab-a020-ee9e7e157760_1	1	[{'property': '', 'dataset': 'OpenStreetMap', ...	road	unclassified	{'primary': 'Tower Gardens', 'common': None, '...	[{'connector_id': '137acfba-67ce-4882-9720-be9...	None	None	None	...	None	None	None	None	POINT (334032.697 390390.027)	0.000000	0.127877	7.849774	LINESTRING (334034.687 390386.645, 334030.706 ...	LINESTRING (334034.687 390386.645, 334030.706 ...
56180	d9dca30b-31ca-4d72-8c6f-b2e6195ae33d_1	1	[{'property': '', 'dataset': 'OpenStreetMap', ...	road	primary	{'primary': 'Water Street', 'common': None, 'r...	[{'connector_id': '137acfba-67ce-4882-9720-be9...	[{'name': None, 'network': None, 'ref': 'A57',...	None	[{'access_type': 'denied', 'when': {'during': ...	...	None	[{'min_speed': None, 'max_speed': {'value': 30...	None	None	POINT (334018.757 390377.991)	0.000000	0.725988	36.258554	LINESTRING (334034.687 390386.645, 334005.825 ...	LINESTRING (334034.687 390386.645, 334005.825 ...
56391	4704f2a4-75b5-47d4-9270-4261f9459742	1	[{'property': 'routes', 'dataset': 'OpenStreet...	road	primary	{'primary': 'Water Street', 'common': None, 'r...	[{'connector_id': 'a62ffd87-a56f-4a02-bf30-67d...	[{'name': None, 'network': None, 'ref': 'A57',...	None	[{'access_type': 'denied', 'when': {'during': ...	...	None	[{'min_speed': None, 'max_speed': {'value': 30...	None	None	POINT (334041.874 390390.851)	NaN	NaN	16.653532	LINESTRING (334049.06 390395.057, 334034.687 3...	LINESTRING (334049.06 390395.057, 334034.687 3...
56178	66a3f6ca-888c-43cd-bc30-50dff8d09325_5	1	[{'property': '', 'dataset': 'OpenStreetMap', ...	road	cycleway	{'primary': 'Water Street', 'common': None, 'r...	[{'connector_id': 'ff54a37c-c0b9-4338-be77-b37...	None	None	[{'access_type': 'denied', 'when': {'during': ...	...	None	None	None	None	POINT (334015.167 390383.574)	0.332346	0.591025	36.779102	LINESTRING (333999.652 390373.703, 333999.652 ...	LINESTRING (333999.652 390373.703, 333999.652 ...
56179	66a3f6ca-888c-43cd-bc30-50dff8d09325_6	1	[{'property': '', 'dataset': 'OpenStreetMap', ...	road	cycleway	{'primary': 'Water Street', 'common': None, 'r...	[{'connector_id': 'ff54a37c-c0b9-4338-be77-b37...	None	None	[{'access_type': 'denied', 'when': {'during': ...	...	None	None	None	None	POINT (334055.463 390408.654)	0.591025	1.000000	58.148253	LINESTRING (334030.706 390393.41, 334030.706 3...	LINESTRING (334030.706 390393.41, 334030.706 3...

5 rows × 25 columns

In [11]:

morpho_edges[('public', 'connected_to', 'public')].head()

morpho_edges[('public', 'connected_to', 'public')].head()

Out[11]:

		geometry
from_public_id	to_public_id
23570	24229	LINESTRING (334597.772 390729.399, 334589.75 3...
	24230	LINESTRING (334597.772 390729.399, 334587.034 ...
	24235	LINESTRING (334597.772 390729.399, 334611.822 ...
	24255	LINESTRING (334597.772 390729.399, 334582.53 3...
23577	24232	LINESTRING (334615.698 390739.427, 334602.944 ...

In [12]:

morpho_edges[('private', 'faced_to', 'public')].head()

morpho_edges[('private', 'faced_to', 'public')].head()

Out[12]:

		geometry
private_id	public_id
183_107526	56159	LINESTRING (334054.645 390363.231, 334032.697 ...
182_-160	56159	LINESTRING (334017.91 390381.351, 334032.697 3...
181_-161	56159	LINESTRING (334058.29 390405.424, 334032.697 3...
180_107446	56159	LINESTRING (333990.617 390408.84, 334032.697 3...
179_107445	56159	LINESTRING (334020.81 390464.168, 334032.697 3...

In [13]:

morpho_edges[('private', 'touched_to', 'private')].head()

morpho_edges[('private', 'touched_to', 'private')].head()

Out[13]:

		weight	geometry	enclosure_index
from_private_id	to_private_id
12_31956	12_31957	55.347745	LINESTRING (334727.903 390226.444, 334783.221 ...	12
12_31957	12_31968	28.277931	LINESTRING (334783.221 390224.611, 334810.774 ...	12
12_31967	12_31968	19.731447	LINESTRING (334829.869 390213.279, 334810.774 ...	12
20_33139	20_33140	7.723210	LINESTRING (334667.044 390104.963, 334659.849 ...	20
	20_33142	72.502424	LINESTRING (334667.044 390104.963, 334600.224 ...	20

In [14]:

morpho_nodes["public"]

morpho_nodes["public"]

Out[14]:

	id	version	sources	subtype	class	names	connectors	routes	subclass_rules	access_restrictions	...	road_flags	speed_limits	width_rules	subclass	geometry	split_from	split_to	length	barrier_geometry	segment_geometry
public_id
56159	a5e01c9b-5290-4eab-a020-ee9e7e157760_1	1	[{'property': '', 'dataset': 'OpenStreetMap', ...	road	unclassified	{'primary': 'Tower Gardens', 'common': None, '...	[{'connector_id': '137acfba-67ce-4882-9720-be9...	None	None	None	...	None	None	None	None	POINT (334032.697 390390.027)	0.000000	0.127877	7.849774	LINESTRING (334034.687 390386.645, 334030.706 ...	LINESTRING (334034.687 390386.645, 334030.706 ...
56180	d9dca30b-31ca-4d72-8c6f-b2e6195ae33d_1	1	[{'property': '', 'dataset': 'OpenStreetMap', ...	road	primary	{'primary': 'Water Street', 'common': None, 'r...	[{'connector_id': '137acfba-67ce-4882-9720-be9...	[{'name': None, 'network': None, 'ref': 'A57',...	None	[{'access_type': 'denied', 'when': {'during': ...	...	None	[{'min_speed': None, 'max_speed': {'value': 30...	None	None	POINT (334018.757 390377.991)	0.000000	0.725988	36.258554	LINESTRING (334034.687 390386.645, 334005.825 ...	LINESTRING (334034.687 390386.645, 334005.825 ...
56391	4704f2a4-75b5-47d4-9270-4261f9459742	1	[{'property': 'routes', 'dataset': 'OpenStreet...	road	primary	{'primary': 'Water Street', 'common': None, 'r...	[{'connector_id': 'a62ffd87-a56f-4a02-bf30-67d...	[{'name': None, 'network': None, 'ref': 'A57',...	None	[{'access_type': 'denied', 'when': {'during': ...	...	None	[{'min_speed': None, 'max_speed': {'value': 30...	None	None	POINT (334041.874 390390.851)	NaN	NaN	16.653532	LINESTRING (334049.06 390395.057, 334034.687 3...	LINESTRING (334049.06 390395.057, 334034.687 3...
56178	66a3f6ca-888c-43cd-bc30-50dff8d09325_5	1	[{'property': '', 'dataset': 'OpenStreetMap', ...	road	cycleway	{'primary': 'Water Street', 'common': None, 'r...	[{'connector_id': 'ff54a37c-c0b9-4338-be77-b37...	None	None	[{'access_type': 'denied', 'when': {'during': ...	...	None	None	None	None	POINT (334015.167 390383.574)	0.332346	0.591025	36.779102	LINESTRING (333999.652 390373.703, 333999.652 ...	LINESTRING (333999.652 390373.703, 333999.652 ...
56179	66a3f6ca-888c-43cd-bc30-50dff8d09325_6	1	[{'property': '', 'dataset': 'OpenStreetMap', ...	road	cycleway	{'primary': 'Water Street', 'common': None, 'r...	[{'connector_id': 'ff54a37c-c0b9-4338-be77-b37...	None	None	[{'access_type': 'denied', 'when': {'during': ...	...	None	None	None	None	POINT (334055.463 390408.654)	0.591025	1.000000	58.148253	LINESTRING (334030.706 390393.41, 334030.706 3...	LINESTRING (334030.706 390393.41, 334030.706 3...
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
55826	c91bfcc0-f0c3-4d8b-86f0-219e304ea73c_1	2	[{'property': '', 'dataset': 'OpenStreetMap', ...	road	trunk	{'primary': 'Strand Street', 'common': None, '...	[{'connector_id': '462f0807-4888-4a3c-bd91-e7d...	None	None	[{'access_type': 'denied', 'when': {'during': ...	...	None	[{'min_speed': None, 'max_speed': {'value': 30...	None	None	POINT (334126.221 390166.28)	0.000000	0.519847	42.759490	LINESTRING (334112.436 390182.618, 334116.051 ...	LINESTRING (334112.436 390182.618, 334116.051 ...
55839	bf145e29-c53d-44d2-9a78-c0546b071a40_1	2	[{'property': '', 'dataset': 'OpenStreetMap', ...	road	trunk	{'primary': 'Strand Street', 'common': None, '...	[{'connector_id': '3617e7cc-e871-45f5-a8a4-ccb...	None	None	[{'access_type': 'denied', 'when': {'during': ...	...	None	[{'min_speed': None, 'max_speed': {'value': 30...	None	None	POINT (334095.885 390172.017)	0.000000	0.672058	40.225191	LINESTRING (334108.506 390156.357, 334086.439 ...	LINESTRING (334108.506 390156.357, 334086.439 ...
55846	3484a50c-97cc-419d-98d4-504e6cf2db09_4	1	[{'property': '', 'dataset': 'OpenStreetMap', ...	road	footway	None	[{'connector_id': '6a832436-a808-439b-9379-e16...	None	None	None	...	None	None	None	None	POINT (334080.751 390185.634)	0.694893	0.766920	6.367964	LINESTRING (334078.252 390183.661, 334078.253 ...	LINESTRING (334078.252 390183.661, 334078.253 ...
55845	3484a50c-97cc-419d-98d4-504e6cf2db09_3	1	[{'property': '', 'dataset': 'OpenStreetMap', ...	road	footway	None	[{'connector_id': '6a832436-a808-439b-9379-e16...	None	None	None	...	None	None	None	None	POINT (334073.571 390180.984)	0.572882	0.694893	10.786927	LINESTRING (334068.889 390178.306, 334068.889 ...	LINESTRING (334068.889 390178.306, 334068.889 ...
55856	d45a56ad-c452-46a6-ab9d-42ec9f35bb54_1	1	[{'property': '', 'dataset': 'OpenStreetMap', ...	road	unclassified	{'primary': 'George's Dock Way', 'common': Non...	[{'connector_id': '16a1387d-5006-4ed0-8760-668...	None	None	[{'access_type': 'denied', 'when': {'during': ...	...	None	[{'min_speed': None, 'max_speed': {'value': 30...	None	None	POINT (333974.723 390256.75)	0.000000	0.041809	8.512544	LINESTRING (333971.855 390259.894, 333977.592 ...	LINESTRING (333971.855 390259.894, 333977.592 ...

801 rows × 25 columns

In [15]:

fig, ax = plt.subplots(figsize=(14, 12), facecolor='#f9f9f9')

morpho_nodes["private"]["building_geometry"].plot(ax=ax, color='#e0e0e0', edgecolor='#c0c0c0', linewidth=0.3, alpha=0.7)
morpho_nodes["public"]["segment_geometry"].plot(ax=ax, color='#404040', linewidth=0.7, alpha=0.6)

c2g.plot_graph(
    nodes=morpho_nodes,
    edges=morpho_edges,
    subplots=False,
    ax=ax,
    bgcolor="#f9f9f9",
    labelcolor="#000000",
    node_color={'private': 'red', 'public': 'blue'},
    edge_color={
        ('private', 'touched_to', 'private'): '#B22222',
        ('public', 'connected_to', 'public'): '#0000FF',
        ('private', 'faced_to', 'public'): '#7B68EE',
    },
    markersize=10,
    linewidth=0.2,
)

fig, ax = plt.subplots(figsize=(14, 12), facecolor='#f9f9f9') morpho_nodes["private"]["building_geometry"].plot(ax=ax, color='#e0e0e0', edgecolor='#c0c0c0', linewidth=0.3, alpha=0.7) morpho_nodes["public"]["segment_geometry"].plot(ax=ax, color='#404040', linewidth=0.7, alpha=0.6) c2g.plot_graph( nodes=morpho_nodes, edges=morpho_edges, subplots=False, ax=ax, bgcolor="#f9f9f9", labelcolor="#000000", node_color={'private': 'red', 'public': 'blue'}, edge_color={ ('private', 'touched_to', 'private'): '#B22222', ('public', 'connected_to', 'public'): '#0000FF', ('private', 'faced_to', 'public'): '#7B68EE', }, markersize=10, linewidth=0.2, )

Out[15]:

<Axes: >

6. Converting to Graph Representations for Machine Learning¶

City2Graph provides seamless conversion between spatial data and graph formats optimized for machine learning. We'll demonstrate conversion to PyTorch Geometric, enabling advanced graph neural network applications for urban analysis.

Graph Format Support:¶

• NetworkX: For traditional graph analysis and algorithms
• PyTorch Geometric: For deep learning on graphs
• GeoDataFrames: For spatial analysis and visualization

This interoperability allows researchers to leverage the best tools for each analysis task.

In [16]:

# Check for PyTorch Geometric availability
import torch

try:
    import torch_geometric
    HAS_TORCH_GEOMETRIC = True
    print("✅ PyTorch Geometric successfully imported")
    print(f"   PyTorch version: {torch.__version__}")
    print(f"   PyTorch Geometric version: {torch_geometric.__version__}")
    print("🚀 Ready for graph representation learning!")
except ImportError:
    HAS_TORCH_GEOMETRIC = False
    print("⚠️  PyTorch Geometric not installed")
    print("   Install with: pip install torch-geometric")
    print("   Graph functionality will be limited to NetworkX")

# Check for PyTorch Geometric availability import torch try: import torch_geometric HAS_TORCH_GEOMETRIC = True print("✅ PyTorch Geometric successfully imported") print(f" PyTorch version: {torch.__version__}") print(f" PyTorch Geometric version: {torch_geometric.__version__}") print("🚀 Ready for graph representation learning!") except ImportError: HAS_TORCH_GEOMETRIC = False print("⚠️ PyTorch Geometric not installed") print(" Install with: pip install torch-geometric") print(" Graph functionality will be limited to NetworkX")

✅ PyTorch Geometric successfully imported
   PyTorch version: 2.9.1
   PyTorch Geometric version: 2.7.0
🚀 Ready for graph representation learning!

6.1 Homogeneous Graph: Private Space Network¶

Let's start with a homogeneous graph focusing on private spaces (tessellation cells) and their adjacency relationships. This represents the spatial structure of plots and parcels in the urban environment.

In [17]:

# Compute spatial features for private spaces (tessellation cells)
morpho_nodes["private"]["area"] = morpho_nodes["private"].geometry.area
morpho_nodes["private"]["perimeter"] = morpho_nodes["private"].geometry.length
morpho_nodes["private"]["compactness"] = (
    4 * np.pi * morpho_nodes["private"]["area"] / (morpho_nodes["private"]["perimeter"] ** 2)
)

print("📊 Computed spatial features for private spaces:")
feature_stats = morpho_nodes["private"][['area', 'perimeter', 'compactness']].describe()
print(feature_stats.round(2))

# Set proper index names for graph conversion
morpho_nodes["private"].index.name = "tess_id"
morpho_edges[('private', 'touched_to', 'private')].index.names = ['from_private_id', 'to_private_id']

print("\n✅ Features computed and indices configured")

# Compute spatial features for private spaces (tessellation cells) morpho_nodes["private"]["area"] = morpho_nodes["private"].geometry.area morpho_nodes["private"]["perimeter"] = morpho_nodes["private"].geometry.length morpho_nodes["private"]["compactness"] = ( 4 * np.pi * morpho_nodes["private"]["area"] / (morpho_nodes["private"]["perimeter"] ** 2) ) print("📊 Computed spatial features for private spaces:") feature_stats = morpho_nodes["private"][['area', 'perimeter', 'compactness']].describe() print(feature_stats.round(2)) # Set proper index names for graph conversion morpho_nodes["private"].index.name = "tess_id" morpho_edges[('private', 'touched_to', 'private')].index.names = ['from_private_id', 'to_private_id'] print("\n✅ Features computed and indices configured")

📊 Computed spatial features for private spaces:
         area  perimeter  compactness
count  1342.0     1342.0          0.0
mean      0.0        0.0          NaN
std       0.0        0.0          NaN
min       0.0        0.0          NaN
25%       0.0        0.0          NaN
50%       0.0        0.0          NaN
75%       0.0        0.0          NaN
max       0.0        0.0          NaN

✅ Features computed and indices configured

In [18]:

if HAS_TORCH_GEOMETRIC:
    # Create homogeneous graph of private spaces
    private_graph = c2g.gdf_to_pyg(
        nodes=morpho_nodes["private"],
        edges=morpho_edges[('private', 'touched_to', 'private')],
        node_feature_cols=['area', 'perimeter', 'compactness'],
        edge_feature_cols=None
    )
    
    print("🎯 Created homogeneous graph:")
    print(f"   • Nodes: {private_graph.num_nodes:,}")
    print(f"   • Edges: {private_graph.num_edges:,}")
    print(f"   • Node features: {private_graph.x.shape[1]} dimensions")
    print(f"   • Feature tensor shape: {private_graph.x.shape}")
    print("\n✅ Ready for graph neural network training!")
    
else:
    print("⚠️ Skipping PyTorch Geometric conversion (not installed)")
    private_graph = None

if HAS_TORCH_GEOMETRIC: # Create homogeneous graph of private spaces private_graph = c2g.gdf_to_pyg( nodes=morpho_nodes["private"], edges=morpho_edges[('private', 'touched_to', 'private')], node_feature_cols=['area', 'perimeter', 'compactness'], edge_feature_cols=None ) print("🎯 Created homogeneous graph:") print(f" • Nodes: {private_graph.num_nodes:,}") print(f" • Edges: {private_graph.num_edges:,}") print(f" • Node features: {private_graph.x.shape[1]} dimensions") print(f" • Feature tensor shape: {private_graph.x.shape}") print("\n✅ Ready for graph neural network training!") else: print("⚠️ Skipping PyTorch Geometric conversion (not installed)") private_graph = None

🎯 Created homogeneous graph:
   • Nodes: 1,342
   • Edges: 615
   • Node features: 3 dimensions
   • Feature tensor shape: torch.Size([1342, 3])

✅ Ready for graph neural network training!

Test Graph Conversions¶

Let's test the round-trip conversions between different graph formats to ensure data integrity:

6.2 Heterogeneous Graph: Complete Morphological Graph¶

Now let's create a heterogeneous graph that captures the full morphological graph with all node and edge types. This provides the complete representation for advanced urban analysis.

In [19]:

# Define center point for the analysis area (Liverpool city centre)
center_point = gpd.GeoSeries([Point(-2.9879004, 53.4062724)], crs='EPSG:4326').to_crs(epsg=27700)

# Create the morphological graph
print("🏗️  Creating morphological graph...")
morpho_nodes, morpho_edges = c2g.morphological_graph(
    buildings_gdf=buildings_gdf,
    segments_gdf=segments_gdf,
    center_point=center_point,
    distance=500,                    # Analysis radius in meters
    clipping_buffer=300,            # Buffer for edge effects
    primary_barrier_col='barrier_geometry',
    contiguity="queen",             # Adjacency rule for tessellation
    keep_buildings=True,            # Preserve building geometries
)

print("✅ Morphological graph created successfully!")
print(f"📊 Network summary:")
print(f"   • Node types: {list(morpho_nodes.keys())}")
print(f"   • Edge types: {list(morpho_edges.keys())}")
print(f"   • Private spaces: {len(morpho_nodes['private']):,}")
print(f"   • Public spaces: {len(morpho_nodes['public']):,}")

for edge_type, edge_gdf in morpho_edges.items():
    print(f"   • {edge_type}: {len(edge_gdf):,} connections")

# Define center point for the analysis area (Liverpool city centre) center_point = gpd.GeoSeries([Point(-2.9879004, 53.4062724)], crs='EPSG:4326').to_crs(epsg=27700) # Create the morphological graph print("🏗️ Creating morphological graph...") morpho_nodes, morpho_edges = c2g.morphological_graph( buildings_gdf=buildings_gdf, segments_gdf=segments_gdf, center_point=center_point, distance=500, # Analysis radius in meters clipping_buffer=300, # Buffer for edge effects primary_barrier_col='barrier_geometry', contiguity="queen", # Adjacency rule for tessellation keep_buildings=True, # Preserve building geometries ) print("✅ Morphological graph created successfully!") print(f"📊 Network summary:") print(f" • Node types: {list(morpho_nodes.keys())}") print(f" • Edge types: {list(morpho_edges.keys())}") print(f" • Private spaces: {len(morpho_nodes['private']):,}") print(f" • Public spaces: {len(morpho_nodes['public']):,}") for edge_type, edge_gdf in morpho_edges.items(): print(f" • {edge_type}: {len(edge_gdf):,} connections")

Removed 9 invalid geometries

🏗️  Creating morphological graph...
✅ Morphological graph created successfully!
📊 Network summary:
   • Node types: ['private', 'public']
   • Edge types: [('private', 'touched_to', 'private'), ('public', 'connected_to', 'public'), ('private', 'faced_to', 'public')]
   • Private spaces: 1,342
   • Public spaces: 801
   • ('private', 'touched_to', 'private'): 615 connections
   • ('public', 'connected_to', 'public'): 1,475 connections
   • ('private', 'faced_to', 'public'): 2,503 connections

/Users/yutasato/Projects/Liverpool/city2graph/.venv/lib/python3.13/site-packages/libpysal/weights/contiguity.py:347: UserWarning: The weights matrix is not fully connected: 
 There are 3 disconnected components.
 There are 2 islands with ids: 32_107405, 32_107413.
  W.__init__(self, neighbors, ids=ids, **kw)

In [20]:

# Compute features for public spaces (street segments)
morpho_nodes["public"]["length"] = morpho_nodes["public"].geometry.length

print("📊 Computed spatial features for public spaces:")
print(f"   • Street length statistics:")
length_stats = morpho_nodes["public"]["length"].describe()
print(f"     - Mean: {length_stats['mean']:.1f}m")
print(f"     - Median: {length_stats['50%']:.1f}m") 
print(f"     - Range: {length_stats['min']:.1f}m - {length_stats['max']:.1f}m")

print(f"\n✅ Features ready for heterogeneous graph creation")

# Compute features for public spaces (street segments) morpho_nodes["public"]["length"] = morpho_nodes["public"].geometry.length print("📊 Computed spatial features for public spaces:") print(f" • Street length statistics:") length_stats = morpho_nodes["public"]["length"].describe() print(f" - Mean: {length_stats['mean']:.1f}m") print(f" - Median: {length_stats['50%']:.1f}m") print(f" - Range: {length_stats['min']:.1f}m - {length_stats['max']:.1f}m") print(f"\n✅ Features ready for heterogeneous graph creation")

📊 Computed spatial features for public spaces:
   • Street length statistics:
     - Mean: 0.0m
     - Median: 0.0m
     - Range: 0.0m - 0.0m

✅ Features ready for heterogeneous graph creation

In [21]:

if HAS_TORCH_GEOMETRIC:
    # Create heterogeneous graph with all morphological relationships
    hetero_graph = c2g.gdf_to_pyg(
        morpho_nodes,
        morpho_edges,
        node_feature_cols={
            "private": ['area', 'perimeter', 'compactness'],
            "public": ['length']
        }
    )
    
    print("🌐 Created heterogeneous morphological graph:")
    print(f"   📊 Node types and counts:")
    for node_type in hetero_graph.node_types:
        num_nodes = hetero_graph[node_type].x.shape[0]
        num_features = hetero_graph[node_type].x.shape[1]
        print(f"     • {node_type}: {num_nodes:,} nodes, {num_features} features")
    
    print(f"   🔗 Edge types and counts:")
    for edge_type in hetero_graph.edge_types:
        num_edges = hetero_graph[edge_type].edge_index.shape[1]
        print(f"     • {edge_type}: {num_edges:,} edges")
    
    print("\n✅ Complete morphological graph ready for heterogeneous GNN training!")
    
else:
    print("⚠️ Skipping PyTorch Geometric conversion (not installed)")
    hetero_graph = None

if HAS_TORCH_GEOMETRIC: # Create heterogeneous graph with all morphological relationships hetero_graph = c2g.gdf_to_pyg( morpho_nodes, morpho_edges, node_feature_cols={ "private": ['area', 'perimeter', 'compactness'], "public": ['length'] } ) print("🌐 Created heterogeneous morphological graph:") print(f" 📊 Node types and counts:") for node_type in hetero_graph.node_types: num_nodes = hetero_graph[node_type].x.shape[0] num_features = hetero_graph[node_type].x.shape[1] print(f" • {node_type}: {num_nodes:,} nodes, {num_features} features") print(f" 🔗 Edge types and counts:") for edge_type in hetero_graph.edge_types: num_edges = hetero_graph[edge_type].edge_index.shape[1] print(f" • {edge_type}: {num_edges:,} edges") print("\n✅ Complete morphological graph ready for heterogeneous GNN training!") else: print("⚠️ Skipping PyTorch Geometric conversion (not installed)") hetero_graph = None

🌐 Created heterogeneous morphological graph:
   📊 Node types and counts:
     • private: 1,342 nodes, 0 features
     • public: 801 nodes, 1 features
   🔗 Edge types and counts:
     • ('private', 'touched_to', 'private'): 615 edges
     • ('public', 'connected_to', 'public'): 1,475 edges
     • ('private', 'faced_to', 'public'): 2,503 edges

✅ Complete morphological graph ready for heterogeneous GNN training!

In [22]:

hetero_graph

hetero_graph

Out[22]:

HeteroData(
  crs=EPSG:27700,
  graph_metadata=<city2graph.base.GraphMetadata object at 0x15a3a3d90>,
  private={
    x=[1342, 0],
    pos=[1342, 2],
  },
  public={
    x=[801, 1],
    pos=[801, 2],
  },
  (private, touched_to, private)={
    edge_index=[2, 615],
    edge_attr=[615, 0],
  },
  (public, connected_to, public)={
    edge_index=[2, 1475],
    edge_attr=[1475, 0],
  },
  (private, faced_to, public)={
    edge_index=[2, 2503],
    edge_attr=[2503, 0],
  }
)

6.3 Using NetworkX¶

City2Graph provides seamless conversion to NetworkX for traditional graph analysis and algorithms. This enables access to the rich ecosystem of graph analysis tools.

In [23]:

morpho_graph = c2g.gdf_to_pyg(
    morpho_nodes,
    morpho_edges,
    node_feature_cols={"private": ['area', 'perimeter', 'compactness'],
                       "public": ['length']},
                       )

# Convert morphological graph to NetworkX for traditional graph analysis
G_morpho = c2g.gdf_to_nx(morpho_nodes, morpho_edges)

print("🔗 Converted to NetworkX:")
print(f"   • Total nodes: {G_morpho.number_of_nodes():,}")
print(f"   • Total edges: {G_morpho.number_of_edges():,}")
print(f"   • Graph type: {'Directed' if G_morpho.is_directed() else 'Undirected'}")

# Check if it's a heterogeneous graph
has_node_types = any('node_type' in data for _, data in G_morpho.nodes(data=True))
print(f"   • Heterogeneous: {'Yes' if has_node_types else 'No'}")

if has_node_types:
    # Count nodes by type
    from collections import Counter
    node_types = [data.get('node_type', 'unknown') for _, data in G_morpho.nodes(data=True)]
    type_counts = Counter(node_types)
    print(f"   • Node type distribution:")
    for node_type, count in type_counts.items():
        print(f"     - {node_type}: {count:,}")

print("\n✅ Ready for NetworkX graph analysis algorithms!")

morpho_graph = c2g.gdf_to_pyg( morpho_nodes, morpho_edges, node_feature_cols={"private": ['area', 'perimeter', 'compactness'], "public": ['length']}, ) # Convert morphological graph to NetworkX for traditional graph analysis G_morpho = c2g.gdf_to_nx(morpho_nodes, morpho_edges) print("🔗 Converted to NetworkX:") print(f" • Total nodes: {G_morpho.number_of_nodes():,}") print(f" • Total edges: {G_morpho.number_of_edges():,}") print(f" • Graph type: {'Directed' if G_morpho.is_directed() else 'Undirected'}") # Check if it's a heterogeneous graph has_node_types = any('node_type' in data for _, data in G_morpho.nodes(data=True)) print(f" • Heterogeneous: {'Yes' if has_node_types else 'No'}") if has_node_types: # Count nodes by type from collections import Counter node_types = [data.get('node_type', 'unknown') for _, data in G_morpho.nodes(data=True)] type_counts = Counter(node_types) print(f" • Node type distribution:") for node_type, count in type_counts.items(): print(f" - {node_type}: {count:,}") print("\n✅ Ready for NetworkX graph analysis algorithms!")

🔗 Converted to NetworkX:
   • Total nodes: 2,143
   • Total edges: 4,593
   • Graph type: Undirected
   • Heterogeneous: Yes
   • Node type distribution:
     - private: 1,342
     - public: 801

✅ Ready for NetworkX graph analysis algorithms!

7. OpenStreetMap¶

As a reference, you can execute the same process using OpenStreetMap dataset, extracted by osmnx.

In [24]:

import osmnx as ox

# Download and create a street network graph for Liverpool, UK
G_osmnx = ox.graph_from_place("Liverpool, UK", network_type="all")

print(f"✅ OSMnx graph created for Liverpool, UK")
print(f"   • Nodes: {len(G_osmnx.nodes):,}")
print(f"   • Edges: {len(G_osmnx.edges):,}")

import osmnx as ox # Download and create a street network graph for Liverpool, UK G_osmnx = ox.graph_from_place("Liverpool, UK", network_type="all") print(f"✅ OSMnx graph created for Liverpool, UK") print(f" • Nodes: {len(G_osmnx.nodes):,}") print(f" • Edges: {len(G_osmnx.edges):,}")

✅ OSMnx graph created for Liverpool, UK
   • Nodes: 45,081
   • Edges: 114,978

In [25]:

# Download POIs (amenities, shops, etc.) in Liverpool, UK
tags = {"building": True}
osm_buildings = ox.features_from_place("Liverpool, UK", tags)

print(f"✅ Retrieved {len(osm_buildings):,} buildings from OSMnx")
osm_buildings.head()

# Download POIs (amenities, shops, etc.) in Liverpool, UK tags = {"building": True} osm_buildings = ox.features_from_place("Liverpool, UK", tags) print(f"✅ Retrieved {len(osm_buildings):,} buildings from OSMnx") osm_buildings.head()

✅ Retrieved 77,492 buildings from OSMnx

Out[25]:

		geometry	building	building:material	building:use	name	emergency	addr:street	shop	website	addr:city	...	service:bicycle:parts	service:bicycle:pump	service:bicycle:second_hand	service:bicycle:spare_parts	type	school:trust	school:trust:name	school:trust:type	manager	last_checked
element	id
node	130190976	POINT (-2.92799 53.37127)	yes	brick	religious	Saint Anne's Parish Hall - 1902	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
	252558860	POINT (-2.91785 53.396)	residential	NaN	NaN	Bradbury House	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
	299317179	POINT (-2.97904 53.39175)	yes	NaN	NaN	Toxteth Ambulance Station	ambulance_station	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
	1563152870	POINT (-2.91166 53.41248)	manufacture	NaN	NaN	Tom Williams Cake Factory	NaN	Broad Green Road	pastry	http://www.cakefactory.co.uk/	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
	1669223582	POINT (-2.96855 53.40601)	yes	NaN	NaN	ALL (Active Learning Laboratory)	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN

5 rows × 378 columns

If you want to directly convert the nx.MultiGraph into torch_geometric.data.Data,

In [26]:

osm_data = c2g.nx_to_pyg(G_osmnx)

osm_data = c2g.nx_to_pyg(G_osmnx)

In [27]:

osm_data

osm_data

Out[27]:

Data(x=[45081, 0], edge_index=[2, 114978], edge_attr=[114978, 0], pos=[45081, 2], graph_metadata=<city2graph.base.GraphMetadata object at 0x14b8aab60>)

Or you can convert it into GeoDataFrame that is compatible to other functions in City2Graph,

In [28]:

osm_street_nodes, osm_street_edges =c2g.nx_to_gdf(G_osmnx)

osm_street_nodes, osm_street_edges =c2g.nx_to_gdf(G_osmnx)

In [29]:

osm_street_nodes.head()

osm_street_nodes.head()

Out[29]:

	y	x	street_count	geometry	highway	ref	junction
324206	53.407123	-2.884331	3	POINT (-2.88433 53.40712)	NaN	NaN	NaN
324209	53.405943	-2.896571	3	POINT (-2.89657 53.40594)	NaN	NaN	NaN
324210	53.406113	-2.896688	3	POINT (-2.89669 53.40611)	motorway_junction	4	NaN
324216	53.406488	-2.899987	3	POINT (-2.89999 53.40649)	NaN	NaN	NaN
324217	53.407391	-2.902198	3	POINT (-2.9022 53.40739)	NaN	NaN	NaN

In [30]:

osm_street_edges.head()

osm_street_edges.head()

Out[30]:

			osmid	highway	lanes	maxspeed	oneway	ref	reversed	length	bridge	geometry	name	junction	service	access	width	tunnel	est_width
324206	324209	0	[28181793, 627409058, 546631471, 1155945617, 1...	motorway	3	[70 mph, 40 mph, 50 mph]	True	M62	False	823.913652	yes	LINESTRING (-2.88433 53.40712, -2.88494 53.407...	NaN	NaN	NaN	NaN	NaN	NaN	NaN
324209	3467956864	0	15215646	trunk	3	40 mph	True	A5080	False	52.584979	NaN	LINESTRING (-2.89657 53.40594, -2.89678 53.405...	Bowring Park Road	NaN	NaN	NaN	NaN	NaN	NaN
324210	11385898804	0	15215652	primary	NaN	40 mph	True	A5080	False	32.304470	NaN	LINESTRING (-2.89669 53.40611, -2.89629 53.406...	Bowring Park Road	NaN	NaN	NaN	NaN	NaN	NaN
324216	21026685	0	4002276	trunk	3	40 mph	True	A5080	False	87.887476	NaN	LINESTRING (-2.89999 53.40649, -2.90028 53.406...	Edge Lane Drive	NaN	NaN	NaN	NaN	NaN	NaN
	21026680	0	4002284	trunk_link	NaN	40 mph	True	NaN	False	61.909425	NaN	LINESTRING (-2.89999 53.40649, -2.90029 53.406...	NaN	NaN	NaN	NaN	NaN	NaN	NaN

To constrcut a morphological graph,

In [31]:

osm_buildings = osm_buildings.to_crs(epsg=27700)
osm_street_edges = osm_street_edges.to_crs(epsg=27700)

osm_buildings = osm_buildings.to_crs(epsg=27700) osm_street_edges = osm_street_edges.to_crs(epsg=27700)

In [32]:

# Exclude rows with point geometries from osm_buildings
osm_buildings = osm_buildings[osm_buildings.geometry.type != "Point"]

# Exclude rows with point geometries from osm_buildings osm_buildings = osm_buildings[osm_buildings.geometry.type != "Point"]

In [33]:

# Define center point for the analysis area (Liverpool city centre)
center_point = gpd.GeoSeries([Point(-2.9879004, 53.4062724)], crs='EPSG:4326').to_crs(epsg=27700)

# Create the morphological graph
print("🏗️  Creating morphological graph...")
morpho_nodes, morpho_edges = c2g.morphological_graph(
    buildings_gdf=osm_buildings,
    segments_gdf=osm_street_edges,
    center_point=center_point,
    distance=500,                    # Analysis radius in meters
    clipping_buffer=300,            # Buffer for edge effects
    primary_barrier_col='barrier_geometry',
    contiguity="queen",             # Adjacency rule for tessellation
    keep_buildings=True,            # Preserve building geometries
    keep_segments=True,             # Preserve street segment geometries
)

# Define center point for the analysis area (Liverpool city centre) center_point = gpd.GeoSeries([Point(-2.9879004, 53.4062724)], crs='EPSG:4326').to_crs(epsg=27700) # Create the morphological graph print("🏗️ Creating morphological graph...") morpho_nodes, morpho_edges = c2g.morphological_graph( buildings_gdf=osm_buildings, segments_gdf=osm_street_edges, center_point=center_point, distance=500, # Analysis radius in meters clipping_buffer=300, # Buffer for edge effects primary_barrier_col='barrier_geometry', contiguity="queen", # Adjacency rule for tessellation keep_buildings=True, # Preserve building geometries keep_segments=True, # Preserve street segment geometries )

🏗️  Creating morphological graph...

/Users/yutasato/Projects/Liverpool/city2graph/.venv/lib/python3.13/site-packages/libpysal/weights/contiguity.py:347: UserWarning: The weights matrix is not fully connected: 
 There are 3 disconnected components.
 There are 2 islands with ids: 50_('way', 659554384), 50_('way', 659554386).
  W.__init__(self, neighbors, ids=ids, **kw)

In [34]:

print(f"   • Node types: {list(morpho_nodes.keys())}")
print(f"   • Edge types: {list(morpho_edges.keys())}")
print(f"   • Private spaces: {len(morpho_nodes['private']):,}")
print(f"   • Public spaces: {len(morpho_nodes['public']):,}")

for edge_type, edge_gdf in morpho_edges.items():
    print(f"   • {edge_type}: {len(edge_gdf):,} connections")

print(f" • Node types: {list(morpho_nodes.keys())}") print(f" • Edge types: {list(morpho_edges.keys())}") print(f" • Private spaces: {len(morpho_nodes['private']):,}") print(f" • Public spaces: {len(morpho_nodes['public']):,}") for edge_type, edge_gdf in morpho_edges.items(): print(f" • {edge_type}: {len(edge_gdf):,} connections")

   • Node types: ['private', 'public']
   • Edge types: [('private', 'touched_to', 'private'), ('public', 'connected_to', 'public'), ('private', 'faced_to', 'public')]
   • Private spaces: 1,489
   • Public spaces: 651
   • ('private', 'touched_to', 'private'): 564 connections
   • ('public', 'connected_to', 'public'): 1,299 connections
   • ('private', 'faced_to', 'public'): 3,276 connections

In [35]:

fig, ax = plt.subplots(figsize=(14, 12), facecolor='#f9f9f9')

morpho_nodes["private"]["building_geometry"].plot(ax=ax, color='#e0e0e0', edgecolor='#c0c0c0', linewidth=0.3, alpha=0.7)
morpho_nodes["public"]["segment_geometry"].plot(ax=ax, color='#404040', linewidth=0.7, alpha=0.6)

c2g.plot_graph(
    nodes=morpho_nodes,
    edges=morpho_edges,
    subplots=False,
    ax=ax,
    bgcolor="#f9f9f9",
    labelcolor="#000000",
    node_color={'private': 'red', 'public': 'blue'},
    edge_color={
        ('private', 'touched_to', 'private'): '#B22222',
        ('public', 'connected_to', 'public'): '#0000FF',
        ('private', 'faced_to', 'public'): '#7B68EE',
    },
    markersize=10,
    linewidth=0.2,
)

fig, ax = plt.subplots(figsize=(14, 12), facecolor='#f9f9f9') morpho_nodes["private"]["building_geometry"].plot(ax=ax, color='#e0e0e0', edgecolor='#c0c0c0', linewidth=0.3, alpha=0.7) morpho_nodes["public"]["segment_geometry"].plot(ax=ax, color='#404040', linewidth=0.7, alpha=0.6) c2g.plot_graph( nodes=morpho_nodes, edges=morpho_edges, subplots=False, ax=ax, bgcolor="#f9f9f9", labelcolor="#000000", node_color={'private': 'red', 'public': 'blue'}, edge_color={ ('private', 'touched_to', 'private'): '#B22222', ('public', 'connected_to', 'public'): '#0000FF', ('private', 'faced_to', 'public'): '#7B68EE', }, markersize=10, linewidth=0.2, )

Out[35]:

<Axes: >

In [36]:

osm_hetero_data = c2g.gdf_to_pyg(morpho_nodes, morpho_edges)

osm_hetero_data = c2g.gdf_to_pyg(morpho_nodes, morpho_edges)

In [37]:

osm_hetero_data

osm_hetero_data

Out[37]:

HeteroData(
  crs=EPSG:27700,
  graph_metadata=<city2graph.base.GraphMetadata object at 0x14bcc2270>,
  private={
    x=[1489, 0],
    pos=[1489, 2],
  },
  public={
    x=[651, 0],
    pos=[651, 2],
  },
  (private, touched_to, private)={
    edge_index=[2, 564],
    edge_attr=[564, 0],
  },
  (public, connected_to, public)={
    edge_index=[2, 1299],
    edge_attr=[1299, 0],
  },
  (private, faced_to, public)={
    edge_index=[2, 3276],
    edge_attr=[3276, 0],
  }
)