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Network analysis in Python

Finding a shortest path using a specific street network is a common GIS problem that has many practical applications. For example navigators are one of those “every-day” applications where routing using specific algorithms is used to find the optimal route between two (or multiple) points.

It is also possible to perform network analysis such as tranposrtation routing in Python. Networkx is a Python module that provides tools for analyzing networks in various different ways. It also contains algorithms such as Dijkstra’s algorithm or A* algoritm that are commonly used to find shortest paths along transportation network.

To be able to conduct network analysis, it is, of course, necessary to have a network that is used for the analyses. OSMnx package that we just explored in previous tutorial, makes it really easy to retrieve routable networks from OpenStreetMap with different transport modes (walking, cycling and driving). OSMnx also combines some functionalities from networkx module to make it straightforward to conduct routing along OpenStreetMap data.

Next we will test the routing functionalities of OSMnx by finding a shortest path between two points based on drivable roads. When fetching netowrk data from OpenStreetMap using OSMnx, it is possible to define the type of street network using the network_type parameter (options: drive, walk and bike).

  • import modules:
[1]:
import osmnx as ox
import networkx as nx
import geopandas as gpd
import matplotlib.pyplot as plt
import pandas as pd
  • Download the OSM data from Kamppi but this time include only such street segments that are meant for cars by specifying 'drive' into network_type:
[2]:
place_name = "Kamppi, Helsinki, Finland"
graph = ox.graph_from_place(place_name, network_type='drive')
  • Plot the graph:
[3]:
fig, ax = ox.plot_graph(graph)
../../_images/notebooks_L6_network-analysis_5_0.png

Okey so now we have retrieved only such streets where it is possible to drive with a car. Let’s confirm this by taking a look at the attributes of the street network. Easiest way to do this is to convert the graph (nodes and edges) into GeoDataFrames.

Converting graph into a GeoDataFrame can be done with function graph_to_gdfs() that we already used in previous tutorial. With parameters nodes and edges, it is possible to control whether to retrieve both nodes and edges from the graph.

  • Let’s retreive the edges as a geodataframe:
[4]:
# Retrieve only edges from the graph
edges = ox.graph_to_gdfs(graph, nodes=False, edges=True)
[5]:
# Check columns
edges.columns
[5]:
Index(['u', 'v', 'key', 'osmid', 'oneway', 'lanes', 'name', 'highway',
       'maxspeed', 'length', 'geometry', 'junction', 'bridge', 'access'],
      dtype='object')
[6]:
# Check crs
edges.crs
[6]:
'+proj=longlat +ellps=WGS84 +datum=WGS84 +no_defs'
[7]:
edges.head()
[7]:
u v key osmid oneway lanes name highway maxspeed length geometry junction bridge access
0 25216594 1372425714 0 23856784 True 2 Mechelininkatu primary 40 40.885 LINESTRING (24.92106 60.16479, 24.92095 60.164... NaN NaN NaN
1 25238874 1372425713 0 [29977177, 30470347] True 3 Mechelininkatu primary 40 16.601 LINESTRING (24.92103 60.16366, 24.92104 60.163... NaN NaN NaN
2 25238944 25216594 0 [372440330, 8135861] True 2 NaN primary 40 25.190 LINESTRING (24.92129 60.16463, 24.92127 60.164... NaN NaN NaN
3 25238944 319896278 0 [25514547, 677423564, 30288797, 30288799] True [3, 2] Mechelininkatu primary 40 242.476 LINESTRING (24.92129 60.16463, 24.92136 60.164... NaN NaN NaN
4 25291537 25291591 0 [30568275, 36729015, 316590744, 316590745, 316... True NaN Fredrikinkatu tertiary 30 139.090 LINESTRING (24.93702 60.16433, 24.93700 60.164... NaN NaN NaN

Okey, so we have quite many columns in our GeoDataFrame. Most of the columns are fairly self-explanatory but the following table describes all of them. We can also see that the CRS of the GeoDataFrame seems to be WGS84 (i.e. epsg: 4326). Most of the attributes come directly from the OpenStreetMap, however, columns u and v are Networkx specific ids. You can click on the links to get more information about each attribute:

Column Description Data type
bridge Bridge feature boolean
geometry Geometry of the feature Shapely.geometry
highway Tag for roads (road type) str / list
lanes Number of lanes int (or nan)
lenght Length of feature (meters) float
maxspeed maximum legal speed limit int /list
name Name of the (street) element str (or nan)
oneway One way road boolean
osmid Unique ids for the element list
u The first node of edge int
v The last node of edge int
  • Let’s take a look what kind of features we have in the highway column:
[8]:
print(edges['highway'].value_counts())
residential      112
tertiary          78
primary           26
secondary         17
unclassified      11
living_street      4
primary_link       1
Name: highway, dtype: int64

Okey, now we can confirm that as a result our street network indeed only contains such streets where it is allowed to drive with a car as there are no e.g. cycleways or footways included in the data.

Let’s continue and find the shortest path between two points based on the distance. As the data is in WGS84 format, we should first reproject our data into a metric system. We can re-project the graph from latitudes and longitudes to an appropriate UTM zone using the project_graph() function from OSMnx.

  • Project the graph:
[9]:
graph_proj = ox.project_graph(graph)
fig, ax = ox.plot_graph(graph_proj)
../../_images/notebooks_L6_network-analysis_15_0.png

We can see a modest change in the appearance of the graph. But let’s take a closer look by seeing how the data values look now:

[10]:
# Get Edges and Nodes
nodes_proj, edges_proj = ox.graph_to_gdfs(graph_proj, nodes=True, edges=True)
[11]:
print("Coordinate system:", edges_proj.crs)
Coordinate system: +proj=utm +zone=35 +ellps=WGS84 +datum=WGS84 +units=m +no_defs
[12]:
edges_proj.head()
[12]:
u v key osmid oneway lanes name highway maxspeed length geometry junction bridge access
0 25216594 1372425714 0 23856784 True 2 Mechelininkatu primary 40 40.885 LINESTRING (384631.322 6671580.071, 384624.750... NaN NaN NaN
1 25238874 1372425713 0 [29977177, 30470347] True 3 Mechelininkatu primary 40 16.601 LINESTRING (384625.787 6671454.380, 384626.281... NaN NaN NaN
2 25238944 25216594 0 [372440330, 8135861] True 2 NaN primary 40 25.190 LINESTRING (384643.473 6671561.534, 384643.045... NaN NaN NaN
3 25238944 319896278 0 [25514547, 677423564, 30288797, 30288799] True [3, 2] Mechelininkatu primary 40 242.476 LINESTRING (384643.473 6671561.534, 384648.006... NaN NaN NaN
4 25291537 25291591 0 [30568275, 36729015, 316590744, 316590745, 316... True NaN Fredrikinkatu tertiary 30 139.090 LINESTRING (385515.553 6671500.134, 385514.557... NaN NaN NaN

Okey, as we can see from the CRS the data is now in UTM projection using zone 35 which is the one used for Finland, and indeed the orientation of the map and the geometry values also confirm this.

  • Furthermore, we can check the epsg code of this projection using pyproj:
[13]:
from pyproj import CRS
CRS(edges_proj.crs).to_epsg()
[13]:
32635

Indeed, the projection is now WGS 84 / UTM zone 35N, EPSG:32635.

Analyzing the network properties

Now as we have seen some of the basic functionalities of OSMnx such as downloading the data and converting data from graph to GeoDataFrame, we can take a look some of the analytical features of omsnx. Osmnx includes many useful functionalities to extract information about the network.

  • To calculate some of the basic street network measures we can use basic_stats() function in OSMnx:
[14]:
# Calculate network statistics
stats = ox.basic_stats(graph_proj, circuity_dist='euclidean')
stats
[14]:
{'n': 124,
 'm': 249,
 'k_avg': 4.016129032258065,
 'intersection_count': 116,
 'streets_per_node_avg': 3.217741935483871,
 'streets_per_node_counts': {0: 0, 1: 8, 2: 1, 3: 71, 4: 44},
 'streets_per_node_proportion': {0: 0.0,
  1: 0.06451612903225806,
  2: 0.008064516129032258,
  3: 0.5725806451612904,
  4: 0.3548387096774194},
 'edge_length_total': 19967.856000000003,
 'edge_length_avg': 80.19219277108435,
 'street_length_total': 13659.232000000002,
 'street_length_avg': 74.64061202185793,
 'street_segments_count': 183,
 'node_density_km': None,
 'intersection_density_km': None,
 'edge_density_km': None,
 'street_density_km': None,
 'circuity_avg': 1.0244213943099583,
 'self_loop_proportion': 0.0,
 'clean_intersection_count': None,
 'clean_intersection_density_km': None}

To be able to extract the more advanced statistics (and some of the missing ones above) from the street network, it is required to have information about the coverage area of the network. Let’s calculate the area of the convex hull of the street network and see what we can get.

[15]:
# Get the Convex Hull of the network
convex_hull = edges_proj.unary_union.convex_hull
# Show output
convex_hull
[15]:
../../_images/notebooks_L6_network-analysis_27_0.svg

Now we can use the Convex Hull above to calculate extended statistics for the network. As some of the metrics are produced separately for each node, they produce a lot of output. Here, we combine the basic and extended statistics into one Pandas Series to keep things in more compact form.

[16]:
# Calculate the area
area = convex_hull.area

# Calculate statistics with density information
stats = ox.basic_stats(graph_proj, area=area)
extended_stats = ox.extended_stats(graph_proj, ecc=True, cc=True)

# Add extened statistics to the basic statistics
for key, value in extended_stats.items():
    stats[key] = value

# Convert the dictionary to a Pandas series for a nicer output
pd.Series(stats)
[16]:
n                                                                                    124
m                                                                                    249
k_avg                                                                            4.01613
intersection_count                                                                   116
streets_per_node_avg                                                             3.21774
streets_per_node_counts                                 {0: 0, 1: 8, 2: 1, 3: 71, 4: 44}
streets_per_node_proportion            {0: 0.0, 1: 0.06451612903225806, 2: 0.00806451...
edge_length_total                                                                19967.9
edge_length_avg                                                                  80.1922
street_length_total                                                              13659.2
street_length_avg                                                                74.6406
street_segments_count                                                                183
node_density_km                                                                  148.885
intersection_density_km                                                           139.28
edge_density_km                                                                  23975.2
street_density_km                                                                16400.5
circuity_avg                                                                 1.27082e-05
self_loop_proportion                                                                   0
clean_intersection_count                                                            None
clean_intersection_density_km                                                       None
avg_neighbor_degree                    {25216594: 2.0, 25238874: 2.0, 25238944: 1.0, ...
avg_neighbor_degree_avg                                                          2.14315
avg_weighted_neighbor_degree           {25216594: 0.04891769597651951, 25238874: 0.12...
avg_weighted_neighbor_degree_avg                                               0.0838789
degree_centrality                      {25216594: 0.024390243902439025, 25238874: 0.0...
degree_centrality_avg                                                          0.0326515
clustering_coefficient                 {25216594: 0, 25238874: 0, 25238944: 0, 252915...
clustering_coefficient_avg                                                     0.0954301
clustering_coefficient_weighted        {25216594: 0, 25238874: 0, 25238944: 0, 252915...
clustering_coefficient_weighted_avg                                            0.0165222
pagerank                               {25216594: 0.008697876082389044, 25238874: 0.0...
pagerank_max_node                                                               25416262
pagerank_max                                                                   0.0239018
pagerank_min_node                                                             1008183915
pagerank_min                                                                  0.00143337
eccentricity                           {3216400385: 1657.5310000000004, 1372233731: 1...
diameter                                                                         2153.57
radius                                                                           1007.06
center                                                                      [1372376937]
periphery                                                                    [319896278]
closeness_centrality                   {25216594: 0.0009352922781262002, 25238874: 0....
closeness_centrality_avg                                                      0.00143723
dtype: object

As we can see, now we have a LOT of information about our street network that can be used to understand its structure. We can for example see that the average node density in our network is 149 nodes/km and that the total edge length of our network is almost 20 kilometers.

Furthermore, we can see that the degree centrality of our network is on average 0.0326515. Degree is a simple centrality measure that counts how many neighbors a node has (here a fraction of nodes it is connected to). Another interesting measure is the PageRank that measures the importance of specific node in the graph. Here we can see that the most important node in our graph seem to a node with osmid 25416262. PageRank was the algorithm that Google first developed (Larry Page & Sergei Brin) to order the search engine results and became famous for.

You can read the Wikipedia article about different centrality measures if you are interested what the other centrality measures mean.

Shortest path analysis

Let’s now calculate the shortest path between two points using the shortest path function in Networkx. First we need to specify the source and target locations for our route. Let’s use the centroid of our network as the source location and the furthest point in East in our network as the target location.

  • Let’s first determine the centroid of our network. We can take advantage of the same Convex Hull that we used previously to determine the centroid of our data.
[17]:
# Get the Convex Hull of the network
convex_hull = edges_proj.unary_union.convex_hull

# Centroid
centroid = convex_hull.centroid

# Show
print(centroid)
POINT (385170.0891607622 6671717.293203074)

As we can see, now we have a centroid of our network determined. We will use this later as an origin point in our routing operation.

  • Let’s now find the easternmost node in our street network. We can do this based on the x coordinates of the nodes:
[18]:
nodes_proj.head()
[18]:
y x osmid highway lon lat geometry
25216594 6.671580e+06 384631.322372 25216594 NaN 24.921057 60.164794 POINT (384631.322 6671580.071)
25238874 6.671454e+06 384625.787221 25238874 NaN 24.921028 60.163665 POINT (384625.787 6671454.380)
25238944 6.671562e+06 384643.473274 25238944 NaN 24.921286 60.164631 POINT (384643.473 6671561.534)
25291537 6.671500e+06 385515.553244 25291537 NaN 24.937023 60.164325 POINT (385515.553 6671500.134)
25291564 6.671673e+06 385779.207015 25291564 NaN 24.941674 60.165948 POINT (385779.207 6671672.709)
  • Let’s find out which node has the largest x-coordinate value. First, let’s ensure that the values are floats:
[19]:
# Get the x coordinates of the nodes
nodes_proj['x'] = nodes_proj["x"].astype(float)
[20]:
# Retrieve the maximum x value (i.e. the most eastern)
maxx = nodes_proj['x'].max()
print(maxx)
385855.0300992895
  • Let’s retrieve the target Point having the largest x-coordinate. We can do this by using the .loc function of Pandas that we have used already many times in earlier tutorials.
[21]:
# Retrieve the node that is the most eastern one and get the Shapely Point geometry out of it
target = nodes_proj.loc[nodes_proj['x']==maxx, 'geometry'].values[0]
print(target)
POINT (385855.0300992895 6671721.810323974)

Okey now we can see that as a result we have a Shapely Point that we can use as a target point in our routing.

Let’s now find the nearest graph nodes (and their node IDs) to these points using OSMnx get_nearest_node. According to the documentation of this function, we need to parse Point coordinates as coordinate-tuples in this order: latitude, longitude(or y, x). As our data is now projected to UTM projection, we need to specify with method parameter that the function uses 'euclidean' distances to calculate the distance from the point to the closest node (with decimal derees, use 'haversine', which determines the great-circle distances). The method parameter is important if you want to know the actual distance between the Point and the closest node which you can retrieve by specifying parameter return_dist=True.

[22]:
# Get origin x and y coordinates
orig_xy = (centroid.y, centroid.x)

# Get target x and y coordinates
target_xy = (target.y, target.x)
[23]:
# Find the node in the graph that is closest to the origin point (here, we want to get the node id)
orig_node = ox.get_nearest_node(graph_proj, orig_xy, method='euclidean')
orig_node
[23]:
301360197
[24]:
# Find the node in the graph that is closest to the target point (here, we want to get the node id)
target_node = ox.get_nearest_node(graph_proj, target_xy, method='euclidean')
target_node
[24]:
317703609

Now we have the IDs for the closest nodes that were found from the graph to the origin and target points that we specified.

  • Let’s retrieve the node information from the nodes_proj GeoDataFrame by passing the ids to the loc indexer
[25]:
# Retrieve the rows from the nodes GeoDataFrame
o_closest = nodes_proj.loc[orig_node]
t_closest = nodes_proj.loc[target_node]
  • Let’s also create a GeoDataFrame that contains these points
[26]:
# Create a GeoDataFrame from the origin and target points
od_nodes = gpd.GeoDataFrame([o_closest, t_closest], geometry='geometry', crs=nodes_proj.crs)
od_nodes.head()
[26]:
y x osmid highway lon lat geometry
301360197 6.671721e+06 385166.707932 301360197 NaN 24.930617 60.166212 POINT (385166.708 6671721.244)
317703609 6.671722e+06 385855.030099 317703609 traffic_signals 24.943012 60.166410 POINT (385855.030 6671721.810)

Okay, as a result we got now the closest node IDs of our origin and target locations. As you can see, the index in this GeoDataFrame corresponds to the IDs that we found with get_nearest_node() function.

  • Now we are ready to do the routing and find the shortest path between the origin and target locations by using the shortest_path() function of networkx. With weight -parameter we can specify that 'length' attribute should be used as the cost impedance in the routing. If specifying the weight parameter, NetworkX will use by default Dijkstra’s algorithm to find the optimal route. We need to specify the graph that is used for routing, and the origin ID (source) and the target ID in between the shortest path will be calculated:
[27]:
# Calculate the shortest path
route = nx.shortest_path(G=graph_proj, source=orig_node, target=target_node, weight='length')

# Show what we have
print(route)
[301360197, 1372441183, 1372441170, 60170471, 1377211668, 1377211666, 25291565, 25291564, 317703609]

As a result we get a list of all the nodes that are along the shortest path.

  • We could extract the locations of those nodes from the nodes_proj GeoDataFrame and create a LineString presentation of the points, but luckily, OSMnx can do that for us and we can plot shortest path by using plot_graph_route() function:
[28]:
# Plot the shortest path
fig, ax = ox.plot_graph_route(graph_proj, route, origin_point=orig_xy, destination_point=target_xy)
../../_images/notebooks_L6_network-analysis_52_0.png

Nice! Now we have the shortest path between our origin and target locations. Being able to analyze shortest paths between locations can be valuable information for many applications. Here, we only analyzed the shortest paths based on distance but quite often it is more useful to find the optimal routes between locations based on the travelled time. Here, for example we could calculate the time that it takes to cross each road segment by dividing the length of the road segment with the speed limit and calculate the optimal routes by taking into account the speed limits as well that might alter the result especially on longer trips than here.

Saving shortest paths to disk

Quite often you need to save the route e.g. as a Shapefile. Hence, let’s continue still a bit and see how we can make a Shapefile of our route with some information associated with it.

  • First we need to get the nodes that belong to the shortest path:
[29]:
# Get the nodes along the shortest path
route_nodes = nodes_proj.loc[route]
route_nodes
[29]:
y x osmid highway lon lat geometry
301360197 6.671721e+06 385166.707932 301360197 NaN 24.930617 60.166212 POINT (385166.708 6671721.244)
1372441183 6.671672e+06 385199.040423 1372441183 NaN 24.931227 60.165777 POINT (385199.040 6671671.820)
1372441170 6.671610e+06 385239.956998 1372441170 NaN 24.931999 60.165235 POINT (385239.957 6671610.080)
60170471 6.671704e+06 385382.616738 60170471 NaN 24.934515 60.166117 POINT (385382.617 6671703.996)
1377211668 6.671789e+06 385514.573340 1377211668 NaN 24.936843 60.166917 POINT (385514.573 6671789.024)
1377211666 6.671703e+06 385570.886277 1377211666 NaN 24.937906 60.166160 POINT (385570.886 6671702.892)
25291565 6.671586e+06 385647.124210 25291565 traffic_signals 24.939344 60.165135 POINT (385647.124 6671586.216)
25291564 6.671673e+06 385779.207015 25291564 NaN 24.941674 60.165948 POINT (385779.207 6671672.709)
317703609 6.671722e+06 385855.030099 317703609 traffic_signals 24.943012 60.166410 POINT (385855.030 6671721.810)

As we can see, now we have all the nodes that were part of the shortest path as a GeoDataFrame.

  • Now we can create a LineString out of the Point geometries of the nodes:
[30]:
from shapely.geometry import LineString, Point

# Create a geometry for the shortest path
route_line = LineString(list(route_nodes.geometry.values))
route_line
[30]:
../../_images/notebooks_L6_network-analysis_57_0.svg

Now we have the route as a LineString geometry.

  • Let’s make a GeoDataFrame out of it having some useful information about our route such as a list of the osmids that are part of the route and the length of the route.
[31]:
# Create a GeoDataFrame
route_geom = gpd.GeoDataFrame([[route_line]], geometry='geometry', crs=edges_proj.crs, columns=['geometry'])

# Add a list of osmids associated with the route
route_geom.loc[0, 'osmids'] = str(list(route_nodes['osmid'].values))

# Calculate the route length
route_geom['length_m'] = route_geom.length

route_geom.head()
[31]:
geometry osmids length_m
0 LINESTRING (385166.708 6671721.244, 385199.040... [301360197, 1372441183, 1372441170, 60170471, ... 951.40388

Now we have a GeoDataFrame that we can save to disk. Let’s still confirm that everything is ok by plotting our route on top of our street network and some buildings, and plot also the origin and target points on top of our map.

  • Get buildings:
[32]:
# Retrieve buildings and reproject
buildings = ox.footprints_from_place(place_name)
buildings_proj = buildings.to_crs(crs=edges_proj.crs)
  • Let’s now plot the route and the street network elements to verify that everything is as it should:
[33]:
# Plot edges and nodes
ax = edges_proj.plot(linewidth=0.75, color='gray')
ax = nodes_proj.plot(ax=ax, markersize=2, color='gray')

# Add buildings
ax = buildings_proj.plot(ax=ax, facecolor='khaki', alpha=0.7)

# Add the route
ax = route_geom.plot(ax=ax, linewidth=2, linestyle='--', color='red')

# Add the origin and destination nodes of the route
ax = od_nodes.plot(ax=ax, markersize=24, color='green')
../../_images/notebooks_L6_network-analysis_63_0.png

Great everything seems to be in order! As you can see, now we have a full control of all the elements of our map and we can use all the aesthetic properties that matplotlib provides to modify how our map will look like. Now we are almost ready to save our data into disk.

  • As there are certain columns with such data values that Shapefile format does not support (such as list or boolean), we need to convert those into strings to be able to export the data to Shapefile:
[34]:
# Columns with invalid values
invalid_cols = ['lanes', 'maxspeed', 'name', 'oneway', 'osmid']

# Iterate over invalid columns and convert them to string format
for col in invalid_cols:
    edges_proj[col] = edges_proj[col].astype(str)

print(edges_proj.dtypes)
u              int64
v              int64
key            int64
osmid         object
oneway        object
lanes         object
name          object
highway       object
maxspeed      object
length       float64
geometry    geometry
junction      object
bridge        object
access        object
dtype: object

Now we can see that most of the attributes are of type object that quite often (such as ours here) refers to a string type of data.

  • Now we are finally ready to parse the output filepaths and save the data into disk:
[35]:
import os

# Parse the place name for the output file names (replace spaces with underscores and remove commas)
place_name_out = place_name.replace(' ', '_').replace(',','')

# Output directory
out_dir = "data"

# Parse output file paths
streets_out = os.path.join(out_dir, "%s_streets.shp" % place_name_out)
route_out = os.path.join(out_dir, "Route_from_a_to_b_at_%s.shp" % place_name_out)
nodes_out = os.path.join(out_dir, "%s_nodes.shp" % place_name_out)
buildings_out = os.path.join(out_dir, "%s_buildings.shp" % place_name_out)
od_out = os.path.join(out_dir, "%s_route_OD_points.shp" % place_name_out)

# Save files
edges_proj.to_file(streets_out)
route_geom.to_file(route_out)
nodes_proj.to_file(nodes_out)
od_nodes.to_file(od_out)
buildings[['geometry', 'name', 'addr:street']].to_file(buildings_out)

Great, now we have saved all the data that was used to produce the maps as Shapefiles.