A Coding Implementation on Spatial Graph Neural Networks for Urban Function Inference Using city2graph, OSMnx, and PyTorch Geometric

In this tutorial, we build an end-to-end spatial graph learning pipeline using city2graph. We start by collecting real urban POI data and street network information from OpenStreetMap, with a synthetic fallback to ensure the workflow remains reliable. We then engineer spatial features, construct multiple proximity graph families, and compare how different graph-building strategies represent the same urban environment. After that, we create both heterogeneous and homogeneous graph structures, convert them into PyTorch Geometric format, and train a GraphSAGE model to predict POI categories from spatial structure. Through this process, we integrate geospatial data processing, graph construction, and GNN-based urban function inference into a single practical workflow.

Installing city2graph and Importing Geospatial and Graph Learning Libraries

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!pip -q install "city2graph[cpu]" osmnx contextily scikit-learn 2>/dev/null import warnings, numpy as np, pandas as pd, geopandas as gpd warnings.filterwarnings("ignore") from shapely.geometry import Point import matplotlib.pyplot as plt import city2graph as c2g print("city2graph version:", getattr(c2g, "version", "unknown")) print("PyTorch / PyG available:", c2g.is_torch_available()) import torch import torch.nn.functional as F from torch_geometric.nn import SAGEConv, to_hetero from torch_geometric.utils import to_undirected from sklearn.preprocessing import StandardScaler from sklearn.neighbors import NearestNeighbors from sklearn.metrics import accuracy_score, f1_score from sklearn.decomposition import PCA SEED = 42 np.random.seed(SEED); torch.manual_seed(SEED)

We begin by installing the required libraries and importing the geospatial, graph learning, and machine learning tools used throughout the tutorial. We verify that city2graph and PyTorch Geometric are available so the rest of the workflow can run properly. We also set a fixed random seed to make the graph construction, training split, and model results more reproducible.

Collecting OpenStreetMap POI Data with a Synthetic Fallback

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CENTER = (35.6595, 139.7005) DIST_M = 1100 TAG_QUERIES = { "food": {"amenity": ["restaurant", "cafe", "fast_food", "bar", "pub"]}, "retail": {"shop": True}, "education": {"amenity": ["school", "university", "college", "kindergarten", "library"]}, "health": {"amenity": ["hospital", "clinic", "pharmacy", "doctors", "dentist"]}, } def to_points(gdf): g = gdf.copy() g["geometry"] = g.geometry.representative_point() return g poi_gdf, segments_gdf = None, None try: import osmnx as ox ox.settings.use_cache = True ox.settings.log_console = False frames = [] for label, tags in TAG_QUERIES.items(): try: f = ox.features_from_point(CENTER, tags=tags, dist=DIST_M) f = f[f.geometry.notna()] if len(f): f = to_points(f)[["geometry"]].copy() f["category"] = label frames.append(f) except Exception as e: print(f" (skip {label}: {e})") if not frames: raise RuntimeError("No POIs returned from Overpass.") poi_gdf = gpd.GeoDataFrame(pd.concat(frames, ignore_index=True), crs="EPSG:4326") G = ox.graph_from_point(CENTER, dist=DIST_M, network_type="walk") segments_gdf = ox.graph_to_gdfs(G, nodes=False, edges=True).reset_index(drop=True)[["geometry"]] print(f"OSM acquisition OK -> {len(poi_gdf)} POIs, {len(segments_gdf)} street segments") except Exception as e: print(f"OSM unavailable ({e}) -> generating synthetic clustered POIs.") rng = np.random.default_rng(SEED) cats = list(TAG_QUERIES.keys()) centers = rng.uniform(-0.01, 0.01, size=(8, 2)) + np.array(CENTER[::-1]) rows = [] for ci, c in enumerate(centers): dom = cats[ci % len(cats)] n = rng.integers(40, 90) pts = c + rng.normal(0, 0.0016, size=(n, 2)) for (lon, lat) in pts: cat = dom if rng.random() {len(poi_gdf)} POIs") if len(poi_gdf) > 700: poi_gdf = poi_gdf.sample(700, random_state=SEED).reset_index(drop=True) metric_crs = poi_gdf.estimate_utm_crs() poi_gdf = poi_gdf.to_crs(metric_crs).reset_index(drop=True) if segments_gdf is not None: segments_gdf = segments_gdf.to_crs(metric_crs) print("Class balance:\n", poi_gdf["category"].value_counts())

We collect real POI data from OpenStreetMap around Shibuya, Tokyo, and group the locations into broad urban function categories such as food, retail, education, and health. We also download the walkable street network so that the POIs can later be connected with urban-form features. If the OSM request fails, we generate a synthetic clustered dataset, which keeps the tutorial runnable even when online data access is unavailable.

Engineering Spatial Features and Building Proximity Graph Families

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poi_gdf["cx"] = poi_gdf.geometry.x poi_gdf["cy"] = poi_gdf.geometry.y coords = poi_gdf[["cx", "cy"]].to_numpy() nn = NearestNeighbors(radius=150.0).fit(coords) poi_gdf["local_density"] = [len(idx) - 1 for idx in nn.radius_neighbors(coords, return_distance=False)] if segments_gdf is not None and len(segments_gdf): try: joined = gpd.sjoin_nearest(poi_gdf[["geometry"]], segments_gdf[["geometry"]], distance_col="dist_street") poi_gdf["dist_street"] = joined.groupby(level=0)["dist_street"].min().reindex(poi_gdf.index).fillna(0.0) except Exception: poi_gdf["dist_street"] = 0.0 else: poi_gdf["dist_street"] = 0.0 poi_gdf["category"] = poi_gdf["category"].astype("category") poi_gdf["label"] = poi_gdf["category"].cat.codes.astype(int) CLASS_NAMES = list(poi_gdf["category"].cat.categories) print("Classes:", CLASS_NAMES) def graph_stats(name, builder): try: nodes, edges = builder() deg = pd.Series(np.r_[edges.index.get_level_values(0), edges.index.get_level_values(1)]).value_counts() return name, len(edges), round(deg.mean(), 2), (nodes, edges) except Exception as e: return name, f"ERR: {e}", None, None builders = { "KNN (k=8)": lambda: c2g.knn_graph(poi_gdf, distance_metric="euclidean", k=8, as_nx=False), "Delaunay": lambda: c2g.delaunay_graph(poi_gdf, as_nx=False), "Gabriel": lambda: c2g.gabriel_graph(poi_gdf, as_nx=False), "RNG": lambda: c2g.relative_neighborhood_graph(poi_gdf, as_nx=False), "EMST": lambda: c2g.euclidean_minimum_spanning_tree(poi_gdf, as_nx=False), "Waxman": lambda: c2g.waxman_graph(poi_gdf, distance_metric="euclidean", r0=150, beta=0.6), } print("\n--- Proximity graph comparison ---") print(f"{'graph':10}{'avg_degree':>12}") built = {} for nm, b in builders.items(): name, ne, avgdeg, payload = graph_stats(nm, b) print(f"{name:10}{str(avgdeg):>12}") if payload: built[nm] = payload fig, axes = plt.subplots(1, 3, figsize=(16, 5)) for ax, key in zip(axes, ["KNN (k=8)", "Delaunay", "EMST"]): if key in built: n_, e_ = built[key] e_.plot(ax=ax, linewidth=0.4, color="#3b7dd8", alpha=0.6) poi_gdf.plot(ax=ax, markersize=4, color="#d83b5c") ax.set_title(key); ax.set_axis_off() plt.suptitle("Spatial graph topologies on the same POI set", y=1.02) plt.tight_layout(); plt.show()

We engineer spatial features for each POI by extracting its projected coordinates, calculating local density, and estimating distance to the nearest street segment. We then assign category labels and build several families of proximity graphs, including KNN, Delaunay, Gabriel, RNG, EMST, and Waxman. We compare their edge counts and average degrees, then visualize selected graph topologies to see how differently they connect the same set of POIs.

Constructing Heterogeneous and Homogeneous Graphs in PyTorch Geometric

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nodes_dict = {} for cat in CLASS_NAMES: sub = poi_gdf[poi_gdf["category"] == cat].copy().reset_index(drop=True) nodes_dict[cat] = sub[["geometry", "cx", "cy", "local_density"]] try: _, bridge_edges = c2g.bridge_nodes(nodes_dict, proximity_method="knn", k=3, distance_metric="euclidean") hetero = c2g.gdf_to_pyg( nodes_dict, bridge_edges, node_feature_cols={cat: ["cx", "cy", "local_density"] for cat in CLASS_NAMES}, ) print("\nHeteroData node types:", hetero.node_types) print("HeteroData edge types:") for et in hetero.edge_types: print(f" {et}: {hetero[et].edge_index.shape[1]} edges") except Exception as e: hetero = None print("Heterogeneous build skipped:", e) nodes, edges = c2g.knn_graph(poi_gdf, distance_metric="euclidean", k=8, as_nx=False) deg = pd.Series(np.r_[edges.index.get_level_values(0), edges.index.get_level_values(1)]).value_counts() nodes["degree"] = deg.reindex(nodes.index).fillna(0).astype(float) for col in ["cx", "cy", "local_density", "dist_street", "label"]: if col not in nodes.columns: nodes[col] = poi_gdf.loc[nodes.index, col].values FEATS = ["cx", "cy", "local_density", "dist_street", "degree"] nodes[FEATS] = StandardScaler().fit_transform(nodes[FEATS].astype(float)) data = c2g.gdf_to_pyg(nodes, edges, node_feature_cols=FEATS, node_label_cols=["label"]) data.edge_index = to_undirected(data.edge_index) data.x = data.x.float() y = data.y.long().view(-1) N, num_classes = data.num_nodes, int(y.max()) + 1 print(f"\nHomogeneous Data: {N} nodes, {data.edge_index.shape[1]} directed-edges, " f"{data.x.shape[1]} features, {num_classes} classes")

We construct a heterogeneous multi-layer graph by separating POIs into node types based on their urban function categories. We then use bridge edges to connect nearby nodes across different layers and convert the result into PyTorch Geometric HeteroData format. After that, we build a homogeneous KNN graph, attach degree and engineered features, standardize them, and prepare the final PyG Data object for GraphSAGE training.

Defining and Training a GraphSAGE Model for POI Classification

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perm = torch.randperm(N, generator=torch.Generator().manual_seed(SEED)) n_tr, n_va = int(0.6 * N), int(0.2 * N) train_mask = torch.zeros(N, dtype=torch.bool); train_mask[perm[:n_tr]] = True val_mask = torch.zeros(N, dtype=torch.bool); val_mask[perm[n_tr:n_tr + n_va]] = True test_mask = torch.zeros(N, dtype=torch.bool); test_mask[perm[n_tr + n_va:]] = True class GraphSAGE(torch.nn.Module): def init(self, in_dim, hidden, out_dim, p=0.3): super().init() self.c1 = SAGEConv(in_dim, hidden) self.c2 = SAGEConv(hidden, hidden) self.lin = torch.nn.Linear(hidden, out_dim) self.p = p def forward(self, x, ei, return_emb=False): h = F.relu(self.c1(x, ei)) h = F.dropout(h, p=self.p, training=self.training) h = F.relu(self.c2(h, ei)) out = self.lin(h) return (out, h) if return_emb else out model = GraphSAGE(data.x.shape[1], 64, num_classes) opt = torch.optim.Adam(model.parameters(), lr=0.01, weight_decay=5e-4) def evaluate(mask): model.eval() with torch.no_grad(): pred = model(data.x, data.edge_index).argmax(1) yt, yp = y[mask].numpy(), pred[mask].numpy() return accuracy_score(yt, yp), f1_score(yt, yp, average="macro") print("\n--- Training GraphSAGE ---") best_val, best_state = 0.0, None for epoch in range(1, 201): model.train(); opt.zero_grad() out = model(data.x, data.edge_index) loss = F.cross_entropy(out[train_mask], y[train_mask]) loss.backward(); opt.step() if epoch % 20 == 0: va_acc, va_f1 = evaluate(val_mask) if va_acc > best_val: best_val, best_state = va_acc, {k: v.clone() for k, v in model.state_dict().items()} print(f"epoch {epoch:3d} | loss {loss.item():.3f} | val_acc {va_acc:.3f} | val_f1 {va_f1:.3f}") if best_state: model.load_state_dict(best_state) te_acc, te_f1 = evaluate(test_mask) print(f"\nTEST accuracy={te_acc:.3f} macro-F1={te_f1:.3f}")

We split the graph nodes into training, validation, and test masks so the model can learn and be evaluated properly. We define a two-layer GraphSAGE model that learns node representations from both node features and graph structure. We train the model for 200 epochs, monitor validation accuracy and macro-F1, save the best model state, and finally report test performance.

Visualizing Embeddings and Running a Heterogeneous GNN Forward Pass

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model.eval() with torch.no_grad(): logits, emb = model(data.x, data.edge_index, return_emb=True) pred = logit

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