Origin–Destination Matrices to Graphs¶

# Sixteen zones as a 4x4 grid of square cells (polygons) with explicit ids
from shapely.geometry import box
cells = []
ids = []
# Iterate rows (y) and columns (x) to build 1x1 degree squares
for i in range(4):      # rows (y = 0..3)
    for j in range(4):  # cols (x = 0..3)
        cells.append(box(j, i, j + 1, i + 1))
        ids.append(f"G{j}{i}")  # e.g., G00, G10, ..., G33
zones_gdf = gpd.GeoDataFrame({"zone_id": ids}, geometry=cells, crs="EPSG:4326")
zones_gdf.head()

# Edge list with single weight column using grid zone ids (subset for clarity)
E = pd.DataFrame({
    "source": ["G00", "G00", "G10", "G01", "G22", "G23", "G12"],
    "target": ["G10", "G01", "G11", "G11", "G32", "G33", "G22"],
    "flow":   [5,     2,     3,     7,     4,     6,     5],
})
nodes_gdf1, edges_gdf1 = c2g.od_matrix_to_graph(
    E, zones_gdf, zone_id_col="zone_id",
    matrix_type="edgelist",
    source_col="source", target_col="target",
    weight_cols=["flow"],
    threshold=None,             # drop zeros only
    include_self_loops=False,
    compute_edge_geometry=True,
    directed=True,
    as_nx=False,
 )

edges_gdf1.head()

# Quick plot of nodes (grid cells) and edges
ax = zones_gdf.boundary.plot(color="#2E86AB", alpha=0.8, linewidth=0.8)
c2g.plot_graph(
    nodes=nodes_gdf1.set_geometry(nodes_gdf1.centroid),
    edges=edges_gdf1,
    ax=ax,
    bgcolor="#f8f9fa",
    node_color="#2E86AB",
    node_alpha=0.8,
    markersize=20,
    edge_color="#E67E22",
    edge_linewidth=np.log1p(edges_gdf1["weight"]) * 1.2,
)
plt.title("Mock edgelist graph on 4x4 grid (directed)")
plt.axis("equal"); plt.axis("off")
plt.show()

# Multi-weight undirected example on 4x4 grid (subset of pairs with reciprocals)
E2 = pd.DataFrame({
    "source": ["G00", "G10", "G01", "G11", "G22", "G32", "G23", "G33"],
    "target": ["G10", "G00", "G11", "G01", "G32", "G22", "G33", "G23"],
    "trips":  [5,     1,     7,     2,     4,     3,     8,     2],
    "cost":   [10,    2,     12,    3,     7,     4,     15,    3],
})
nodes_gdf2, edges_gdf2 = c2g.od_matrix_to_graph(
    E2, zones_gdf, zone_id_col="zone_id",
    matrix_type="edgelist",
    source_col="source", target_col="target",
    weight_cols=["trips", "cost"],
    threshold=3, threshold_col="trips",
    include_self_loops=False,
    compute_edge_geometry=True,
    directed=False,  # undirected: sum reciprocals
    as_nx=False,
 )

ax = zones_gdf.boundary.plot(color="#2E86AB", alpha=0.8, linewidth=0.8)
c2g.plot_graph(
    nodes=nodes_gdf2.set_geometry(nodes_gdf2.centroid),
    edges=edges_gdf2,
    ax=ax,
    bgcolor="#f8f9fa",
    node_color="#2E86AB",
    node_alpha=0.8,
    markersize=20,
    edge_color="#9B59B6",
    edge_linewidth=np.log1p(edges_gdf2["weight"]) * 1.2,
)
plt.title("Mock edgelist graph on 4x4 grid (undirected, primary=trips)")
plt.axis("equal"); plt.axis("off")
plt.show()

# Build an adjacency DataFrame matching the 4x4 grid zone ids
ids = zones_gdf["zone_id"]
# Create a sparse 16x16 matrix with a few flows
A = pd.DataFrame(0, index=ids, columns=ids, dtype=float)
# add some directed flows
A.loc["G00", "G10"] = 5
A.loc["G00", "G01"] = 2
A.loc["G10", "G11"] = 3
A.loc["G01", "G11"] = 7
A.loc["G22", "G32"] = 4
A.loc["G23", "G33"] = 6
A.loc["G12", "G22"] = 5
nodes_gdf3, edges_gdf3 = c2g.od_matrix_to_graph(
    A, zones_gdf, zone_id_col="zone_id",
    matrix_type="adjacency",
    include_self_loops=False,
    threshold=None,
    directed=True,
 )

ax = zones_gdf.boundary.plot(color="#2E86AB", alpha=0.8, linewidth=0.8)
c2g.plot_graph(
    nodes=nodes_gdf3.set_geometry(nodes_gdf3.centroid),
    edges=edges_gdf3,
    ax=ax,
    bgcolor="#f8f9fa",
    node_color="#2E86AB",
    node_alpha=0.8, 
    markersize=20,
    edge_color="#27AE60",
    edge_linewidth=np.log1p(edges_gdf3["weight"]) * 1.2,
)
plt.title("Mock adjacency graph on 4x4 grid (directed)")
plt.axis("equal"); plt.axis("off")
plt.show()

# Paths (adjust to your environment if needed)
# Relative to repository root
ZONE_GPKG = "../examples/data/Middle_layer_Super_Output_Areas_December_2021_Boundaries_EW_BGC_V3_-1334546435986816930.gpkg"
OD_CSV   = "../examples/data/odmg/odmg01ew/ODMG01EW_MSOA.csv"

zones_london = gpd.read_file(ZONE_GPKG)
od_london = pd.read_csv(OD_CSV)
print(f"zones_london: {len(zones_london)} rows, CRS={zones_london.crs}")
od_london.head(3)

# Column mapping for ODMG dataset
source_col = "Migrant MSOA one year ago code"
target_col = "Middle layer Super Output Areas code"
weight_col = "Count"
zone_id_col = "MSOA21CD"

od_nodes, od_edges = c2g.od_matrix_to_graph(
    od_london, zones_london, zone_id_col=zone_id_col,
    matrix_type="edgelist",
    source_col=source_col, target_col=target_col,
    weight_cols=[weight_col],
    threshold=None,
    include_self_loops=False,
    compute_edge_geometry=True,
    directed=False,
    as_nx=False,
 )
len(od_nodes), len(od_edges)

# Inspect a few rows
od_nodes.head()

od_edges.head()

od_nodes.head()

# Filter for flows >= 10
top_edges = od_edges[od_edges[weight_col] >= 10]

c2g.plot_graph(
    nodes=zones_london.centroid,
    edges=top_edges,
    )

# Compute percentile ranks for weights
percentile_ranks = top_edges[weight_col].rank(pct=True)

c2g.plot_graph(
    nodes=zones_london.centroid,
    edges=top_edges,
    edge_alpha=percentile_ranks,
    )

# Create subplots: left for network, right for degree centrality
fig, axs = plt.subplots(1, 2, figsize=(24, 12))

axs[0].set_title("England & Wales MSOA Migration Network: Flows ≥10\n(Alpha by Percentile Rank)", fontsize=22, color='white')
c2g.plot_graph(
    nodes=zones_london.centroid,
    edges=top_edges,
    ax=axs[0],
    edge_alpha=percentile_ranks,
    )

# Right subplot: Degree centrality
axs[1].set_title("England & Wales MSOA Migration Network: Degree Centrality\n(Migration Flows 2021 - Quantile Classification)", fontsize=22, color='white')
od_nodes.plot(
    column='degree_centrality',
    ax=axs[1],
    cmap='viridis',
    edgecolor='white',
    linewidth=0.1,
    legend=True,
    scheme='quantiles',
    k=4,
    legend_kwds={'title': 'Degree Centrality (Quantiles)', 'loc': 'upper left', 'bbox_to_anchor': (1, 1), 'fontsize': 14}
)
axs[1].set_axis_off()
axs[1].set_facecolor('#f8f9fa')

plt.tight_layout()
plt.show()