From 8c43786d59a3305f077ced4d748a2b9d15cdc3cf Mon Sep 17 00:00:00 2001 From: wangzhao0217 Date: Thu, 6 Mar 2025 21:53:19 +0000 Subject: [PATCH] update directness and Efficiency cals --- .gitignore | 3 +- R/net_eval.R | 160 ++++++++++++------- plot/Aberdeen City_radar_chart_cbd_1.jpg | Bin 0 -> 87069 bytes plot/Aberdeen City_radar_chart_cbd_2.jpg | Bin 0 -> 94634 bytes plot/City of Edinburgh_radar_chart_cbd_1.jpg | Bin 0 -> 85390 bytes plot/City of Edinburgh_radar_chart_cbd_2.jpg | Bin 0 -> 91770 bytes plot/Dundee City_radar_chart_cbd_1.jpg | Bin 0 -> 87524 bytes plot/Dundee City_radar_chart_cbd_2.jpg | Bin 0 -> 88645 bytes plot/Glasgow City_radar_chart_cbd_1.jpg | Bin 0 -> 88582 bytes plot/Glasgow City_radar_chart_cbd_2.jpg | Bin 0 -> 88367 bytes 10 files changed, 108 insertions(+), 55 deletions(-) create mode 100644 plot/Aberdeen City_radar_chart_cbd_1.jpg create mode 100644 plot/Aberdeen City_radar_chart_cbd_2.jpg create mode 100644 plot/City of Edinburgh_radar_chart_cbd_1.jpg create mode 100644 plot/City of Edinburgh_radar_chart_cbd_2.jpg create mode 100644 plot/Dundee City_radar_chart_cbd_1.jpg create mode 100644 plot/Dundee City_radar_chart_cbd_2.jpg create mode 100644 plot/Glasgow City_radar_chart_cbd_1.jpg create mode 100644 plot/Glasgow City_radar_chart_cbd_2.jpg diff --git a/.gitignore b/.gitignore index fe8093c..08c3e81 100644 --- a/.gitignore +++ b/.gitignore @@ -5,4 +5,5 @@ Doc Test.Rmd Test.R cohesive_network_region_boundary.geojson -inputdata/ \ No newline at end of file +inputdata/ +network_eval_file/ \ No newline at end of file diff --git a/R/net_eval.R b/R/net_eval.R index 9894f16..473a93c 100644 --- a/R/net_eval.R +++ b/R/net_eval.R @@ -196,73 +196,125 @@ compute_od_accessibility = function(od_data, rnet_core, lads, city_name = "City ### Function: Compute Directness and Efficiency compute_directness_efficiency = function(rnet_core, lads, city_name = "City of Edinburgh") { - city_boundary = lads |> filter(LAD23NM == city_name) - rnet_core_zone = sf::st_intersection(rnet_core, city_boundary) |> st_cast("LINESTRING") - - network_sfnet = as_sfnetwork(rnet_core_zone, directed = FALSE) - network_sfnet = network_sfnet |> - activate("edges") |> - mutate(weight = as.numeric(st_length(geometry))) - - g = network_sfnet |> as.igraph() - - comp = components(g) - largest_comp_id = which.max(comp$csize) - lcc_nodes = V(g)[comp$membership == largest_comp_id] - g_lcc = induced_subgraph(g, lcc_nodes) - - dist_matrix_g = distances(g_lcc, weights = E(g_lcc)$weight) - nodes_sf = network_sfnet |> - activate("nodes") |> - st_as_sf() + # 1) Choose a planar coordinate system for distances in meters. + # For Great Britain, EPSG:27700 is common. + target_crs = 27700 - coords = st_coordinates(nodes_sf) + # 2) Reproject boundary and network lines to the chosen CRS + lads_proj = st_transform(lads, target_crs) + rnet_core_proj = st_transform(rnet_core, target_crs) - node_coords = nodes_sf |> - as.data.frame() |> - bind_cols(data.frame(x = coords[,1], y = coords[,2])) + # 3) Clip the network to the chosen city + city_boundary = lads_proj |> filter(LAD23NM == city_name) + rnet_core_zone = st_intersection(rnet_core_proj, city_boundary) + rnet_core_zone = st_cast(rnet_core_zone, "LINESTRING") # ensure LINESTRING geometry - node_coords_lcc = node_coords[as.numeric(lcc_nodes), ] + # 4) Build an initial sfnetwork (UNDIRECTED) + network_sfnet = as_sfnetwork(rnet_core_zone, directed = FALSE) - dist_matrix_e = as.matrix(dist(node_coords_lcc[, c("x","y")])) + # 5) Subdivide lines at all intersections + # This ensures real intersections become shared nodes + network_sfnet_subdiv = network_sfnet %>% + convert(to_spatial_subdivision) %>% + activate("edges") %>% + mutate(weight = st_length(geometry)) # edge weights in meters - valid_pairs = upper.tri(dist_matrix_g, diag = FALSE) & is.finite(dist_matrix_g) & dist_matrix_g > 0 + # Convert to igraph for distance computations + g = as.igraph(network_sfnet_subdiv) - # Directness - directness_ratios = dist_matrix_e[valid_pairs] / dist_matrix_g[valid_pairs] - D = mean(directness_ratios, na.rm = TRUE) + # 6) Compute distance matrices: + # dist_matrix_g = shortest-path distances on the network + # dist_matrix_e = straight-line (Euclidean) distances + dist_matrix_g = distances(g, weights = E(g)$weight) - # Global Efficiency - sum_inv_dG = sum(1/dist_matrix_g[valid_pairs], na.rm = TRUE) - sum_inv_dE = sum(1/dist_matrix_e[valid_pairs], na.rm = TRUE) - E_glob = sum_inv_dG / sum_inv_dE + # Extract node coordinates in the same planar CRS + nodes_sf = network_sfnet_subdiv %>% + activate("nodes") %>% + st_as_sf() - # Local Efficiency - calc_local_eff = function(node_id, distG, distE, g_graph) { - neighbors_idx = as.numeric(neighbors(g_graph, node_id)) - if (length(neighbors_idx) < 2) { - return(NA) - } - distG_sub = distG[neighbors_idx, neighbors_idx] - distE_sub = distE[neighbors_idx, neighbors_idx] - valid_pairs_local = upper.tri(distG_sub, diag=FALSE) & is.finite(distG_sub) & distG_sub > 0 - if (sum(valid_pairs_local) == 0) { + coords = st_coordinates(nodes_sf) + dist_matrix_e = as.matrix(dist(coords)) + + # ------------------------------------------------------------------ + # 7) Fraction-Weighted Directness & Global Efficiency + # + # 1) Among connected node pairs only + # 2) Multiply by the fraction of all node pairs that are connected + # ------------------------------------------------------------------ + all_pairs_mask = upper.tri(dist_matrix_g, diag = FALSE) + + connected_mask = all_pairs_mask & + is.finite(dist_matrix_g) & + (dist_matrix_g > 0) + + # Fraction of connected pairs + n_all_pairs = sum(all_pairs_mask) + n_conn_pairs = sum(connected_mask) + frac_connected = n_conn_pairs / n_all_pairs + + # Directness among connected pairs + directness_ratios_conn = dist_matrix_e[connected_mask] / dist_matrix_g[connected_mask] + D_conn = mean(directness_ratios_conn, na.rm = TRUE) + + # Fraction-weighted Directness + D_fraction_weighted = D_conn * frac_connected + + # Global Efficiency among connected pairs + E_glob_conn = sum(1 / dist_matrix_g[connected_mask], na.rm = TRUE) / + sum(1 / dist_matrix_e[connected_mask], na.rm = TRUE) + + # Fraction-weighted Global Efficiency + E_glob_fraction_weighted = E_glob_conn * frac_connected + + # ------------------------------------------------------------------ + # 8) Local Efficiency + # + # Standard approach: for each node's neighbors, ignore pairs that + # aren't connected. If < 2 neighbors, local efficiency = NA. + # ------------------------------------------------------------------ + calc_local_eff = function(node_id, distG, distE, igraph_obj) { + nbrs = as.numeric(neighbors(igraph_obj, node_id)) + if (length(nbrs) < 2) { return(NA) } - sum_inv_dG_sub = sum(1/distG_sub[valid_pairs_local], na.rm = TRUE) - sum_inv_dE_sub = sum(1/distE_sub[valid_pairs_local], na.rm = TRUE) - E_glob_i = sum_inv_dG_sub / sum_inv_dE_sub - return(E_glob_i) + distG_sub = distG[nbrs, nbrs] + distE_sub = distE[nbrs, nbrs] + + valid_sub = upper.tri(distG_sub, diag = FALSE) & + is.finite(distG_sub) & + (distG_sub > 0) + if (sum(valid_sub) == 0) return(NA) + + sum_invG = sum(1 / distG_sub[valid_sub], na.rm = TRUE) + sum_invE = sum(1 / distE_sub[valid_sub], na.rm = TRUE) + if (sum_invE == 0) return(NA) + + return(sum_invG / sum_invE) } - E_glob_i_values = sapply(seq_len(vcount(g_lcc)), function(i) calc_local_eff(i, dist_matrix_g, dist_matrix_e, g_lcc)) - E_loc = mean(E_glob_i_values, na.rm = TRUE) + E_loc_values = sapply(seq_len(vcount(g)), function(i) { + calc_local_eff(i, dist_matrix_g, dist_matrix_e, g) + }) + E_loc = mean(E_loc_values, na.rm = TRUE) + # ------------------------------------------------------------------ + # 9) Return all metrics + # ------------------------------------------------------------------ return(list( - D = D, - E_glob = E_glob, - E_loc = E_loc + # Fraction of connected pairs + frac_connected = frac_connected, + + # Within-connected subgraphs only + D_conn = D_conn, # directness among connected pairs + E_glob_conn = E_glob_conn, # global efficiency among connected pairs + + # Fraction-weighted directness & efficiency + D_fraction_weighted = D_fraction_weighted, + E_glob_fraction_weighted = E_glob_fraction_weighted, + + # Local Efficiency + E_loc = E_loc )) } @@ -302,8 +354,8 @@ generate_radar_chart = function(city_name, # 6. 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