adds back improved closeness

docs/src/pages/metrics/networks.md

@@ -42,8 +42,9 @@ This effect is amplified for denser regions of the network.
 - Segmentised versions of centrality measures should not be computed on dual graph topologies because street segment
 lengths would be duplicated for each permutation of dual edge spanning street intersections. By way of example,
 the contribution of a single edge segment at a four-way intersection would be duplicated three times.
-- Global closeness is strongly discouraged because it does not behave suitably for localised graphs. Harmonic
-closeness should be used instead.
+- The usual formulations of closeness or normalised closeness are discouraged because these do not behave
+suitably for localised graphs. Harmonic closeness or Hillier normalisation (which resembles a simplified form of
+Improved Closeness Centrality proposed by Wasserman and Faust) should be used instead.
 - Network decomposition can be a useful strategy when working at small distance thresholds, and confers advantages
 such as more regularly spaced snapshots and fewer artefacts at small distance thresholds where street edges
 intersect distance thresholds. However, the regular spacing of the decomposed segments will introduce spikes in the
@@ -110,9 +111,7 @@ may therefore be preferable when working at small thresholds on decomposed netwo
  Compute node-based network centrality using the shortest path heuristic.
 :::note
 Node weights are taken into account when computing centralities. These would typically be initialised at 1 unless
-manually specified. Consider use of
-[`graphs.nx_weight_by_dissolved_edges`](/tools/graphs#nx-weight-by-dissolved-edges) when working with complex
-network representations.
+manually specified.
 :::
 ### Parameters
 <div class="param-set">
@@ -213,10 +212,11 @@ network representations.
 | key                   | formula | notes |
 | ----------------------| :------:| ----- |
 | node_density          | $$\sum_{j\neq{i}}^{n}1$$ | A summation of nodes. |
-| node_farness          | $$\sum_{j\neq{i}}^{n}d_{(i,j)}$$ | A summation of distances in metres. |
-| node_cycles           | $$\sum_{j\neq{i}j=cycle}^{n}1$$ | A summation of network cycles. |
-| node_harmonic         | $$\sum_{j\neq{i}}^{n}\frac{1}{Z_{(i,j)}}$$ | Harmonic closeness is an appropriate form of closeness centrality for localised implementations constrained by the threshold $d_{max}$. |
+| node_harmonic         | $$\sum_{j\neq{i}}^{n}\frac{1}{d_{(i,j)}}$$ | Harmonic closeness is an appropriate form of closeness centrality for localised implementations constrained by the threshold $d_{max}$. |
+| node_hillier          | $$\frac{(n-1)^2}{\sum_{j \neq i}^{n} d_{(i,j)}}$$ | The square of node density divided by farness. This is also a simplified form of Improved Closeness Centrality. |
 | node_beta             | $$\sum_{j\neq{i}}^{n} \\ \exp(-\beta\cdot d[i,j])$$ | Also known as the gravity index. This is a spatial impedance metric differentiated from other closeness centralities by the use of an explicit $\beta$ parameter, which can be used to model the decay in walking tolerance as distances increase. |
+| node_cycles           | $$\sum_{j\neq{i}j=cycle}^{n}1$$ | A summation of network cycles. |
+| node_farness          | $$\sum_{j\neq{i}}^{n}d_{(i,j)}$$ | A summation of distances in metres. |
 | node_betweenness      | $$\sum_{j\neq{i}}^{n}\sum_{k\neq{j}\neq{i}}^{n}1$$ | Betweenness centrality summing all shortest-paths traversing each node $i$. |
 | node_betweenness_beta | $$\sum_{j\neq{i}}^{n}\sum_{k\neq{j}\neq{i}}^{n} \\ \exp(-\beta\cdot d[j,k])$$ | Applies a spatial impedance decay function to betweenness centrality. $d$ represents the full distance from any $j$ to $k$ node pair passing through node $i$. |
 
@@ -281,9 +281,7 @@ network representations.
  Compute node-based network centrality using the simplest path (angular) heuristic.
 :::note
 Node weights are taken into account when computing centralities. These would typically be initialised at 1 unless
-manually specified. Consider use of
-[`graphs.nx_weight_by_dissolved_edges`](/tools/graphs#nx-weight-by-dissolved-edges) when working with complex
-network representations.
+manually specified.
 :::
 ### Parameters
 <div class="param-set">
@@ -383,7 +381,10 @@ network representations.
 
 | key                   | formula | notes |
 | ----------------------| :------:| ----- |
-| node_harmonic_simplest    | $$\sum_{j\neq{i}}^{n}\frac{1}{Z_{(i,j)}}$$ | Harmonic closeness is an appropriate form of closeness centrality for localised implementations constrained by the threshold $d_{max}$. |
+| node_density_simplest | $$\sum_{j\neq{i}}^{n}1$$ | A summation of nodes. |
+| node_harmonic_simplest    | $$\sum_{j\neq{i}}^{n}\frac{1}{d_{(i,j)}}$$ | Harmonic closeness is an appropriate form of closeness centrality for localised implementations constrained by the threshold $d_{max}$. |
+| node_hillier_simplest | $$\frac{(n-1)^2}{\sum_{j \neq i}^{n} d_{(i,j)}}$$ | The square of node density divided by farness. This is also a simplified form of Improved Closeness Centrality. |
+| node_farness_simplest | $$\sum_{j\neq{i}}^{n}d_{(i,j)}$$ | A summation of distances in metres. |
 | node_betweenness_simplest | $$\sum_{j\neq{i}}^{n}\sum_{k\neq{j}\neq{i}}^{n}1$$ | Betweenness centrality summing all shortest-paths traversing each node $i$. |
 
 The following keys use the simplest-path (shortest-angular-path) heuristic, and are available when the `angular` parameter is explicitly set to `True`:

docs/src/pages/rustalgos/rustalgos.md

@@ -2726,7 +2726,7 @@ datapoints are not located with high spatial precision.
 
 
 
-<span class="name">node_xs</span><span class="annotation">: list[float]</span>
+<span class="name">node_lives</span><span class="annotation">: list[bool]</span>
 
 
 
@@ -2741,7 +2741,7 @@ datapoints are not located with high spatial precision.
 
 
 
-<span class="name">node_lives</span><span class="annotation">: list[bool]</span>
+<span class="name">node_xs</span><span class="annotation">: list[float]</span>
 
 
 

pyproject.toml

@@ -1,6 +1,6 @@
 [project]
 name = "cityseer"
-version = '4.6.7'
+version = '4.6.8'
 description = "Computational tools for network-based pedestrian-scale urban analysis"
 readme = "README.md"
 requires-python = ">=3.10, <3.12"