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Merge pull request #403 from bedupako12mas/Centrality-Week12
Centrality week12
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‎.github/workflows/boost_version.yml

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# - 1.56 is the minimum version we ask (Aug 2014)
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on:
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workflow_dispatch:
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push:
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paths:
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- '.github/workflows/boost_version.yml'

‎.github/workflows/check-queries.yml

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# - the latest postgis version
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on:
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workflow_dispatch:
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push:
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- '.github/workflows/check-queries.yml'

‎.github/workflows/clang.yml

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# - postgis 3
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on:
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workflow_dispatch:
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push:
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paths:
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- '.github/workflows/clang.yml'

‎.github/workflows/tidy-check.yml

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name: clang-tidy check
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on:
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workflow_dispatch:
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pull_request:
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branches-ignore:
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- 'gh-pages'

‎NEWS.md

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milestone for 3.7.0
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](https://github.com/pgRouting/pgrouting/issues?utf8=%E2%9C%93&q=milestone%3A%22Release%203.7.0%22)
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**New experimental functions**
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* Metrics
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* pgr_betweennessCentrality
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**Official functions changes**
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* [#2605](https://github.com/pgRouting/pgrouting/pull/2605) Standarize

‎doc/metrics/CMakeLists.txt

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SET(LOCAL_FILES
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metrics-family.rst
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pgr_betweennessCentrality.rst
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)
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)
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foreach (f ${LOCAL_FILES})
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configure_file(${f} "${PGR_DOCUMENTATION_SOURCE_DIR}/${f}")
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list(APPEND LOCAL_DOC_FILES ${PGR_DOCUMENTATION_SOURCE_DIR}/${f})
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endforeach()
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set(PROJECT_DOC_FILES ${PROJECT_DOC_FILES} ${LOCAL_DOC_FILES} PARENT_SCOPE)
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‎doc/metrics/metrics-family.rst

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..
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****************************************************************************
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pgRouting Manual
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Copyright(c) pgRouting Contributors
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This documentation is licensed under a Creative Commons Attribution-Share
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Alike 3.0 License: https://creativecommons.org/licenses/by-sa/3.0/
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****************************************************************************
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|
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Metrics - Family of functions
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===============================================================================
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.. rubric:: Experimental
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.. include:: experimental.rst
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:start-after: begin-warn-expr
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:end-before: end-warn-expr
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.. index experimental from here
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* :doc:`pgr_betweennessCentrality` - Calculates relative betweenness centrality using Brandes Algorithm
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.. index experimental to here
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.. toctree::
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:hidden:
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pgr_betweennessCentrality
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See Also
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-------------------------------------------------------------------------------
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.. rubric:: Indices and tables
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* :ref:`genindex`
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* :ref:`search`

‎doc/metrics/pgr_betweennessCentrality.rst

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``pgr_betweennessCentrality``
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===============================================================================
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``pgr_betweennessCentrality`` - Returns the relative betweeness centrality of
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all vertices in a graph using Brandes Algorithm.
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``pgr_betweennessCentrality`` - Calculates the relative betweeness centrality
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using Brandes Algorithm
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.. figure:: images/boost-inside.jpeg
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:target: https://www.boost.org/doc/libs/1_84_0/libs/graph/doc/betweenness_centrality.html
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Boost Graph Inside
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.. rubric:: Availability
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.. TODO: Add availability
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* Version 3.7.0
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* New **experimental** function:
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* ``pgr_betweennessCentrality``
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Description
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-------------------------------------------------------------------------------
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The Brandes Algorithm for utilises the sparse nature of graphs to evaluating the
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betweenness centrality score of all edges/vertices.
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We use Boost's implementation which runs in :math:`\Theta(VE)` time and uses :math:`\Theta(VE)` space.
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The Brandes Algorithm takes advantage of the sparse graphs for evaluating the
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betweenness centrality score of all vertices.
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Betweenness centrality measures the extent to which a vertex lies on the
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shortest paths between all other pairs of vertices. Vertices with a high
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betweenness centrality score may have considerable influence in a network by the
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virtue of their control over the shortest paths passing between them.
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The removal of these vertices will affect the network by disrupting the
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it, as most of the shortest paths between vertices pass through them.
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This implementation work for both directed and undirected graphs.
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- Running time: :math:`\Theta(VE)`
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- Running space: :math:`\Theta(VE)`
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- Throws when there are no edges in the graph
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Signatures
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-------------------------------------------------------------------------------
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pgr_betweennessCentrality(`Edges SQL`_, [``directed``])
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| Returns set of ```(seq, vid, centrality)```
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| OR EMPTY SET
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| Returns set of ``(vid, centrality)``
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.. TODO: Fix this when docqueries are made
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:Example: For a directed subgraph with edges :math:`\{1, 2, 3, 4\}`.
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:Example: For a directed graph with edges :math:`\{1, 2, 3, 4\}`.
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.. literalinclude:: betweennessCentrality.queries
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:start-after: -- q1
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:end-before: Implicit Cases (directed)
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:end-before: -- q2
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.. rubric:: Explanation
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* The betweenness centrality are between parenthesis.
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* The leaf vertices have betweenness centrality :math:`0`.
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* Betweenness centrality of vertex :math:`6` is higher than of vertex :math:`10`.
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* Removing vertex :math:`6` will create three graph components.
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* Removing vertex :math:`10` will create two graph components.
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.. graphviz::
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digraph G {
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5, 7, 15 [shape=circle;style=filled;width=.5;color=deepskyblue;fontsize=8;fixedsize=true;];
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6, 10 [shape=circle;style=filled;width=.5;color=green;fontsize=8;fixedsize=true;];
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5 [pos="0,0!";label="5 (0)"];
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6 [pos="0,1!"label="6 (0.5)"];
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7 [pos="0,2!"label="7 (0)"];
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10 [pos="1,1!"label="10 (0.25)"];
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15 [pos="2,1!"label="15 (0)"];
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5 -> 6 [dir=both;label="1 "];
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6->7 [dir=both;label="4 "];
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10->6 [label="3"];
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15->10 [label="4"];
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}
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Parameters
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-------------------------------------------------------------------------------
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:width: 81
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:widths: auto
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:header-rows: 1
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* - Column
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- Type
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- Description
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* - ``seq``
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- ``INTEGER``
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- Sequential Value starting from ``1``
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* - ``vid``
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- ``BIGINT``
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- Identifier of the vertex
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* - ``centrality``
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- ``FLOAT``
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- relative betweenness centrality score of the vertex (will be in range [0,1])
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- ``FLOAT``
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- Relative betweenness centrality score of the vertex (will be in range [0,1])
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-------------------------------------------------------------------------------
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* Boost `centrality
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* Boost's `betweenness_centrality
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<https://www.boost.org/doc/libs/1_84_0/libs/graph/doc/betweenness_centrality.html>`_
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* Queries uses the :doc:`sampledata` network.
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* Queries use the :doc:`sampledata` network.
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.. rubric:: Indices and tables
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‎doc/src/experimental.rst

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:start-after: index from here
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:doc:`metrics-family`
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.. include:: metrics-family.rst
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:start-after: index experimental from here
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:end-before: index experimental to here
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transformation-family
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components-family
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ordering-family
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metrics-family
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- :doc:`pgr_transitiveClosure`
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- :doc:`pgr_lengauerTarjanDominatorTree`
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- :doc:`pgr_hawickCircuits`
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- :doc:`pgr_betweennessCentrality`
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.. toctree::
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:hidden:
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pgr_transitiveClosure
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pgr_lengauerTarjanDominatorTree
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pgr_hawickCircuits
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See Also

‎doc/src/release_notes.rst

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milestone for 3.7.0
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<https://github.com/pgRouting/pgrouting/issues?utf8=%E2%9C%93&q=milestone%3A%22Release%203.7.0%22>`__
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.. rubric:: New experimental functions
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* Metrics
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* pgr_betweennessCentrality
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* `#2605 <https://github.com/pgRouting/pgrouting/pull/2605>`__ Standarize

‎docqueries/metrics/betweennessCentrality.pg

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'SELECT id, source, target, cost, reverse_cost
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FROM edges where id < 5'
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) ORDER BY vid;
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/* Implicit Cases (directed) */
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SELECT * FROM pgr_betweennessCentrality(
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'SELECT id, source, target, cost, reverse_cost
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FROM edges where id < 2'
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) ORDER BY vid;
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SELECT * FROM pgr_betweennessCentrality(
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'SELECT id, source, target, cost, reverse_cost
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FROM edges where id < 3'
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) ORDER BY vid;
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SELECT * FROM pgr_betweennessCentrality(
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'SELECT id, source, target, cost, reverse_cost
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FROM edges where id < 4'
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) ORDER BY vid;
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SELECT * FROM pgr_betweennessCentrality(
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'SELECT id, source, target, cost, reverse_cost
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FROM edges where id < 5'
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) ORDER BY vid;
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/* Explicit Cases (undirected) */
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SELECT * FROM pgr_betweennessCentrality(
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'SELECT id, source, target, cost, reverse_cost
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FROM edges where id < 2', directed => false
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) ORDER BY vid;
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SELECT * FROM pgr_betweennessCentrality(
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'SELECT id, source, target, cost, reverse_cost
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FROM edges where id < 3', directed => false
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) ORDER BY vid;
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SELECT * FROM pgr_betweennessCentrality(
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'SELECT id, source, target, cost, reverse_cost
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FROM edges where id < 4', directed => false
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) ORDER BY vid;
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SELECT * FROM pgr_betweennessCentrality(
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'SELECT id, source, target, cost, reverse_cost
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FROM edges where id < 5', directed => false
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) ORDER BY vid;
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/* Explicit Cases (directed) */
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SELECT * FROM pgr_betweennessCentrality(
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'SELECT id, source, target, cost, reverse_cost
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FROM edges where id < 2', directed => true
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) ORDER BY vid;
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SELECT * FROM pgr_betweennessCentrality(
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'SELECT id, source, target, cost, reverse_cost
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FROM edges where id < 3', directed => true
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) ORDER BY vid;
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SELECT * FROM pgr_betweennessCentrality(
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'SELECT id, source, target, cost, reverse_cost
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FROM edges where id < 4', directed => true
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) ORDER BY vid;
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SELECT * FROM pgr_betweennessCentrality(
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'SELECT id, source, target, cost, reverse_cost
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FROM edges where id < 5', directed => true
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) ORDER BY vid;
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/* -- q2 */

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