From f1d4a214bdace3363d7fd23b1945adf5b668c476 Mon Sep 17 00:00:00 2001 From: Gabriel Gomez Date: Mon, 16 Jun 2025 17:30:26 -0500 Subject: [PATCH 1/7] WIP msf docs --- algorithms/msf.md | 85 +++++++++++++++++++++++++++++++++++++++++++ images/city_plan.png | Bin 0 -> 103134 bytes 2 files changed, 85 insertions(+) create mode 100644 algorithms/msf.md create mode 100644 images/city_plan.png diff --git a/algorithms/msf.md b/algorithms/msf.md new file mode 100644 index 0000000..92142a6 --- /dev/null +++ b/algorithms/msf.md @@ -0,0 +1,85 @@ +--- +title: "Minimum Spanning Forest (MSF)" +description: "Minimum Spanning Forest (MSF)" +parent: "Algorithms" +--- + +# Minimum Spanning Forest (MSF) + +## Overview + +The Minimum Spanning Forest (MSF) identifies the minimum weight acyclic graph (tree) spanning every node in each connected component in the graph, disregarding edge directions. Any nodes that shared a weakly connected component still share that component in the MSF subgraph. + +MSF serves as a common algorithm in scenarios such as: +- + +## Algorithm Details + +MSF initializes by assigning each node to its own component. It iteratively scans for the minimum edges linking nodes across different components and merges them, ignoring the directionality of edges throughout the process. The algorithm terminates when no further merges occur, producing a collection of trees. + +## Syntax + +```cypher +CALL algo.msf([config]) +``` + +### Parameters + +The procedure accepts an optional configuration `Map` with the following parameters: + +| Name | Type | Default | Description | +|---------------------|--------|------------------------|----------------------------------------------------------------------------| +| `nodeLabels` | Array | All labels | Array of node labels to filter which nodes are included in the computation | +| `relationshipTypes` | Array | All relationship types | Array of relationship types to define which edges are traversed | +| `objective` | string | 'minimum' | 'minimum' or 'maximum' What to optimize in the spanning tree | +| `weightAttribute` | string | Unweighted | The atrribute to use as the tree weight. | + +### Return Values +The procedure returns a stream of records with the following fields: + +| Name | Type | Description | +|----------|--------|-----------------------------------------------| +| `edge` | Edge | An Edge entity which is part of the MSF graph | +| `weight` | Double | The weight of the Edge | + +## Examples: + +Lets take this Social Graph as an example: + +![City Graph](../images/city_plan.png) + +There are 3 different communities in this graph: +- Alice, Bob, Charlie +- David, Emma +- Frank + +### Create the Graph + +```cypher +CREATE + (CityHall:GOV), + (CourtHouse:GOV), + (FireStation:GOV), + (Electricity:UTIL), + (Water:UTIL), + (Building_A:RES), + (Building_B:RES), + (CityHall)-[rA:ROAD {cost: 5}]->(CourtHouse), + (CityHall)-[rB:ROAD {cost: 7}]->(FireStation), + (CourtHouse)-[rC:ROAD {cost: 4}]->(Building_A), + (FireStation)-[rD:ROAD {cost: 6}]->(Building_B), + (Building_A)-[rF:ROAD {cost: 8}]->(Building_B), + (Electricity)-[rG:ROAD {cost: 3}]->(Building_A), + (Water)-[rH:ROAD {cost: 2}]->(Building_B), + (CityHall)-[tA:TRAM {cost: 3}]->(Building_A), + (CourtHouse)-[tB:TRAM {cost: 5}]->(Building_B), + (FireStation)-[tC:TRAM {cost: 4}]->(Electricity) + RETURN * +``` +### Example: Find cheapest road network: +```cypher +CALL algo.WCC(null) yield node, componentId +``` + +#### Expected Results + diff --git a/images/city_plan.png b/images/city_plan.png new file mode 100644 index 0000000000000000000000000000000000000000..9da8fc5ffd7b13dafbb6339e2708b74895ef3240 GIT binary patch literal 103134 zcmeGEgBd476m%Fsx`r<47(zuvVnBux zZ~&!SV(56+9?$tczxQ8wK98Rhfb6~Recvmtb**d7OJzkF8tMzwR8&+nDB1g}R8&W9 zP*ELlK6)5_!m^mF0{`3RqAGKjD!+|k3cfjLc}L+66;)x_@onQn@cl6-SsfQDs*@j) zfA>|qwVi_tf~?iGU9}bDMNA#-xsA;nP0YDH?VaGasi?#xJ)MkAZOvV;n3!8yJBYI^ z;OkhfSeuEnXbC9XRB*ayZe=a&?QE{*t*CD5ZEGrQ#v&;}LoMbh0(Y=CcQwA^X>aG? zBH}52jdEiV_!{{!&ov1#XEO^C)%y?r{SEj|{F;@ktCI*1kB5f`w+A1$qq8LsuduK% z&&^vrw{CI4Z*aMIIk*~oayhtM|Mv#>&0S2Lt({!09UZP9H#9bJbaNHI=H_N?CSqZ1 zAz)%=CctH4%xA{M%WG!LWo*XB%VoyLXC@@Td;69JugSH4AMa{y@&7#E!R6m=fDPe6 z{)UH_`zEqv8DyLOx4Y&J 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zBxu5lR_@{Gw*1gN4C3w}6M8_S?|27YgWh|4sbSvcZag>y?TWlS>&%;8@87+pkIu6h z@LUDyND<)yPX`0frRx7~0aXVRD2iazqyuz}OrU97ea8SmB+r^4A-hDf@zJo90d z@nO9r9ZBDpvEd1bU+p5>`ykm9PnyxSOGLK#})N`PPvvf*E@J(qvLivyH#l)xJGh`*sLhIsM>b8f-tPR5~( zOTiAUhqh~LwqfOi(S&}lQgzk&{!qthJ@;}(z~_LHtRlp0_^7BTbf{FL3<7gY1i2B~ zbC8lqExlF-Y{CUvfk!GM9$=Han-!V*r9vQ4r(k7eWo}`SYd=F`G-sC|DPW$+M~1> W{`TDIx!gDOoLE_<8(G)yJ^g?C5%LBA literal 0 HcmV?d00001 From 5c7a7783b4d4ef35796071d7e87ed4951f5b98ac Mon Sep 17 00:00:00 2001 From: Gabriel Gomez Date: Tue, 17 Jun 2025 11:03:15 -0500 Subject: [PATCH 2/7] MSF example graph and weights --- algorithms/msf.md | 43 ++++++++++++++++++++++++------------------- images/city_plan.png | Bin 103134 -> 189584 bytes 2 files changed, 24 insertions(+), 19 deletions(-) diff --git a/algorithms/msf.md b/algorithms/msf.md index 92142a6..1bf612d 100644 --- a/algorithms/msf.md +++ b/algorithms/msf.md @@ -11,7 +11,9 @@ parent: "Algorithms" The Minimum Spanning Forest (MSF) identifies the minimum weight acyclic graph (tree) spanning every node in each connected component in the graph, disregarding edge directions. Any nodes that shared a weakly connected component still share that component in the MSF subgraph. MSF serves as a common algorithm in scenarios such as: -- +- Designing a cost-effective road network connecting several cities. +- Identifying core connections in a social network. +- Optimizing the layout of power grids to minimize cable length. ## Algorithm Details @@ -44,14 +46,11 @@ The procedure returns a stream of records with the following fields: ## Examples: -Lets take this Social Graph as an example: +Lets take this City as an example: ![City Graph](../images/city_plan.png) -There are 3 different communities in this graph: -- Alice, Bob, Charlie -- David, Emma -- Frank + ### Create the Graph @@ -64,22 +63,28 @@ CREATE (Water:UTIL), (Building_A:RES), (Building_B:RES), - (CityHall)-[rA:ROAD {cost: 5}]->(CourtHouse), - (CityHall)-[rB:ROAD {cost: 7}]->(FireStation), - (CourtHouse)-[rC:ROAD {cost: 4}]->(Building_A), - (FireStation)-[rD:ROAD {cost: 6}]->(Building_B), - (Building_A)-[rF:ROAD {cost: 8}]->(Building_B), - (Electricity)-[rG:ROAD {cost: 3}]->(Building_A), - (Water)-[rH:ROAD {cost: 2}]->(Building_B), - (CityHall)-[tA:TRAM {cost: 3}]->(Building_A), - (CourtHouse)-[tB:TRAM {cost: 5}]->(Building_B), - (FireStation)-[tC:TRAM {cost: 4}]->(Electricity) - RETURN * + (CityHall)-[rA:ROAD {cost: 2.2}]->(CourtHouse), + (CityHall)-[rB:ROAD {cost: 8.0}]->(FireStation), + (CourtHouse)-[rC:ROAD {cost: 3.4}]->(Building_A), + (FireStation)-[rD:ROAD {cost: 3.0}]->(Building_B), + (Building_A)-[rF:ROAD {cost: 5.2}]->(Building_B), + (Electricity)-[rG:ROAD {cost: 0.7}]->(Building_A), + (Water)-[rH:ROAD {cost: 2.3}]->(Building_B), + (CityHall)-[tA:TRAM {cost: 1.5}]->(Building_A), + (CourtHouse)-[tB:TRAM {cost: 7.3}]->(Building_B), + (FireStation)-[tC:TRAM {cost: 1.2}]->(Electricity) ``` ### Example: Find cheapest road network: ```cypher -CALL algo.WCC(null) yield node, componentId +CALL algo.MSF() YIELD edge, weight ``` #### Expected Results - +| Edge | weight | +|-----------|--------| +| `[:ROAD]` | 0.7 | +| `[:TRAM]` | 1.2 | +| `[:TRAM]` | 1.5 | +| `[:ROAD]` | 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(68%) rename images/{city_mst.png => city_msf.png} (100%) diff --git a/algorithms/mst.md b/algorithms/msf.md similarity index 68% rename from algorithms/mst.md rename to algorithms/msf.md index f9e4934..7cf8bff 100644 --- a/algorithms/mst.md +++ b/algorithms/msf.md @@ -1,30 +1,30 @@ --- -title: "Minimum Spanning Tree (MST)" -description: "Minimum Spanning Tree (MST)" +title: "Minimum Spanning Forest (MSF)" +description: "Minimum Spanning Forest (MSF)" parent: "Algorithms" --- -# Minimum Spanning Tree (MST) +# Minimum Spanning Forest (MSF) ## Overview -The Minimum Spanning Tree (MST) finds the relationships with minimum weights such that any weakly connected component in the graph stays connected. It treats all edges as bi-directional and ensures that any pair of nodes that previously shared a path will still share a unique path in the MST subgraph. +The Minimum Spanning Forest (MSF) finds the relationships with minimum weights such that any weakly connected component in the graph stays connected. It treats all edges as bi-directional and ensures that any pair of nodes that previously shared a path will still share a unique path in the MSF subgraph. -MST serves as a common algorithm in scenarios such as: +MSF serves as a common algorithm in scenarios such as: - Designing a cost-effective road network connecting several cities. - Power Grid / Utility cost optimization. - Identifying redundancies in networks. ## Algorithm Details -MST first assigns each node to its own component. It iteratively scans for the minimum edges linking nodes across different components and merges them, ignoring the direction of edges throughout the process. The algorithm terminates when no further merges occur, producing a collection of trees. +MSF first assigns each node to its own component. It iteratively scans for the minimum edges linking nodes across different components and merges them, ignoring the direction of edges throughout the process. The algorithm terminates when no further merges occur, producing a collection of trees. -The procedure finds a minimum or maximum weight spanning tree based on the specified `objective` and optimizes for the given `weightAttribute`. If no attribute is given, MST returns any collection of spanning trees. If any specified edges do not have the given weight attribute, or the value of the attribute is non-numeric, then they are treated as if they had infinite weight. Such an edge would only be included in the minimum spanning tree if no other edges with a valid weight attribute bridge the components it connects. +The procedure finds a minimum or maximum weight spanning forest based on the specified `objective` and optimizes for the given `weightAttribute`. If no attribute is given, MSF returns any collection of spanning trees. If any specified edges do not have the given weight attribute, or the value of the attribute is non-numeric, then they are treated as if they had infinite weight. Such an edge would only be included in the minimum spanning tree if no other edges with a valid weight attribute bridge the components it connects. ## Syntax ```cypher -CALL algo.mst([config]) +CALL algo.MSF([config]) ``` ### Parameters @@ -43,7 +43,7 @@ The procedure returns a stream of records with the following fields: | Name | Type | Description | |----------|--------|-----------------------------------------------| -| `edge` | Edge | An edge entity which is part of the MST graph | +| `edge` | Edge | An edge entity which is part of the MSF graph | | `weight` | Double | The weight of the Edge | @@ -77,15 +77,15 @@ RETURN * Suppose you are an urban planner tasked with designing a new transportation network for a town. There are several vital buildings that must be connected by this new network. A cost estimator has already provided you with the estimated cost for some of the potential routes between these buildings. -Your goal is to connect every major building with the lowest total cost, even if travel between some buildings requires multiple stops and different modes of transport. The Minimum Spanning Tree algorithm helps you achieve this by identifying the most cost-effective network. +Your goal is to connect every major building with the lowest total cost, even if travel between some buildings requires multiple stops and different modes of transport. The Minimum Spanning Forest algorithm helps you achieve this by identifying the most cost-effective network. ![City Graph](../images/city_plan.png) ```cypher -CALL algo.mst({weightAttribute: 'cost'}) YIELD edge, weight +CALL algo.MSF({weightAttribute: 'cost'}) YIELD edge, weight ``` #### Expected Results The algorithm would yeild the following edge objects and their weights: -![City MST Graph](../images/city_mst.png) \ No newline at end of file +![City MSF Graph](../images/city_msf.png) \ No newline at end of file diff --git a/images/city_mst.png b/images/city_msf.png similarity index 100% rename from images/city_mst.png rename to images/city_msf.png

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zBxu5lR_@{Gw*1gN4C3w}6M8_S?|27YgWh|4sbSvcZag>y?TWlS>&%;8@87+pkIu6h z@LUDyND<)yPX`0frRx7~0aXVRD2iazqyuz}OrU97ea8SmB+r^4A-hDf@zJo90d z@nO9r9ZBDpvEd1bU+p5>`ykm9PnyxSOGLK#})N`PPvvf*E@J(qvLivyH#l)xJGh`*sLhIsM>b8f-tPR5~( zOTiAUhqh~LwqfOi(S&}lQgzk&{!qthJ@;}(z~_LHtRlp0_^7BTbf{FL3<7gY1i2B~ zbC8lqExlF-Y{CUvfk!GM9$=Han-!V*r9vQ4r(k7eWo}`SYd=F`G-sC|DPW$+M~1> W{`TDIx!gDOoLE_<8(G)yJ^g?C5%LBA From a894f34221c0b4599f8bbf10d46f2ce33f45c7b4 Mon Sep 17 00:00:00 2001 From: Gabriel Gomez Date: Tue, 8 Jul 2025 13:17:55 -0500 Subject: [PATCH 3/7] update docs to reflect changes --- algorithms/{msf.md => mst.md} | 22 ++++++++++++---------- 1 file changed, 12 insertions(+), 10 deletions(-) rename algorithms/{msf.md => mst.md} (66%) diff --git a/algorithms/msf.md b/algorithms/mst.md similarity index 66% rename from algorithms/msf.md rename to algorithms/mst.md index 1bf612d..78a8e9d 100644 --- a/algorithms/msf.md +++ b/algorithms/mst.md @@ -1,28 +1,30 @@ --- -title: "Minimum Spanning Forest (MSF)" -description: "Minimum Spanning Forest (MSF)" +title: "Minimum Spanning Tree (MST)" +description: "Minimum Spanning Tree (MST)" parent: "Algorithms" --- -# Minimum Spanning Forest (MSF) +# Minimum Spanning Forest (MST) ## Overview -The Minimum Spanning Forest (MSF) identifies the minimum weight acyclic graph (tree) spanning every node in each connected component in the graph, disregarding edge directions. Any nodes that shared a weakly connected component still share that component in the MSF subgraph. +The Minimum Spanning Tree (MST) identifies the minimum weight acyclic graph (tree) spanning every node in each connected component in the graph, disregarding edge directions. Any nodes that shared a weakly connected component still share that component in the MST subgraph. -MSF serves as a common algorithm in scenarios such as: +MST serves as a common algorithm in scenarios such as: - Designing a cost-effective road network connecting several cities. - Identifying core connections in a social network. - Optimizing the layout of power grids to minimize cable length. ## Algorithm Details -MSF initializes by assigning each node to its own component. It iteratively scans for the minimum edges linking nodes across different components and merges them, ignoring the directionality of edges throughout the process. The algorithm terminates when no further merges occur, producing a collection of trees. +MST first assigns each node to its own component. It iteratively scans for the minimum edges linking nodes across different components and merges them, ignoring the directionality of edges throughout the process. The algorithm terminates when no further merges occur, producing a collection of trees. + +Finds the minimum or maximum weight spanning tree uses the given attribute as the weight. If no attribute is given, returns any spanning tree. If an edge of the given types must be included in the minimum spanning tree. ## Syntax ```cypher -CALL algo.msf([config]) +CALL algo.mst([config]) ``` ### Parameters @@ -33,8 +35,8 @@ The procedure accepts an optional configuration `Map` with the following paramet |---------------------|--------|------------------------|----------------------------------------------------------------------------| | `nodeLabels` | Array | All labels | Array of node labels to filter which nodes are included in the computation | | `relationshipTypes` | Array | All relationship types | Array of relationship types to define which edges are traversed | -| `objective` | string | 'minimum' | 'minimum' or 'maximum' What to optimize in the spanning tree | -| `weightAttribute` | string | Unweighted | The atrribute to use as the tree weight. | +| `objective` | string | 'minimize' | 'minimize' or 'maximize' what to optimize in the spanning tree | +| `weightAttribute` | string | Unweighted | the atrribute to use as the tree weight. | ### Return Values The procedure returns a stream of records with the following fields: @@ -76,7 +78,7 @@ CREATE ``` ### Example: Find cheapest road network: ```cypher -CALL algo.MSF() YIELD edge, weight +CALL algo.mst() YIELD edge, weight ``` #### Expected Results From b59f0ebe9adcf5faf0ee53f9d2199c4cb41b9531 Mon Sep 17 00:00:00 2001 From: Gabriel Gomez Date: Mon, 14 Jul 2025 22:17:42 -0500 Subject: [PATCH 4/7] clarification and typos --- algorithms/mst.md | 16 ++++++++-------- 1 file changed, 8 insertions(+), 8 deletions(-) diff --git a/algorithms/mst.md b/algorithms/mst.md index 78a8e9d..b8df2f9 100644 --- a/algorithms/mst.md +++ b/algorithms/mst.md @@ -4,22 +4,22 @@ description: "Minimum Spanning Tree (MST)" parent: "Algorithms" --- -# Minimum Spanning Forest (MST) +# Minimum Spanning Tree (MST) ## Overview -The Minimum Spanning Tree (MST) identifies the minimum weight acyclic graph (tree) spanning every node in each connected component in the graph, disregarding edge directions. Any nodes that shared a weakly connected component still share that component in the MST subgraph. +The Minimum Spanning Tree (MST) identifies the minimum weight acyclic graph (tree) spanning every node in each weakly connected component in the graph, disregarding edge directions. Any nodes that shared a weakly connected component still share that component in the MST subgraph. MST serves as a common algorithm in scenarios such as: - Designing a cost-effective road network connecting several cities. -- Identifying core connections in a social network. -- Optimizing the layout of power grids to minimize cable length. +- Power Grid / Utility cost optimization. +- Identifying redundancies in networks. ## Algorithm Details -MST first assigns each node to its own component. It iteratively scans for the minimum edges linking nodes across different components and merges them, ignoring the directionality of edges throughout the process. The algorithm terminates when no further merges occur, producing a collection of trees. +MST first assigns each node to its own component. It iteratively scans for the minimum edges linking nodes across different components and merges them, ignoring the direction of edges throughout the process. The algorithm terminates when no further merges occur, producing a collection of trees. -Finds the minimum or maximum weight spanning tree uses the given attribute as the weight. If no attribute is given, returns any spanning tree. If an edge of the given types must be included in the minimum spanning tree. +The procedure finds a minimum or maximum weight spanning tree based on the specified attribute. If no attribute is given, returns any spanning tree. If any specified edges do not have the given weight attribute, or the value of the attribute is non-numeric, then they are treated as if they had infinite weight. Such an edge would only be included in the minimum spanning tree if no other edges with a valid weight attribute bridge the components it connects. ## Syntax @@ -43,7 +43,7 @@ The procedure returns a stream of records with the following fields: | Name | Type | Description | |----------|--------|-----------------------------------------------| -| `edge` | Edge | An Edge entity which is part of the MSF graph | +| `edge` | Edge | An edge entity which is part of the MSF graph | | `weight` | Double | The weight of the Edge | ## Examples: @@ -78,7 +78,7 @@ CREATE ``` ### Example: Find cheapest road network: ```cypher -CALL algo.mst() YIELD edge, weight +CALL algo.mst({weightAttribute: 'cost'}) YIELD edge, weight ``` #### Expected Results From 1acf46cc3f84c7d8eb7562711f5207507734380f Mon Sep 17 00:00:00 2001 From: Gabriel Gomez Date: Mon, 14 Jul 2025 22:23:23 -0500 Subject: [PATCH 5/7] spelling --- algorithms/mst.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/algorithms/mst.md b/algorithms/mst.md index b8df2f9..71f7055 100644 --- a/algorithms/mst.md +++ b/algorithms/mst.md @@ -8,7 +8,7 @@ parent: "Algorithms" ## Overview -The Minimum Spanning Tree (MST) identifies the minimum weight acyclic graph (tree) spanning every node in each weakly connected component in the graph, disregarding edge directions. Any nodes that shared a weakly connected component still share that component in the MST subgraph. +The Minimum Spanning Tree (MST) identifies the minimum weight acyclic graph (tree) spanning every node in each weakly connected component in the graph, disregarding edge directions. Any nodes that shared a weakly connected component still share that component in the MST sub-graph. MST serves as a common algorithm in scenarios such as: - Designing a cost-effective road network connecting several cities. @@ -36,14 +36,14 @@ The procedure accepts an optional configuration `Map` with the following paramet | `nodeLabels` | Array | All labels | Array of node labels to filter which nodes are included in the computation | | `relationshipTypes` | Array | All relationship types | Array of relationship types to define which edges are traversed | | `objective` | string | 'minimize' | 'minimize' or 'maximize' what to optimize in the spanning tree | -| `weightAttribute` | string | Unweighted | the atrribute to use as the tree weight. | +| `weightAttribute` | string | Unweighted | the attribute to use as the tree weight. | ### Return Values The procedure returns a stream of records with the following fields: | Name | Type | Description | |----------|--------|-----------------------------------------------| -| `edge` | Edge | An edge entity which is part of the MSF graph | +| `edge` | Edge | An edge entity which is part of the MST graph | | `weight` | Double | The weight of the Edge | ## Examples: From 1142822656d6837ee727bed99216cdf16230c749 Mon Sep 17 00:00:00 2001 From: Gabriel Gomez Date: Tue, 15 Jul 2025 13:14:47 -0500 Subject: [PATCH 6/7] rearanging example --- algorithms/mst.md | 33 ++++++++++++++++----------------- images/city_mst.png | Bin 0 -> 647400 bytes images/city_plan.png | Bin 189584 -> 900369 bytes 3 files changed, 16 insertions(+), 17 deletions(-) create mode 100644 images/city_mst.png diff --git a/algorithms/mst.md b/algorithms/mst.md index 71f7055..f9e4934 100644 --- a/algorithms/mst.md +++ b/algorithms/mst.md @@ -8,7 +8,7 @@ parent: "Algorithms" ## Overview -The Minimum Spanning Tree (MST) identifies the minimum weight acyclic graph (tree) spanning every node in each weakly connected component in the graph, disregarding edge directions. Any nodes that shared a weakly connected component still share that component in the MST sub-graph. +The Minimum Spanning Tree (MST) finds the relationships with minimum weights such that any weakly connected component in the graph stays connected. It treats all edges as bi-directional and ensures that any pair of nodes that previously shared a path will still share a unique path in the MST subgraph. MST serves as a common algorithm in scenarios such as: - Designing a cost-effective road network connecting several cities. @@ -19,7 +19,7 @@ MST serves as a common algorithm in scenarios such as: MST first assigns each node to its own component. It iteratively scans for the minimum edges linking nodes across different components and merges them, ignoring the direction of edges throughout the process. The algorithm terminates when no further merges occur, producing a collection of trees. -The procedure finds a minimum or maximum weight spanning tree based on the specified attribute. If no attribute is given, returns any spanning tree. If any specified edges do not have the given weight attribute, or the value of the attribute is non-numeric, then they are treated as if they had infinite weight. Such an edge would only be included in the minimum spanning tree if no other edges with a valid weight attribute bridge the components it connects. +The procedure finds a minimum or maximum weight spanning tree based on the specified `objective` and optimizes for the given `weightAttribute`. If no attribute is given, MST returns any collection of spanning trees. If any specified edges do not have the given weight attribute, or the value of the attribute is non-numeric, then they are treated as if they had infinite weight. Such an edge would only be included in the minimum spanning tree if no other edges with a valid weight attribute bridge the components it connects. ## Syntax @@ -29,7 +29,7 @@ CALL algo.mst([config]) ### Parameters -The procedure accepts an optional configuration `Map` with the following parameters: +The procedure accepts an optional configuration `Map` with the following optional parameters: | Name | Type | Default | Description | |---------------------|--------|------------------------|----------------------------------------------------------------------------| @@ -46,11 +46,6 @@ The procedure returns a stream of records with the following fields: | `edge` | Edge | An edge entity which is part of the MST graph | | `weight` | Double | The weight of the Edge | -## Examples: - -Lets take this City as an example: - -![City Graph](../images/city_plan.png) @@ -75,18 +70,22 @@ CREATE (CityHall)-[tA:TRAM {cost: 1.5}]->(Building_A), (CourtHouse)-[tB:TRAM {cost: 7.3}]->(Building_B), (FireStation)-[tC:TRAM {cost: 1.2}]->(Electricity) +RETURN * ``` -### Example: Find cheapest road network: + +## Examples: + +Suppose you are an urban planner tasked with designing a new transportation network for a town. There are several vital buildings that must be connected by this new network. A cost estimator has already provided you with the estimated cost for some of the potential routes between these buildings. + +Your goal is to connect every major building with the lowest total cost, even if travel between some buildings requires multiple stops and different modes of transport. The Minimum Spanning Tree algorithm helps you achieve this by identifying the most cost-effective network. + +![City Graph](../images/city_plan.png) + ```cypher CALL algo.mst({weightAttribute: 'cost'}) YIELD edge, weight ``` #### Expected Results -| Edge | weight | -|-----------|--------| -| `[:ROAD]` | 0.7 | -| `[:TRAM]` | 1.2 | -| `[:TRAM]` | 1.5 | -| `[:ROAD]` | 2.2 | -| `[:ROAD]` | 2.3 | -| `[:ROAD]` | 3.0 | +The algorithm would yeild the following edge objects and their weights: + +![City MST Graph](../images/city_mst.png) \ No newline at end of file diff --git a/images/city_mst.png b/images/city_mst.png new file mode 100644 index 0000000000000000000000000000000000000000..771a27fc7813699d840b33cacd0a886587ec303d GIT binary patch literal 647400 zcmeFZc|6p6`#-LPN~jb?s8f+FQI@hMZD?f4HpZ4LV{Bm%h9WtssO)5^3}MV*j5T|u zEYS?cz9h>mw(Q38eZ5cTKHb0j{`~v<@193JJWT7nmg{)cpn?v7FOr7)-8W)=0HTCiAm|^#&XE{Yc%@k>bEENciuL0?Zz;5_Ze=Z zg&Ik}%Xst0DO+~#$Wy!b2VCN=TISuQxMSyYwqsR;Gm7Ia^>_B|J*XgDJ&#D2*k-hB 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