▣ MODEL KIT

Run Graph Algorithms API

What it does

Graph Algorithms gives you traversal, path, and graph-structure utilities for directed and undirected graphs. Send a graph with vertices and edges, then use the specific algorithm endpoint to get the result back in a compact JSON shape.

Use breadth-first search or depth-first search when you need the visit order from a chosen start vertex. Breadth-first search returns { start, visited }, while Depth-first search returns the same response shape with a different traversal strategy. For directed graphs, both follow edge direction; for undirected graphs, edges are treated as bidirectional.

Use Topological sort on a directed graph when you need an ordering of vertices in a DAG. It returns { order }, which is useful for dependency resolution, build pipelines, task scheduling, and other workflows where prerequisites must come before dependents.

For weighted directed graphs, Shortest path returns either a single { start, end, reachable, distance, path } result when you supply end, or a { start, paths } map of distances and paths to all reachable vertices. Minimum spanning tree returns the selected edges and totalWeight for a spanning tree covering the graph, and Distance matrix returns a symmetric or asymmetric matrix depending on whether the graph is undirected or directed. These endpoints fit graph analysis, routing logic, and operations planning where you need explicit paths or pairwise distances.

▣ ENDPOINT 01 / 06

POST

Breadth-first search traversal through all vertices in a graph.

https://api.eu.apyhub.com/modernsoftware-pro/run-graph-algorithms/breadth-first-search

QUICKSTART

GUIDE

Quickstart

Run a breadth-first search from the start vertex on the graph you send in the JSON body.

curl -X POST "https://api.eu.apyhub.com/modernsoftware-pro/run-graph-algorithms/breadth-first-search?start=home" \
  -H "apy-token: $APY_TOKEN" \
  -H "Content-Type: application/json" \
  -d '{
    "graph": {
      "type": "undirected",
      "vertices": [
        { "id": "home" },
        { "id": "about" },
        { "id": "contact" }
      ],
      "edges": [
        { "f": "home", "t": "about" },
        { "f": "about", "t": "contact" }
      ]
    }
  }'

What you'll get back

Returns a JSON object with a start string and a visited array of strings. start is the starting vertex you supplied, and visited lists the vertices visited by the breadth-first search.

{
  "start": "home",
  "visited": ["home", "about", "contact"]
}

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API key

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About this endpoint

What it does

Performs a breadth-first search traversal on the provided graph starting from the specified vertex. It returns the start vertex and the traversal order of visited vertices.

Query Parameter(s)

Attribute	Type	Mandatory	Description
start	String	Yes	Start vertex ID. Must match the pattern `^[a-zA-Z0-9_:-]{1,40}$`.

Request Body

Parameter	Type	Mandatory	Description
graph	Object	Yes	The graph to analyze with the selected algorithm. All endpoints share the same `Graph` type, so that you can create the payload once and use it across all endpoints.
graph.type	ENUM	Yes	Graph type: `directed` - edges have an direction from vertex A to vertex B that the algorithm must follow. `undirected` - edges do not have a direction. Allowed values: `directed`, `undirected`.
graph.edges	Object Array	Yes	List of weighted edges between graph vertices, without duplicates. For directed graphs the order of vertices matters, A->B and B->A count as separate edges.
graph.edges[].f	String	Yes	One of the two vertex IDs connected with an edge. For directed graphs: the starting vertex `from`. Must match the pattern `^[a-zA-Z0-9_:-]{1,40}$`.
graph.edges[].t	String	Yes	One of the two vertex IDs connected with an edge. For directed graphs: the ending vertex `to`. Must match the pattern `^[a-zA-Z0-9_:-]{1,40}$`.
graph.edges[].weight	Integer	No	Edge weight (unused in this algorithm). Default: `1`. Range: `0 - 2^40`.
graph.vertices	Object Array	Yes	List of up to 1000 vertices comprising the graph.
graph.vertices[].id	String	Yes	Unique ID (1-40 characters, letters, digits, underscores, colons, hyphens). Must match the pattern `^[a-zA-Z0-9_:-]{1,40}$`.

Response

Returns a JSON object with a start string field and a visited string array field. start is the starting vertex ID used for the traversal, and visited lists the vertex IDs in breadth-first visit order.

Parameter	Type	Mandatory	Description
start	String	Yes	Starting vertex ID returned by the traversal.
visited	String Array	Yes	Vertex IDs visited by breadth-first search, in traversal order.

▣ ENDPOINT 02 / 06

POST

Depth-first search traversal through all vertices in a graph.

https://api.eu.apyhub.com/modernsoftware-pro/run-graph-algorithms/depth-first-search

QUICKSTART

GUIDE

Quickstart

Run a depth-first search starting from the start vertex on the graph you send in the JSON body.

curl -X POST "https://api.eu.apyhub.com/modernsoftware-pro/run-graph-algorithms/depth-first-search?start=A" \
  -H "apy-token: $APY_TOKEN" \
  -H "Content-Type: application/json" \
  -d '{"graph":{"type":"directed","vertices":[{"id":"A"},{"id":"B"},{"id":"C"}],"edges":[{"f":"A","t":"B"},{"f":"B","t":"C"}]}}'

What you'll get back

Returns a JSON object with a start string and a visited array of strings. start echoes the starting vertex, and visited lists the vertices reached by the depth-first search.

{
  "start": "A",
  "visited": ["A", "B", "C"]
}

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API key

Loading your default key…

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About this endpoint

What it does

Performs a depth-first search traversal on the provided graph, starting from the vertex specified by start, and returns the traversal order.

Query Parameter(s)

Attribute	Type	Mandatory	Description
start	String	Yes	Start vertex ID. Pattern: `^[a-zA-Z0-9_:-]{1,40}$`.

Request Body

Parameter	Type	Mandatory	Description
graph	Object	Yes	The graph to analyze. Includes `type`, `vertices`, and `edges`.
graph.type	ENUM	Yes	Graph type: `directed`, `undirected`.
graph.vertices	Object Array	Yes	List of up to 1000 vertices comprising the graph. Each item has an `id`.
graph.vertices[].id	String	Yes	Unique vertex ID, 1-40 characters. Pattern: `^[a-zA-Z0-9_:-]{1,40}$`.
graph.edges	Object Array	Yes	List of weighted edges between graph vertices, without duplicates.
graph.edges[].f	String	Yes	One of the two vertex IDs connected with an edge. For directed graphs: the starting vertex (`from`). Pattern: `^[a-zA-Z0-9_:-]{1,40}$`.
graph.edges[].t	String	Yes	One of the two vertex IDs connected with an edge. For directed graphs: the ending vertex (`to`). Pattern: `^[a-zA-Z0-9_:-]{1,40}$`.
graph.edges[].weight	Integer	No	Edge weight. Default: `1`. Range: `0 - 2^40`. Unused in this algorithm.

Response

Returns a JSON object with a start string field and a visited array of strings field. start identifies the starting vertex used for the traversal, and visited contains the traversal order.

Parameter	Type	Mandatory	Description
start	String	Yes	Start vertex ID returned by the service.
visited	String Array	Yes	Vertex IDs in the order they were visited during depth-first search.

▣ ENDPOINT 03 / 06

POST

Topological sort of the vertices in a directed, acyclic graph.

https://api.eu.apyhub.com/modernsoftware-pro/run-graph-algorithms/topological-sort

QUICKSTART

GUIDE

Quickstart

This example sorts a small directed graph topologically.

curl -X POST "https://api.eu.apyhub.com/modernsoftware-pro/run-graph-algorithms/topological-sort" \
  -H "apy-token: $APY_TOKEN" \
  -H "Content-Type: application/json" \
  -d '{"graph":{"type":"directed","vertices":[{"id":"A"},{"id":"B"},{"id":"C"}],"edges":[{"f":"A","t":"B"},{"f":"B","t":"C"}]}}'

What you'll get back

Returns a JSON object with an order array of strings — the topological ordering of the graph's vertex IDs.

{
  "order": ["A", "B", "C"]
}

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API key

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About this endpoint

What it does

Returns a topological ordering of the vertices in a directed graph. You send the graph definition in the request body, and the response contains an order array of vertex IDs.

Request Body

Parameter	Type	Mandatory	Description
graph	Object	Yes	The graph to analyze. This endpoint works only on `directed` graphs.
graph.type	ENUM	Yes	Graph type. Allowed value: `directed`.
graph.vertices	Object Array	Yes	List of up to 1000 vertices comprising the graph. Each item has an `id` string matching `^[a-zA-Z0-9_:-]{1,40}$`.
graph.vertices[].id	String	Yes	Unique vertex ID, 1-40 characters. Pattern: `^[a-zA-Z0-9_:-]{1,40}$`.
graph.edges	Object Array	Yes	List of weighted edges between graph vertices, without duplicates. Edge direction matters, so `A -> B` and `B -> A` are separate edges.
graph.edges[].f	String	Yes	Starting vertex of the directed edge. Pattern: `^[a-zA-Z0-9_:-]{1,40}$`.
graph.edges[].t	String	Yes	Ending vertex of the directed edge. Pattern: `^[a-zA-Z0-9_:-]{1,40}$`.
graph.edges[].weight	Integer	No	Edge weight. Default: `1`. Range: `0 - 2^40`. Unused in this algorithm.

Response

Returns a JSON object with an order string array field containing the topological ordering of the vertices.

Parameter	Type	Mandatory	Description
order	String Array	Yes	Topological ordering of the graph's vertices.

▣ ENDPOINT 04 / 06

POST

Finds the shortest path between vertices in a directed graph.

https://api.eu.apyhub.com/modernsoftware-pro/run-graph-algorithms/shortest-path

QUICKSTART

GUIDE

Quickstart

Find the shortest path from one start vertex to another in a directed graph.

curl -X POST "https://api.eu.apyhub.com/modernsoftware-pro/run-graph-algorithms/shortest-path?start=vertex_a&end=vertex_b" \
  -H "apy-token: $APY_TOKEN" \
  -H "Content-Type: application/json" \
  -d '{
    "graph": {
      "type": "directed",
      "vertices": [
        { "id": "vertex_a" },
        { "id": "vertex_b" },
        { "id": "vertex_c" }
      ],
      "edges": [
        { "f": "vertex_a", "t": "vertex_c", "weight": 2 },
        { "f": "vertex_c", "t": "vertex_b", "weight": 3 }
      ]
    }
  }'

What you'll get back

Returns a JSON object in one of two shapes. For a single destination, it includes start, end, reachable as a boolean, distance as an integer or null, and path as an array of vertex IDs or null.

{
  "start": "vertex_a",
  "end": "vertex_b",
  "reachable": true,
  "distance": 5,
  "path": ["vertex_a", "vertex_c", "vertex_b"]
}

If no end is provided, it returns a JSON object with start and a paths object mapping each reachable vertex ID to an object containing distance and path.

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API key

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About this endpoint

What it does

Finds the shortest path in a directed graph from the start vertex, using the graph provided in the request body. If the end query parameter is supplied, the response describes the shortest path to that specific vertex; otherwise, the response returns shortest-path results from the start vertex to all reachable vertices.

Query Parameter(s)

Attribute	Type	Mandatory	Description
end	String	No	End vertex ID. Pattern: `^[a-zA-Z0-9_:-]{1,40}$`. If provided, the algorithm finds the shortest path only to that vertex.
start	String	Yes	Start vertex ID. Pattern: `^[a-zA-Z0-9_:-]{1,40}$`.

Request Body

Parameter	Type	Mandatory	Description
graph	Object	Yes	The graph to analyze. Required fields: `type`, `vertices`, `edges`.
graph.type	ENUM	Yes	Graph type. Allowed value: `directed`.
graph.edges	Object Array	Yes	List of weighted edges between graph vertices, without duplicates. For directed graphs, vertex order matters (`A -> B` and `B -> A` are separate edges).
graph.edges[].f	String	Yes	Starting vertex ID of the directed edge. Pattern: `^[a-zA-Z0-9_:-]{1,40}$`.
graph.edges[].t	String	Yes	Ending vertex ID of the directed edge. Pattern: `^[a-zA-Z0-9_:-]{1,40}$`.
graph.edges[].weight	Integer	No	Edge weight, the cost of following the edge. Default: `1`. Range: `0 - 2^40`
graph.vertices	Object Array	Yes	List of up to 1000 vertices comprising the graph.
graph.vertices[].id	String	Yes	Unique vertex ID. Pattern: `^[a-zA-Z0-9_:-]{1,40}$` (1-40 characters; letters, digits, underscores, colons, hyphens).

Response

Returns a JSON object. The response shape depends on whether end is supplied: either an object with start, end, reachable, distance, and path, or an object with start and paths.

Parameter	Type	Mandatory	Description
start	String	Yes	Start vertex ID.
end	String	Yes	End vertex ID. Present in the single-target response shape.
reachable	Boolean	Yes	Whether the `end` vertex is reachable from `start`. Present in the single-target response shape.
distance	Integer	Yes	Shortest-path distance. Nullable in the single-target response shape. In the multi-target response, each entry under `paths` includes a non-null integer distance.
path	String Array	Yes	Shortest path as an array of vertex IDs. Nullable in the single-target response shape. In the multi-target response, each entry under `paths` includes a path array.
paths	Object	Yes	Map of target vertex IDs to shortest-path results. Each value contains `distance` and `path`.

▣ ENDPOINT 05 / 06

POST

Finds the minimum spanning tree covering all vertices in a graph.

https://api.eu.apyhub.com/modernsoftware-pro/run-graph-algorithms/minimum-spanning-tree

QUICKSTART

GUIDE

Quickstart

Find a minimum spanning tree for a simple weighted graph.

curl -X POST "https://api.eu.apyhub.com/modernsoftware-pro/run-graph-algorithms/minimum-spanning-tree" \
  -H "apy-token: $APY_TOKEN" \
  -H "Content-Type: application/json" \
  -d '{
    "graph": {
      "type": "undirected",
      "vertices": [
        { "id": "A" },
        { "id": "B" },
        { "id": "C" }
      ],
      "edges": [
        { "f": "A", "t": "B", "weight": 1 },
        { "f": "C", "t": "B", "weight": 2 },
        { "f": "A", "t": "C", "weight": 3 }
      ]
    }
  }'

What you'll get back

Returns a JSON object with an edges array and a totalWeight integer. edges contains the selected tree edges, each with f, t, and optionally weight; totalWeight is the sum of the chosen edge weights.

{
  "edges": [
    { "f": "A", "t": "B", "weight": 1 },
    { "f": "C", "t": "B", "weight": 2 }
  ],
  "totalWeight": 3
}

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API key

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Request body

About this endpoint

What it does

Finds the minimum spanning tree for the graph you provide and returns the selected tree edges together with their combined weight.

Request Body

Parameter	Type	Mandatory	Description
graph	Object	Yes	The graph to analyze. Include the graph `type`, `vertices`, and `edges`.
graph.type	ENUM	Yes	Graph type. Allowed values: `directed`, `undirected`.
graph.vertices	Object Array	Yes	List of up to 1000 vertices comprising the graph.
graph.vertices[].id	String	Yes	Unique vertex ID, 1-40 characters. Allowed characters: letters, digits, underscores, colons, hyphens.
graph.edges	Object Array	Yes	List of weighted edges between graph vertices, without duplicates. For directed graphs, edge direction matters.
graph.edges[].f	String	Yes	One of the two vertex IDs connected by the edge. For directed graphs, this is the starting vertex (`from`). Format: 1-40 characters; letters, digits, underscores, colons, hyphens.
graph.edges[].t	String	Yes	One of the two vertex IDs connected by the edge. For directed graphs, this is the ending vertex (`to`). Format: 1-40 characters; letters, digits, underscores, colons, hyphens.
graph.edges[].weight	Integer	No	Edge weight / cost. Default: `1`. Minimum: `0`.

Response

Returns a JSON object with two required fields: edges is an array of edge objects, and totalWeight is an integer. The edges array contains the edges selected for the minimum spanning tree, and totalWeight is their combined weight.

Parameter	Type	Mandatory	Description
edges	Object Array	Yes	The edges included in the minimum spanning tree. Each item contains `f` and `t`, and may include `weight`.
edges[].f	String	Yes	First vertex ID for the returned edge.
edges[].t	String	Yes	Second vertex ID for the returned edge.
edges[].weight	Integer	No	Edge weight. Default: `1`. Range: `0 - 2^40`
totalWeight	Integer	Yes	Total weight of the returned minimum spanning tree.

Notes

If you send a directed graph to this API:

The algorithm treats it as it were an undirected graph.
In case there are two directed edges A->B and B->A with different weights, the algorithm uses the edge with the lower weight. If the weights are equal, it takes the first of the edges defined in the input JSON.

The output JSON preserves the order of vertices in the edge definitions: if you define your undirected edge as B-A, and the edge is a part of the minimum spanning tree, it is listed in the output json as B-A, not as A-B.

The input graph must be connected.

▣ ENDPOINT 06 / 06

POST

Computes the distance matrix between all pairs of vertices in a graph.

https://api.eu.apyhub.com/modernsoftware-pro/run-graph-algorithms/distance-matrix

QUICKSTART

GUIDE

Quickstart

Send a graph in the request body to calculate its distance matrix.

curl -X POST "https://api.eu.apyhub.com/modernsoftware-pro/run-graph-algorithms/distance-matrix" \
  -H "apy-token: $APY_TOKEN" \
  -H "Content-Type: application/json" \
  -d '{"graph":{"type":"directed","vertices":[{"id":"A"},{"id":"B"}],"edges":[{"f":"A","t":"B","weight":1}]}}'

What you'll get back

Returns a JSON object with either a distance-matrix-asymmetric object or a distance-matrix-symmetric object. Each of those is an object whose keys are vertex IDs and whose values are arrays of integers representing distances.

{
  "distance-matrix-asymmetric": {
    "A": [0, 1],
    "B": [-1, 0]
  }
}

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API key

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Request body

About this endpoint

What it does

Computes the distance matrix for the graph provided in the request body. The response returns a JSON object containing one of:

distance-matrix-symmetric for undirected graphs (with the lower triangle of the distance matrix).
distance-matrix-asymmetric for directed graphs

Request Body

Parameter	Type	Mandatory	Description
graph	Object	Yes	The graph to analyze. Contains the graph `type`, `vertices`, and `edges`.
graph.type	ENUM	Yes	Graph type. Allowed values: `directed`, `undirected`.
graph.vertices	Object Array	Yes	List of graph vertices, up to 384 vertices for directed graphs or 512 vertices for undirected graphs.
graph.vertices[].id	String	Yes	Unique vertex ID. Format: 1-40 characters; letters, digits, underscores, colons, and hyphens (`^[a-zA-Z0-9_:-]{1,40}$`).
graph.edges	Object Array	Yes	List of weighted edges between graph vertices, without duplicates. For directed graphs, edge order matters (`A -> B` and `B -> A` are separate edges).
graph.edges[].f	String	Yes	One endpoint of the edge. For directed graphs, this is the starting vertex (`from`). Format: 1-40 characters; letters, digits, underscores, colons, and hyphens (`^[a-zA-Z0-9_:-]{1,40}$`).
graph.edges[].t	String	Yes	One endpoint of the edge. For directed graphs, this is the ending vertex (`to`). Format: 1-40 characters; letters, digits, underscores, colons, and hyphens (`^[a-zA-Z0-9_:-]{1,40}$`).
graph.edges[].weight	Integer	No	Edge weight, or cost of following the edge. Default: `1`. Range: `0 - 2^40`

Response

Returns a JSON object with one of two possible top-level fields: either distance-matrix-asymmetric (for directed graphs) or distance-matrix-symmetric (for undirected graphs), both of which are objects whose values are arrays of integers. The asymmetric form is used when distances from A to B may differ from B to A; the symmetric form is used when those distances are always the same.

Parameter	Type	Mandatory	Description
distance-matrix-asymmetric	Object	No	Calculated distance matrix where distances A -> B and B -> A may vary. The object's properties are additional keys that represent vertex ID-s, whose values are integer arrays: the distances to all points (see detailed notes below).
distance-matrix-symmetric	Object	No	Calculated lower triangle of the distance matrix (below the diagonal) where distances A -> B and B -> A are always the same. The object's properties are additional keys that represent vertex ID-s, whose values are integer arrays: the distances to previous vertices in the matrix (see detailed notes below).

Notes

If the given two vertices are unreachable from each other, the returned distance for them is -1.
If there is an integer overflow during calculations, the API returns 422 Unprocessable Entity error.
Structure of distance-matrix-asymmetric object:
- Each key is the ID of a single vertex from the input graph. The order of vertices in the object matters (see below).
- The value for each key is an array of integers: distances too all points:
  - For the graph of N vertices, each array will have exactly N integers.
  - For I-th vertex, the I-th integer of an array is always 0: this is the distance from the given vertex to itself, on the diagonal.
  - The J-th integer corresponds to the J-th vertex from distance-matrix-asymmetric object.
Structure of distance-matrix-symmetric object:
- Each key is the ID of a single vertex from the input graph. The order of vertices in the object matters (see below).
- The value for each key is an array of integers: distances too all previous vertices:
  - For I-th vertex, the size of the integer array is always I-1 (the first vertex in distance-matrix-symmetric object always has the array of size 0).
  - The J-th integer corresponds to the J-th vertex in distance-matrix-symmetric object.
  - Effectively, the structure describes the lower triangle of the full distance matrix (below the diagonal). The API takes advantage of the fact that distances A->B and B->A are always the same in order to reduce the output JSON size approximately 2 times compared to returning the full distance matrix.

▣ COMMON ERRORS

Errors any endpoint can return

400bad_request

Required parameter missing or malformed body.

401unauthorized

API key missing, revoked, or not authorized for this service.

429rate_limited

Your plan's per-second rate exceeded. Retry with exponential backoff.

503upstream_busy

Backend temporarily unavailable. Try again in a few seconds.

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