Advanced Search via API

The /search endpoint supports comprehensive filtering by all graph properties. Combine multiple parameters to find exactly the graphs you need.

All endpoints return JSON by default. Use Accept: text/html header or access via browser for HTML responses.

Basic Filters

n, n_min, n_max

Filter by number of vertices (exact or range)

m, m_min, m_max

Filter by number of edges (exact or range)

min_degree, max_degree

Filter by minimum or maximum degree

Examples:

/search?n=7                    # All 7-vertex graphs
/search?n_min=6&n_max=8        # Graphs with 6, 7, or 8 vertices
/search?n=6&m_min=10           # 6-vertex graphs with at least 10 edges

Structural Properties

diameter, diameter_min, diameter_max

Filter by graph diameter

radius, radius_min, radius_max

Filter by graph radius

girth, girth_min, girth_max

Filter by girth (shortest cycle length)

triangle_count, triangle_count_min, triangle_count_max

Filter by number of triangles

Examples:

/search?n=8&diameter=2                      # 8-vertex graphs with diameter 2
/search?n=7&girth_min=4                     # 7-vertex graphs with girth ≥ 4
/search?n=6&radius_min=2&radius_max=3      # 6-vertex graphs with radius 2 or 3

Tags

tags

Filter by named graph types (complete, cycle, path, star, wheel, petersen, etc.)

tag_mode

Use OR (default) to match ANY tag, or AND to match ALL tags

Available tags: bipartite, complete, complete-bipartite, complete-multipartite, cubic, cycle, eulerian, fan, ladder, line-graph, path, petersen, planar, prism, regular, star, strongly-regular, tree, triangle-free, vertex-transitive, wheel, windmill

Examples:

/search?tags=complete                           # All complete graphs
/search?tags=bipartite&tags=planar&tag_mode=OR  # Graphs that are bipartite OR planar
/search?tags=bipartite&tags=planar&tag_mode=AND # Graphs that are bipartite AND planar

Cospectral Mates

has_cospectral_mate

Filter by cospectrality. Values: adj, kirchhoff, signless, lap, nb, nbl, dist, or none

Examples:

/search?n=8&has_cospectral_mate=adj        # 8-vertex graphs with adjacency cospectral mates
/search?n=7&has_cospectral_mate=kirchhoff  # 7-vertex graphs with Kirchhoff cospectral mates
/search?n=6&has_cospectral_mate=none       # 6-vertex graphs with NO cospectral mates

Switching Mechanisms

has_mechanism

Filter by known switching mechanisms. Values: gm (Godsil-McKay), any, or none

Examples:

/search?n=8&has_mechanism=gm    # Graphs with GM switching mechanisms
/search?n=8&has_mechanism=any   # Graphs with any known mechanism
/search?n=8&has_mechanism=none  # Graphs with no known mechanism

Pagination

limit

Number of results per page (default: 100, max: 1000)

offset

Number of results to skip

Examples:

/search?n=7&limit=50                  # First 50 results
/search?n=7&limit=50&offset=50       # Results 51-100

Complex Queries

Combine multiple filters for sophisticated searches:

# 8-vertex bipartite planar graphs with diameter ≤ 3 and adjacency cospectral mates
/search?n=8&tags=bipartite&tags=planar&tag_mode=AND&diameter_max=3&has_cospectral_mate=adj

# 7-vertex regular graphs with girth ≥ 4 and no cospectral mates
/search?n=7&tags=regular&girth_min=4&has_cospectral_mate=none

# Cubic graphs (3-regular) with 8 vertices and exactly 1 triangle
/search?n=8&tags=cubic&triangle_count=1

Other Endpoints