Function Repository Resource:

HypergraphNeighborhoodVolumes

Find the volumes of successively larger neighborhoods around nodes in a hypergraph

Contributed by: Stephen Wolfram

ResourceFunction["HypergraphNeighborhoodVolumes"][graph]

finds the count of neighbors within successive distances for each vertex in graph.

ResourceFunction["HypergraphNeighborhoodVolumes"][graph,{v₁,v₂,…}]

finds the counts for the vertices v_i.

ResourceFunction["HypergraphNeighborhoodVolumes"][graph,All,r]

finds counts from all vertices out to maximum radius r.

ResourceFunction["HypergraphNeighborhoodVolumes"][graph,{v₁,v₂,…},Automatic]

finds counts only out to the minimum radius for any of the vertices v_i.

ResourceFunction["HypergraphNeighborhoodVolumes"][graph,"Random"→n,…]

finds counts for n randomly chosen vertices.

Details and Options

The hypergraph is assumed to be undirected.

ResourceFunction["HypergraphNeighborhoodVolumes"] uses ParallelMap.

The first element in each list is the zero-radius volume, followed by the distance one-radius volume, and so on.

The volume of the neighborhood of vertex v at radius r is the number of vertices connected to v within a distance of r hyperedges.

Neighbor counts for each vertex of a hypergraph:

In[1]:=

Out[1]=

Count neighbors for each vertex:

In[2]:=

Out[2]=

Count neighbors for a subset of vertices:

In[3]:=

Out[3]=

Count neighbors for a random sampling of vertices:

In[4]:=

Out[4]=