Vertices¶

Vertices (or nodes) are the fundamental elements of a graph, representing entities or points in your network.

Vertex Type¶

Each vertex has the following properties:

type(vertex_type) :: v
v%id           ! Unique identifier (integer)
v%degree       ! Number of connections (integer)
v%feature(:)   ! Feature vector (real32, allocatable)

Adding Vertices¶

Basic Addition¶

Add a vertex without features:

call graph%add_vertex()

This creates a vertex with no features and an automatically assigned ID.

With Features¶

Add a vertex with a feature vector:

! Add vertex with 3D features
call graph%add_vertex(feature=[1.0, 2.0, 3.0])

Important: The first vertex you add sets the feature dimension for all subsequent vertices. All vertices must have the same feature size:

call graph%add_vertex(feature=[1.0, 2.0])  ! Sets feature size to 2
call graph%add_vertex(feature=[3.0, 4.0])  ! OK - same size
call graph%add_vertex(feature=[5.0])        ! ERROR - wrong size

With Custom ID¶

Specify a custom identifier:

call graph%add_vertex(feature=[1.0, 2.0], id=100)

Batch Addition¶

For efficiency when adding many vertices, pre-allocate space:

! Allocate space for 1000 vertices with 10 features each
call graph%set_num_vertices(1000, num_vertex_features=10)

! Then populate vertex data
do i = 1, 1000
  graph%vertex(i)%feature = compute_features(i)
  graph%vertex(i)%id = i
end do

Accessing Vertices¶

By Index¶

Access vertices using array notation:

! Get vertex properties
write(*,*) 'ID:', graph%vertex(3)%id
write(*,*) 'Degree:', graph%vertex(3)%degree
write(*,*) 'Features:', graph%vertex(3)%feature

Iterating All Vertices¶

Loop through all vertices:

do i = 1, graph%num_vertices
  write(*,*) 'Vertex', i
  write(*,*) '  ID:', graph%vertex(i)%id
  write(*,*) '  Degree:', graph%vertex(i)%degree
  write(*,*) '  Features:', graph%vertex(i)%feature
end do

Modifying Vertices¶

Updating Features¶

Modify vertex feature vectors:

! Replace entire feature vector
graph%vertex(5)%feature = [10.0, 20.0, 30.0]

! Modify individual components
graph%vertex(5)%feature(2) = 25.0

Removing Vertices¶

Remove one or more vertices:

! Remove single vertex
call graph%remove_vertices([3])

! Remove multiple vertices
call graph%remove_vertices([2, 5, 7])

Important effects:

All edges connected to removed vertices are also removed
Remaining vertices are renumbered sequentially
The adjacency matrix is automatically updated

Vertex Degrees¶

The degree of a vertex is the number of edges connected to it:

Undirected graphs: Total number of connections
Directed graphs: Number of outgoing edges

Calculate degrees:

! Calculate for all vertices
call graph%calculate_degree()

! Access individual degrees
write(*,*) 'Vertex 1 has', graph%vertex(1)%degree, 'connections'

Vertex Features¶

Feature vectors can represent any numerical properties of vertices, such as:

Node attributes in a network
Coordinates in space
Embedding vectors
Physical properties

The feature size is determined by the first vertex added and applies to all vertices in the graph.