Graph Modifications (2) 

We can combine graphs with the "Star", "Path", and "Cycle" graphs:

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We can split vertices using VertexCleaving:

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Structured Graphs (1) 

We can generate various types of graphs:

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Basic and Structural Properties (1) 

We can determine whether a graph possesses specific characteristics or belongs to a particular category:

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Graph Isomorphism (1) 

We can identify all the non-isomorphic components of a graph:

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Connectivity (1) 

We can count the different connected components in a graph:

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Graph Values (1) 

We can create the degree histogram and identify different adjacency values and graph weights in a graph:

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Isolates and Self-loops (1) 

We can identify and count the isolates and self-loops in a graph:

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Connectivity (2) 

We can identify non-neighbors and common neighbors:

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We can examine the edge and vertex boundaries of a graph:

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Graph Search (2) 

We can determine the ancestors, descendants, and predecessors of a graph:

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We can determine the depth-first search and breadth-first search order of the graph:

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Cliques and Covers (2) 

We can identify the clique number and the number of cliques within a graph:

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We can identify the Steiner tree, the girth and the asteroidal triple within the graph:

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