Vertex (graph theory)

As a node or edge is called in graph theory an element of the node set of a graph. Is the graph, its vertex set is commonly referred to with (english vertex ). Graphs exist with the node set or from an associated set of edges (English edge), which describes how the individual nodes of the graph are connected by edges.

Special nodes

• A universal node is a node that is adjazent to all other nodes in the graph.
• A simplicial node is a node that forms together with all its neighbors a clique, ie, a complete subgraph of the initial graph.
• An isolated node is a node in an undirected graph with no neighbors, so a node of degree zero. In a directed graph an isolated node has no predecessors and successors, and thus has input and out-degree zero.