Data Structure(Terminologies of a graph)

 

Terminologies of Graphs in Data Structures:

Following are the basic terminologies of graphs in data structures:

• An edge is one of the two primary units used to form graphs. Each edge has two ends, which are vertices to which it is attached.
• If two vertices are endpoints of the same edge, they are adjacent.
• A vertex's outgoing edges are directed edges that point to the origin.
• A vertex's incoming edges are directed edges that point to the vertex's destination.
• The total number of edges occurring to a vertex in a graph is its degree.
• The out-degree of a vertex in a directed graph is the total number of outgoing edges, whereas the in-degree is the total number of incoming edges.
• A vertex with an in-degree of zero is referred to as a source vertex, while one with an out-degree of zero is known as sink vertex.
• An isolated vertex is a zero-degree vertex that is not an edge's endpoint.
• A path is a set of alternating vertices and edges, with each vertex connected by an edge.
• The path that starts and finishes at the same vertex is known as a cycle.
• A path with unique vertices is called a simple path.
• For each pair of vertices x, y, a graph is strongly connected if it contains a directed path from x to y and a directed path from y to x.
•  A directed graph is weakly connected if all of its directed edges are replaced with undirected edges, resulting in a connected graph. A weakly linked graph's vertices have at least one out-degree or in-degree.
• A tree is a connected forest. The primary form of the tree is called a rooted tree, which is a free tree.
• A spanning subgraph that is also a tree is known as a spanning tree.
• A connected component is the unconnected graph's most connected subgraph.
• A bridge, which is an edge of removal, would sever the graph.
• Forest is a graph without a cycle.