![]() The directed graph above has the following degrees, indegrees, and outdegrees: Vertex ID The indegree of a vertex and the sum of tail endpoints count toward the outdegree of a vertex. Recall that any directed edge has two distinct ends: a head (the end with an arrowhead) and a tail. In a directed graph it is important to distinguish between indegree and outdegree. In a directed graph, we define degree exactly the same as above (and note that "adjacent" does not imply any direction or lack of direction). The following is a vertex degree table of the graph above. We can equivalentlyĭefine the degree of a vertex as the cardinality of its neighborhood and say that for any vertex v, deg(v) = |N(v)|. The degree of a vertex v is denoted deg(v). ![]() The degree of a vertex is the total number of vertices adjacent to the vertex. Example: The picture above represents the following graph: In other words, each element of E is a pair of elements of V. More formally, we define a graph G as an ordered pair G = (V, E) where ![]() Each edge in a graph joins two distinct nodes. Corresponding to the connections (or lack thereof) in a network are edges (or links) in a graph. A graph is a formal mathematical representation of a network ("a collection of objects connected in some fashion").Įach object in a graph is called a node (or vertex). ![]()
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