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The maximum degree of a graph is denoted by (), and is the maximum of 's vertices' degrees. The minimum degree of a graph is denoted by (), and is the minimum of 's vertices' degrees. In the multigraph shown on the right, the maximum degree is 5 and the minimum degree is 0. In a regular graph, every vertex has the same degree, and so we can ...
The degree of a node in a network (sometimes referred to incorrectly as the connectivity) is the number of connections or edges the node has to other nodes. If a network is directed, meaning that edges point in one direction from one node to another node, then nodes have two different degrees, the in-degree, which is the number of incoming edges, and the out-degree, which is the number of ...
Child: A child node is a node extending from another node. For example, a computer with internet access could be considered a child node of a node representing the internet. The inverse relationship is that of a parent node. If node C is a child of node A, then A is the parent node of C. Degree: the degree of a node is the number of children of ...
It exactly preserves the degree sequence of a given graph by assigning stubs (half-edges) to nodes based on their degrees and then randomly pairing the stubs to form edges. The preservation of the degree sequence is exact in the sense that all realizations of the model result in graphs with the same predefined degree distribution.
k-degenerate graphs have also been called k-inductive graphs. degree 1. The degree of a vertex in a graph is its number of incident edges. [2] The degree of a graph G (or its maximum degree) is the maximum of the degrees of its vertices, often denoted Δ(G); the minimum degree of G is the minimum of its vertex degrees, often denoted δ(G).
A node graph in the context of software architecture refers to an organization of software functionality into atomic units known as nodes, and where nodes can be connected to each other via links. The manipulation of nodes and links in the node graph can be often be accomplished through a programmable API or through a visual interface by using ...
Another important characteristic of scale-free networks is the clustering coefficient distribution, which decreases as the node degree increases. This distribution also follows a power law. This implies that the low-degree nodes belong to very dense sub-graphs and those sub-graphs are connected to each other through hubs.
Note that an edge is the only graphlet with two nodes. GDDs generalize the degree distribution to other graphlets: they measure for each 2-5-node graphlet G i, =,,...,, such as a triangle or a square, the number of nodes "touching" k graphlets G i at a particular node. A node at which a graphlet is "touched" is topologically relevant, since it ...