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A graph with 6 vertices and 7 edges where the vertex number 6 on the far-left is a leaf vertex or a pendant vertex. In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph ...
The degree or valency of a vertex is the number of edges that are incident to it, where a loop is counted twice. The degree of a graph is the maximum of the degrees of its vertices. In an undirected simple graph of order n, the maximum degree of each vertex is n − 1 and the maximum size of the graph is n(n − 1) / 2 .
Specifically, a small-world network is defined to be a graph where the typical distance L between two randomly chosen nodes (the number of steps required) grows proportionally to the logarithm of the number of nodes N in the network [14] snark A snark is a simple, connected, bridgeless cubic graph with chromatic index equal to 4. source
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
V a set of vertices or nodes, E a set of edges or lines, r : E → {{x,y} : x, y ∈ V}, assigning to each edge an unordered pair of endpoint nodes. Some authors allow multigraphs to have loops, that is, an edge that connects a vertex to itself, [2] while others call these pseudographs, reserving the term multigraph for the case with no loops. [3]
In this way, each node encodes an object and according to a fast heuristic, the tree is descended to the leaves which provide each object with more detail. When a leaf is reached, other methods could be used when higher detail is needed, such as Catmull 's recursive subdivision [2] .
An undirected graph. In graph theory an undirected graph has two kinds of incidence matrices: unoriented and oriented.. The unoriented incidence matrix (or simply incidence matrix) of an undirected graph is a matrix B, where n and m are the numbers of vertices and edges respectively, such that
In 2012, Bauer and colleagues reminded us that centrality indices only rank nodes but do not quantify the difference between them. [4] In 2013, Sikic and colleagues presented strong evidence that centrality indices considerably underestimate the power of non-hub nodes. [5] The reason is quite clear.