COMPLETE GRAPH Meaning and
Definition
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A complete graph refers to a mathematical concept in the field of graph theory. It is defined as a graph in which every pair of distinct vertices is connected by an edge. In simpler terms, a complete graph is a graph where every node is directly connected to every other node in the graph.
A complete graph with n vertices is denoted by the symbol Kn. This implies that there are n nodes in the graph, and each of these nodes has an edge connecting it to every other node. A complete graph is considered a special case of a simple graph, where there are no self-loops or parallel edges.
The key characteristic of a complete graph is that it is maximally connected. Every vertex has a direct connection to all other vertices, making it fully interconnected. The number of edges in a complete graph can be calculated using the formula E = n(n−1)/2, where n represents the number of vertices.
Complete graphs find applications in various fields, including computer science, network theory, and social network analysis. Due to their complete connectivity, they are often used to model scenarios where every pair of elements in a system must be connected or taken into consideration. Additionally, complete graphs form a foundational construct in the study of graph theory and serve as an important reference in understanding the properties and characteristics of other graph structures.
Common Misspellings for COMPLETE GRAPH
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Etymology of COMPLETE GRAPH
The word "complete graph" has its etymology rooted in mathematics.
The term "complete" is derived from the Latin word "completus", which means "filled up" or "finished". In mathematics, "complete" refers to a structure or set that contains all possible elements or connections.
The term "graph" in this context refers to a collection of vertices (also known as nodes) connected by edges (also known as links or arcs).
Therefore, a "complete graph" signifies a graph in which every pair of vertices is connected by an edge. In other words, it is a fully connected graph where each vertex is directly connected to every other vertex in the set.
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