SUBGRAPHS Meaning and
Definition
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Subgraphs refer to smaller, self-contained sections of a larger graph. A graph is a mathematical structure consisting of a set of vertices or nodes, connected by edges or arcs. In this context, subgraphs are subsets of these vertices and edges that form a smaller, isolated graph within the larger one.
A subgraph must maintain the same structure and properties as the original graph. It contains a subset of its vertices and edges, while preserving the relationships and connectivity between these elements. All edges between the vertices within the subgraph must also be present in the larger graph.
Subgraphs can be used to analyze specific sections of a graph, simplifying complex networks and allowing researchers to focus on particular interactions or patterns. They are often employed in fields like computer science, physics, and social network analysis to understand the behavior, characteristics, or properties of a graph or network.
Subgraphs can vary in size, from containing only a few nodes to encompassing a significant portion of the original graph. They can also be disconnected or connected, depending on the relationships between the subset of vertices.
In summary, subgraphs are smaller, self-contained sections of a large graph that maintain the same structure and connectivity as the original. They are used to analyze specific portions of a graph and simplify its complexity by allowing researchers to focus on selected vertices and connections.
Etymology of SUBGRAPHS
The word "subgraphs" is derived from the combination of two terms: "sub-" and "graphs".
1. "Sub-" is a prefix that comes from the Latin word "sub", meaning "under" or "below". It is commonly used to indicate something that is smaller in size or lower in rank or position than something else. In the context of graphs, "sub-" signifies a smaller or more specific part or portion of a graph.
2. "Graphs" refers to a mathematical concept that represents a collection of interconnected objects or entities. In mathematical graph theory, a graph consists of a set of vertices (also called nodes) and a set of edges (also called arcs or links) that connect these vertices. The study of graphs includes various properties, structures, and algorithms related to their analysis and representation.
