In graph theory, extensions and generalizations of graphs refer to various constructs and modifications of standard graph representations, allowing for additional features or alternative interpretations. Here are some common concepts related to extensions and generalizations of graphs: ### Extensions of Graphs 1. **Subgraphs**: A subgraph is formed by a subset of the vertices and edges of a graph. It retains some or all of the connections present in the original graph.
Graph databases are a type of database specifically designed to represent and store data in the form of graphs, which consist of nodes (entities) and edges (relationships). This model excels in scenarios where relationships and connections between data points are crucial and often complex. ### Key Characteristics of Graph Databases: 1. **Nodes and Edges**: - **Nodes**: Represent entities or objects, such as people, places, products, etc.
Category theory is a branch of mathematics that focuses on the abstract study of mathematical structures and relationships between them. It provides a unifying framework to understand various mathematical concepts across different fields by focusing on the relationships (morphisms) between objects rather than the objects themselves. Here are some key concepts in category theory: 1. **Categories**: A category consists of objects and morphisms (arrows) that map between these objects. Each morphism has a source object and a target object.