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 The theory of graphs is the study of graphs in mathematics which are mathematical structures used to model pairly relationships between objects. In this context a graph consists of vertices (also known as nodes or points) which are connected by edges (also known as links or lines). A distinction is developed between undirected graphs, where edges symmetrically connect two vertices, and directed graphs, where edges asymmetrically join two vertices; see Graph (discrete mathematics) for more comprehensive descriptions and other differences in the forms of graphs generally considered. Graphs are among the prime study objects in discrete mathematics. Graphs can be used to model many types of relationships and processes in physical , biological and social systems, and information. The graphs will describe several functional problems. Highlighting their application to real-world systems, the word network is often described as a graph in which attributes (e.g. names) are connected with the vertices and edges, and the topic that communicates and understands the real-world systems as a network is called network science. Graph-theoretical methods have proved especially useful in linguistics in various forms, since natural language often lends itself well to discrete structure. Modeled of a hierarchical graph, Compositional semantics and Syntax   traditionally follow tree-based structures, whose expressive power lies in the principle of compositionality.  

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