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Influence graphs model whether certain people can influence the behavior of others.Finally, collaboration graphs model whether two people work together in a particular way, such as acting in a movie together.More contemporary approaches such as model the syntax of natural language using , which are . finite-state morphology, using ) are common in the analysis of language as a graph.Within , especially as applied to computers, modeling word meaning is easier when a given word is understood in terms of related words; are therefore important in . Indeed, the usefulness of this area of mathematics to linguistics has borne organizations such as , as well as various ' Net' projects, such as , , and others.A graph in this context is made up of , nodes, or points which are connected by edges, arcs, or lines.A graph may be undirected, meaning that there is no distinction between the two vertices associated with each edge, or its edges may be from one vertex to another; see for more detailed definitions and for other variations in the types of graph that are commonly considered. Refer to the for basic definitions in graph theory.The vertices belonging to an edge are called the ends or end vertices of the edge.A vertex may exist in a graph and not belong to an edge.

Traditionally, and compositional semantics follow tree-based structures, whose expressive power lies in the , modeled in a hierarchical graph.

A similar approach can be taken to problems in social media, travel, biology, computer chip design, and many other fields.

The development of to handle graphs is therefore of major interest in computer science. Complementary to systems focusing on rule-based in-memory manipulation of graphs are geared towards -safe, storing and querying of .

In , graphs can represent local connections between interacting parts of a system, as well as the dynamics of a physical process on such systems.

Similarly, in graphs can be used to represent functional connections between brain areas that interact to give rise to various cognitive processes, where the vertices represent different areas of the brain and the edges represent the connections between those areas.To avoid ambiguity, this type of graph may be described precisely as and .Other senses of graph stem from different conceptions of the edge set.Graphs are also used to represent the micro-scale channels of , in which the vertices represent the pores and the edges represent the smaller channels connecting the pores.

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