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Graphs in functional programming can model real-world situations by representing relationships between entities and tracking changes over time.

In functional programming, a graph is a data structure that consists of nodes and edges. Nodes represent entities, and edges represent relationships between these entities. This structure is particularly useful in modelling real-world situations where relationships between entities are complex and non-linear. For example, in a social network, each person can be represented as a node, and the relationships between people can be represented as edges. This allows us to model complex relationships and interactions in a clear and structured way.

Moreover, graphs can be used to track changes over time. Each node can have a state, and this state can change over time. For example, in a traffic simulation, each node could represent a junction, and the state of the node could represent the number of cars at the junction. The edges could represent roads, and the state of the edge could represent the number of cars on the road. By updating the states of the nodes and edges over time, we can simulate the flow of traffic.

In functional programming, graphs are often represented using adjacency lists or adjacency matrices. These data structures allow us to efficiently perform operations such as finding all the neighbours of a node, checking whether two nodes are connected, and finding the shortest path between two nodes. These operations are fundamental to many real-world applications, such as route planning in a navigation system.

Furthermore, functional programming languages often provide powerful abstractions for working with graphs. For example, in Haskell, we can use the 'Graph' type to represent a graph, and we can use functions such as 'neighbors' and 'shortestPath' to manipulate the graph. These abstractions make it easier to write code that models real-world situations.

In conclusion, graphs are a powerful tool in functional programming for modelling real-world situations. They allow us to represent complex relationships between entities, track changes over time, and perform operations that are fundamental to many real-world applications.

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