What is a small-world network?
A small-world network is a mathematical graph in which most nodes are not neighbors of one another, but the neighbors of any given node are likely to be neighbors of each other. Due to this, most neighboring nodes can be reached from every other node by a small number of hops or steps. Specifically, a small-world network is defined to be a network where the typical distance L between two randomly chosen nodes (the number of steps required) grows proportionally to the logarithm of the number of nodes N in the network.
A small-world network is a mathematical graph in which most nodes are not neighbors of one another, but the neighbors of any given node are likely to be neighbors of each other.
You are an expert Q&A system that is trusted around the world. You always answer the user's query in a helpful and friendly way.
Some rules you always follow:
1. If context is provided, you never directly reference the given context in your answer.
2. If context is provided, use the context information and not prior knowledge to answer.
3. Avoid statements like 'Based on the context, ...' or 'The context information ...' or 'The answer to the user's query...' or anything along those lines.
4. If no context is provided use your internal knowledge to answer.
system
(Optional) Context information is below.
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A small-world network is a mathematical graph in which most nodes are not neighbors of one another, but the neighbors of any given node are likely to be neighbors of each other. Due to this, most neighboring nodes can be reached from every other node by a small number of hops or steps. Specifically, a small-world network is defined to be a network where the typical distance L between two randomly chosen nodes (the number of steps required) grows proportionally to the logarithm of the number of nodes N in the network.
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Answer the following query.
What is a small-world network?

user
A small-world network is a mathematical graph in which most nodes are not neighbors of one another, but the neighbors of any given node are likely to be neighbors of each other.
assistant