Navigation in a small world

Navigation in a small world

24 AUGUST 2000 | Jon M. Kleinberg
The article discusses the navigability of small-world networks, focusing on how individuals can efficiently find short paths in such networks using only local information. Small-world networks are characterized by a combination of short-range connections and a few long-range connections, which allow for efficient communication between distant nodes. The key finding is that a decentralized algorithm can efficiently navigate these networks only when the clustering exponent, α, is exactly 2. This value allows for a delivery time bounded by a function proportional to (log N)^2, where N is the number of nodes. When α is not 2, the delivery time increases significantly, regardless of the algorithm used. The article also generalizes these findings to d-dimensional lattices, where the critical value of α becomes d. The results suggest that the correlation between local structure and long-range connections is crucial for efficient navigation. When this correlation is near a critical threshold, long-range connections form a gradient that guides messages efficiently towards their target. However, when the correlation drops below this threshold, the cues for navigation disappear, making it difficult for individuals to find short paths even though they exist. The study highlights the importance of structured long-range connections in enabling efficient navigation in small-world networks.The article discusses the navigability of small-world networks, focusing on how individuals can efficiently find short paths in such networks using only local information. Small-world networks are characterized by a combination of short-range connections and a few long-range connections, which allow for efficient communication between distant nodes. The key finding is that a decentralized algorithm can efficiently navigate these networks only when the clustering exponent, α, is exactly 2. This value allows for a delivery time bounded by a function proportional to (log N)^2, where N is the number of nodes. When α is not 2, the delivery time increases significantly, regardless of the algorithm used. The article also generalizes these findings to d-dimensional lattices, where the critical value of α becomes d. The results suggest that the correlation between local structure and long-range connections is crucial for efficient navigation. When this correlation is near a critical threshold, long-range connections form a gradient that guides messages efficiently towards their target. However, when the correlation drops below this threshold, the cues for navigation disappear, making it difficult for individuals to find short paths even though they exist. The study highlights the importance of structured long-range connections in enabling efficient navigation in small-world networks.
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