The small-world phenomenon refers to the idea that people are connected by short chains of acquaintances. This concept was popularized by Stanley Milgram's experiments in the 1960s, which showed that people in the U.S. could be connected through a short chain of acquaintances, leading to the "six degrees of separation" principle. Various network models have been proposed to study this phenomenon, with Watts and Strogatz's model being one of the most refined. Their model suggests that social networks have both local and long-range connections, which contribute to the small-world phenomenon. However, existing models fail to explain how individuals using only local information can effectively construct short paths in social networks. The paper introduces an infinite family of network models that generalize the Watts-Strogatz model. It shows that for one of these models, there exists a decentralized algorithm capable of finding short paths with high probability. The paper also proves that there is a unique model within this family for which decentralized algorithms are effective. The paper analyzes decentralized algorithms, where individuals use only local information to transmit messages through a network. It shows that existing models cannot explain the success of such algorithms in finding short paths. The paper defines a new model that incorporates both local and long-range connections, and shows that for a specific value of the exponent r (r=2), there exists a decentralized algorithm that can find short paths with high probability. The paper also provides lower bounds for other distributions, showing that for values of r less than or greater than 2, no decentralized algorithm can find short paths with high probability. The paper concludes that the small-world phenomenon is not just about the existence of short paths, but also about the presence of structural cues that allow individuals to navigate the network. When the correlation between local structure and long-range connections is near a critical threshold, the structure of the long-range connections forms a gradient that allows individuals to guide a message efficiently toward a target. However, when this correlation drops below the critical value, these cues disappear, and individuals are unable to find short paths.The small-world phenomenon refers to the idea that people are connected by short chains of acquaintances. This concept was popularized by Stanley Milgram's experiments in the 1960s, which showed that people in the U.S. could be connected through a short chain of acquaintances, leading to the "six degrees of separation" principle. Various network models have been proposed to study this phenomenon, with Watts and Strogatz's model being one of the most refined. Their model suggests that social networks have both local and long-range connections, which contribute to the small-world phenomenon. However, existing models fail to explain how individuals using only local information can effectively construct short paths in social networks. The paper introduces an infinite family of network models that generalize the Watts-Strogatz model. It shows that for one of these models, there exists a decentralized algorithm capable of finding short paths with high probability. The paper also proves that there is a unique model within this family for which decentralized algorithms are effective. The paper analyzes decentralized algorithms, where individuals use only local information to transmit messages through a network. It shows that existing models cannot explain the success of such algorithms in finding short paths. The paper defines a new model that incorporates both local and long-range connections, and shows that for a specific value of the exponent r (r=2), there exists a decentralized algorithm that can find short paths with high probability. The paper also provides lower bounds for other distributions, showing that for values of r less than or greater than 2, no decentralized algorithm can find short paths with high probability. The paper concludes that the small-world phenomenon is not just about the existence of short paths, but also about the presence of structural cues that allow individuals to navigate the network. When the correlation between local structure and long-range connections is near a critical threshold, the structure of the long-range connections forms a gradient that allows individuals to guide a message efficiently toward a target. However, when this correlation drops below the critical value, these cues disappear, and individuals are unable to find short paths.