The Navigability of Strong Ties: Small Worlds, Tie Strength, and Network Topology

A searchable small world (SSW) is a (large) network in which ties are locally clustered, average interpoint distance is low, and a decentralized search algorithm assigned to pass messages from random nodes to random target using only local information is able to find shortest paths according to Kleinberg's [33] criteria for efficient search. Our hypothesis regarding the navigability of strong ties in empirical social network topologies is that strong ties, in addition to being clustered, often give unique access to valued resources and there are some conditions and tipping points at which issues of uncertainty in survival often lead to the co-evolution of broad strong-tie accessibility to particular resources along with strong-tie SSW network topologies. These typologies solve, independently of weaker ties, both the small distance and the searchability problems. Examples discussed include kinship and marriage as self-reproducing networks [49], corporate cultures and business networks in self-sustaining economies [50], and circumstances where strong ties are instrumental in finding a job [10a]. Strong-tie SSW network dynamics and architectures can be investigated as part of the self-organizing morphogenetics of how cultures reproduce themselves at multiple levels of organization. To the extent that it fits the small-world navigability model, Middle Eastern segmentary strong-tie organization is a particularly strong example. Preliminary testing for signatures of complex dynamics supports a new approach to the study of self-organization in kinship and marriage networks, one that is potentially applicable as well to corporate cultures and business networks.