In mathematical modeling of social networks, link-centric preferential attachment[1] [2] is a node's propensity to re-establish links to nodes it has previously been in contact with in time-varying networks.[3] This preferential attachment model relies on nodes keeping memory of previous neighbors up to the current time.[1] [4]
In real social networks individuals exhibit a tendency to re-connect with past contacts (ex. family, friends, co-workers, etc.) rather than strangers. In 1970, Mark Granovetter examined this behaviour in the social networks of a group of workers and identified tie strength, a characteristic of social ties describing the frequency of contact between two individuals. From this comes the idea of strong and weak ties,[5] where an individual's strong ties are those she has come into frequent contact with. Link-centric preferential attachment aims to explain the mechanism behind strong and weak ties as a stochastic reinforcement process for old ties in agent-based modeling where nodes have long-term memory.
In a simple model for this mechanism, a node's propensity to establish a new link can be characterized solely by
n
P(n)={c\overn+c}
where c is an offset constant. The probability for a node to re-connect with old ties is then
1-P(n)={n\overn+c}.
More complex models may take into account other variables, such as frequency of contact, contact and intercontact duration, as well as short term memory effects.[1]
Effects on the spreading of contagions / weakness of strong ties
Understanding the evolution of a network's structure and how it can influence dynamical processes has become an important part of modeling the spreading of contagions.[6] [7] In models of social and biological contagion spreading on time-varying networks link-centric preferential attachment can alter the spread of the contagion to the entire population. Compared to the classic rumour spreading process where nodes are memory-less, link-centric preferential attachment can cause not only a slower spread of the contagion but also one less diffuse. In these models an infected node's chances of connecting to new contacts diminishes as their size of their social circle
n