Preferential attachment model

updated: 2022-11-09
#network-science/random-networks #network-science/citation-dynamics

Preferential attachment is a universal and fundamental mechanism underlying the growth of networks. It manifestes a rich-gets-richer phenomenon and yields heavy-tailed distributions.

How it works

In a  preferential attachment model, a new node (say ) initially has free arms and provides each arm to an existing node (say ) with probability proportional to the number of citations that node has at that time. A network is generated by repeating this process.

Initial attractiveness

Because every node has no citation when it appears, the probability of the first citation is zero, which breaks the model. A common workaround is to give some fixed number of citations (say c_0) to new papers as a kind of “log-in bonus”, which is called initial attractiveness. Then, the probability of getting one free arm from a new node is , where ct is the number of accumulated citations at time t. A common choice c_0 = 1.

• Finite-Time Fluctuations in the Degree Statistics of Growing Networks | SpringerLink
• Phys. Rev. Lett. 85, 4633 (2000) - Structure of Growing Networks with Preferential Linking
• The first-mover advantage in scientific publication - IOPscience

Recency

Recency is a natural consequence of the exponential growth. It appers even for a pure preferential attachment model.

A model showing the increase in time of the average and median reference age and the decrease in time of the Price Index | SpringerLink

Models & Applications

• Price's model - Wikipedia Probably a first model of the growth of citation networks.
• Barabási–Albert model - Wikipedia A simplified version of the Price's model.
• Long-term citation model Bayesian approachThis model has added components such as recency and fitness
• Price's model with initial attraciveness Impact of the initial attractiveness Application to study the first-mover advantage

Related models:

Long term citation model