Abstract
In this work we investigate how future actions are influenced by the previous ones, in the specific contexts of scientific collaborations and friendships on social networks. We describe the activity of the agents, providing a model for the formation of the bipartite network of actions and their features. Therefore we only require to know the chronological order in which the actions are performed, and not the order in which the agents are observed. Moreover, the total number of possible features is not specified a priori but is allowed to increase along time, and new actions can independently show some new-entry features or exhibit some of the old ones. The choice of the old features is driven by a degree-fitness method: indeed, the probability that a new action shows one of the old features does not solely depend on the popularity of that feature (i.e. the number of previous actions showing it), but it is also affected by some individual traits of the agents or the features themselves, synthesized in certain quantities, called fitnesses or weights, that can have different forms and different meaning according to the specific setting considered. We show some theoretical properties of the model and provide statistical tools for the parameters’ estimation. The model has been tested on three different datasets and the numerical results are provided and discussed.
Highlights
In the last years complex networks established as a proper tool for the description of the interactions within large systems [1,2,3,4]
Even if the original mechanism was already present in the literature in a slightly different form [6, 7], the paper of Barabasi-Albert boosted the attractiveness of complex networks and other scholars delved into the investigation of the properties of generative
The probability to exhibit one of the features already observed is defined as a mixture of random choice and preferential attachment with weights, i.e. the probability of connection depends both on the features’ degrees and the fitness of the agents involved and/or of the features themselves. These weights Wt,j,k can have different forms and meanings according to the specific setting considered: the weight at time-step t of the observed feature k can depend on some characteristics of k itself, or it can be directly established by the agent performing action t; it may represent the inclination of the agent performing action t in adopting the previous observed features, or some properties of the agent performing the previous action j with k among its features
Summary
In the last years complex networks established as a proper tool for the description of the interactions within large systems [1,2,3,4]. The renewed attention to this field can be dated back to the well known Barabasi-Albert model [5], in which the authors provide an explanation of the power-law distribution of node degrees in the World Wide Web (WWW) via a dynamic generative network model. The success of this proposal resides in the fact that only this simple rule, called preferential attachment, is able to reproduce with good accuracy the degree distribution of many real networks, such as the WWW. Even if the original mechanism was already present in the literature in a slightly different form [6, 7], the paper of Barabasi-Albert boosted the attractiveness of complex networks and other scholars delved into the investigation of the properties of generative.
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