A Geometric Graph Model of Citation Networks with Linearly Growing Node-Increment

@inproceedings{Liu2016AGG,
  title={A Geometric Graph Model of Citation Networks with Linearly Growing Node-Increment},
  author={Qi Liu and Zheng Xie and Enming Dong and Jianping Li},
  booktitle={FSDM},
  year={2016}
}
Due to the fact that the numbers of annually published papers have witnessed a linear growth in some citation networks, a geometric model is thus proposed to predict some statistical features of those networks, in which the academic influence scopes of the papers are denoted through specific geometric areas related to time and space. In the model, nodes (papers) are uniformly and randomly sprinkled onto a cluster of circles of the Minkowski space whose centers are on the time axis. Edges… 
1 Citations

Figures and Tables from this paper

Modeling the time-periodicity of in-degree distributions in scientific citation networks
TLDR
A geometric model is established, in which the sizes of the influence zones of nodes follow the same power-law distribution and decrease with their ages, which reproduces the time-periodicity of the in-degree distributions of the empirical data, and accounts for the presence of citation burst.

References

SHOWING 1-10 OF 28 REFERENCES
Modeling the Citation Network by Network Cosmology
TLDR
An inhomogenous causal network model is proposed to model the citation network, the connection mechanism of which well expresses some features of citation.
Nonuniversal power law scaling in the probability distribution of scientific citations
TLDR
A model for the distribution of scientific citations is developed and it is found that papers having few citations are cited mainly by the direct mechanism, and papers already having many citations (“classics”) are cited mostly by the indirect mechanism.
Understanding the Scientific Enterprise: Citation Analysis, Data and Modeling
TLDR
The present chapter aims at providing a brief overview of the progress recently made in the analysis of bibliographic databases by focusing on studies devoted to the statistical description of distributions of citations received by individual publications.
Characterizing and Modeling Citation Dynamics
TLDR
This work investigates bibliometric data of papers published in journals of the American Physical Society, searching for the type of function which best describes the observed citation distributions, and proposes a linear preferential attachment with time dependent initial attractiveness which successfully reproduces the empirical citation distributions.
Network growth by copying.
  • P. Krapivsky, S. Redner
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2005
TLDR
A growing network model in which a new node attaches to a randomly selected node, as well as to all ancestors of the target node, produces a sparse, ultrasmall network where the average node degree grows logarithmically with network size while the network diameter equals 2.
Graph evolution: Densification and shrinking diameters
TLDR
A new graph generator is provided, based on a forest fire spreading process that has a simple, intuitive justification, requires very few parameters, and produces graphs exhibiting the full range of properties observed both in prior work and in the present study.
A general theory of bibliometric and other cumulative advantage processes
  • D. Price
  • Mathematics
    J. Am. Soc. Inf. Sci.
  • 1976
TLDR
It is shown that such a stochastic law is governed by the Beta Function, containing only one free parameter, and this is approximated by a skew or hyperbolic distribution of the type that is widespread in bibliometrics and diverse social science phenomena.
Clustering and preferential attachment in growing networks.
  • M. Newman
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2001
TLDR
It is shown that the probability of a pair of scientists collaborating increases with the number of other collaborators they have in common, and that the probabilities of a particular scientist acquiring new collaborators increases withThe number of his or her past collaborators.
Connectivity of growing random networks.
TLDR
A solution for the time- and age-dependent connectivity distribution of a growing random network is presented and the power law N(k) approximately k(-nu) is found, where the exponent nu can be tuned to any value in the range 2.
Structure of growing networks with preferential linking.
TLDR
The model of growing networks with the preferential attachment of new links is generalized to include initial attractiveness of sites and it is shown that the relation beta(gamma-1) = 1 between the exponents is universal.
...
...