• Corpus ID: 14347662

Motif Conservation Laws for the Configuration Model

@article{Wegner2014MotifCL,
  title={Motif Conservation Laws for the Configuration Model},
  author={Anatol E. Wegner},
  journal={ArXiv},
  year={2014},
  volume={abs/1408.6303}
}
  • A. Wegner
  • Published 26 August 2014
  • Mathematics
  • ArXiv
The observation that some subgraphs, called motifs, appear more often in real networks than in their randomized counterparts has attracted much attention in the scientific community. In the prevalent approach the detection of motifs is based on comparing subgraph counts in a network with their counterparts in the configuration model with the same degree distribution as the network. In this short note we derive conservation laws that relate motif counts in the configuration model. 
1 Citations

Figures from this paper

Subgraph covers - An information theoretic approach to motif analysis in networks
  • A. Wegner
  • Computer Science, Mathematics
    ArXiv
  • 2014
TLDR
This paper proposes an alternative approach to motif analysis where network motifs are defined to be connectivity patterns that occur in a subgraph cover that represents the network using minimal total information.

References

SHOWING 1-10 OF 10 REFERENCES
Network motifs come in sets: correlations in the randomization process.
  • Reid GinozaA. Mugler
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2010
TLDR
The most common algorithms used to generate the ensemble from the real network change subgraph counts in a highly correlated manner, such that one subgraph's status as a motif may not be independent from the statuses of the other subgraphs.
Random graphs containing arbitrary distributions of subgraphs
  • B. KarrerM. Newman
  • Mathematics, Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2010
TLDR
This paper proposes and analyzes a class of random graph models that incorporates general subgraphs, allowing for nontreelike neighborhoods while still remaining solvable for many fundamental network properties.
Random graphs with clustering.
  • M. Newman
  • Computer Science
    Physical review letters
  • 2009
TLDR
It is shown how standard random-graph models can be generalized to incorporate clustering and give exact solutions for various properties of the resulting networks, including sizes of network components, size of the giant component if there is one, position of the phase transition at which the giant components forms, and position ofThe phase transition for percolation on the network.
Network motifs: simple building blocks of complex networks.
TLDR
Network motifs, patterns of interconnections occurring in complex networks at numbers that are significantly higher than those in randomized networks, are defined and may define universal classes of networks.
On the uniform generation of random graphs with prescribed degree sequences
TLDR
A new method based on the ``go with the winners'' Monte Carlo method is presented, which can be used to evaluate the reliability of the other two methods and demonstrate that the deviations of the switching and matching algorithms under realistic conditions are small.
Superfamilies of Evolved and Designed Networks
Random graphs with arbitrary degree distributions and their applications.
TLDR
It is demonstrated that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world, while in others there is a measurable discrepancy between theory and reality, perhaps indicating the presence of additional social structure in the network that is not captured by the random graph.
Electronic address: wegner@mis.mpg
  • Electronic address: wegner@mis.mpg
Random graphs with clustering. Physical review letters
  • Random graphs with clustering. Physical review letters
  • 2009
graphs with arbitrary degree distributions and their applications
  • Physical Review E
  • 2001