Detecting degree symmetries in networks.

@article{Holme2006DetectingDS,
  title={Detecting degree symmetries in networks.},
  author={Petter Holme},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2006},
  volume={74 3 Pt 2},
  pages={
          036107
        }
}
  • P. Holme
  • Published 3 May 2006
  • Mathematics, Computer Science
  • Physical review. E, Statistical, nonlinear, and soft matter physics
The surrounding of a vertex in a network can be more or less symmetric. We derive measures of a specific kind of symmetry of a vertex which we call degree symmetry--the property that many paths going out from a vertex have overlapping degree sequences. These measures are evaluated on artificial and real networks. Specifically we consider vertices in the human metabolic network. We also measure the average degree-symmetry coefficient for different classes of real-world network. We find that most… 

Figures and Tables from this paper

Characterization of Symmetry of Complex Networks
TLDR
Using three indexes based on the natural action of the automorphism group Aut ( Γ ) of Γ on the vertex set V of a given network Γ = Γ ( V, E ) , one can get a quantitative characterization of how symmetric a network is and can compare the symmetry property of different networks.
Hidden Symmetries in Real and Theoretical Networks
Emergence of symmetry in complex networks.
TLDR
An improved version of the Barabaśi-Albert model integrating similar linkage pattern successfully reproduces the symmetry of real networks, indicating that similar linkagepattern is the underlying ingredient that is responsible for the emergence of symmetry in complex networks.
Concentric network symmetry
Symmetry in complex networks
Resilience of Small Social Networks
The ability of a network to retain one or more specified properties under perturbation of its structure is referred to as resilience. In this thesis, we focus on the resilience of small social
Quasi-symmetries in complex networks: a dynamical model approach
TLDR
This work defines the ‘dual-network’, a weighted network that effectively encodes all the information of quasi-symmetries in the original network, and provides a benchmark to determine whether a network has a more complex pattern than that of a random network with regard to quasi-SYMMetries.
Scale-free tree graphs are more symmetrical
TLDR
It is found that, in contrast to random tree graph models, scale-free tree graphs are richly symmetric, and normalized symmetry can eliminate the effect degree distribution of graphs to symmetry.
Network Specializations, Symmetries, and Spectral Properties
TLDR
This dissertation introduces three techniques for network sciences, a series of new models for describing network growth, and a generalization of network symmetry, called latent symmetry, which is extended to work for every automorphism.
On Automorphism Groups of Networks
...
...

References

SHOWING 1-10 OF 33 REFERENCES
Analysis of weighted networks.
  • M. Newman
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2004
TLDR
It is pointed out that weighted networks can in many cases be analyzed using a simple mapping from a weighted network to an unweighted multigraph, allowing us to apply standard techniques for unweighting graphs to weighted ones as well.
Assortative mixing in networks.
  • M. Newman
  • Computer Science
    Physical review letters
  • 2002
TLDR
This work proposes a model of an assortatively mixed network and finds that networks percolate more easily if they are assortative and that they are also more robust to vertex removal.
Modularity from fluctuations in random graphs and complex networks.
TLDR
It is shown both numerically and analytically that random graphs and scale-free networks have modularity and it is argued that this fact must be taken into consideration to define statistically significant modularity in complex networks.
A measure of similarity between graph vertices
TLDR
It is pointed out that Kleinberg's "hub and authority" method to identify web-pages relevant to a given query can be viewed as a special case of the similarity matrix definition in the case where one of the graphs has two vertices and a unique directed edge between them.
Currency and commodity metabolites: their identification and relation to the modularity of metabolic networks.
TLDR
It is argued that cross-modular edges are the key for the robustness of metabolism, found to be more modular than random networks but far from perfectly divisible into modules.
Social network analysis - methods and applications
TLDR
This paper presents mathematical representation of social networks in the social and behavioral sciences through the lens of dyadic and triadic interaction models, which provide insights into the structure and dynamics of relationships between actors and groups.
Functional cartography of complex metabolic networks
TLDR
A methodology is proposed that can find functional modules in complex networks, and classify nodes into universal roles according to their pattern of intra- and inter-module connections, which yields a ‘cartographic representation’ of complex networks.
SimRank: a measure of structural-context similarity
TLDR
A complementary approach, applicable in any domain with object-to-object relationships, that measures similarity of the structural context in which objects occur, based on their relationships with other objects is proposed.
...
...