June  2008, 3(2): 345-359. doi: 10.3934/nhm.2008.3.345

On the relationships between topological measures in real-world networks

1. 

Delft University of Technology, P.O. Box 5031, Delft, 2600 GA, Netherlands, Netherlands

Received  September 2007 Revised  November 2007 Published  March 2008

Over the past several years, a number of measures have been introduced to characterize the topology of complex networks. We perform a statistical analysis of real data sets, representing the topology of different real-world networks. First, we show that some measures are either fully related to other topological measures or that they are significantly limited in the range of their possible values. Second, we observe that subsets of measures are highly correlated, indicating redundancy among them. Our study thus suggests that the set of commonly used measures is too extensive to concisely characterize the topology of complex networks. It also provides an important basis for classification and unification of a definite set of measures that would serve in future topological studies of complex networks.
Citation: Almerima Jamakovic, Steve Uhlig. On the relationships between topological measures in real-world networks. Networks & Heterogeneous Media, 2008, 3 (2) : 345-359. doi: 10.3934/nhm.2008.3.345
[1]

Abdon Atangana, Zakia Hammouch, Kolade M. Owolabi, Gisele Mephou. Preface: New trends on numerical analysis and analytical methods with their applications to real world problems. Discrete & Continuous Dynamical Systems - S, 2019, 12 (3) : ⅰ-ⅰ. doi: 10.3934/dcdss.201903i

[2]

Changjun Yu, Honglei Xu, Kok Lay Teo. Preface: Advances in theory and real world applications of control and dynamic optimization. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 0-0. doi: 10.3934/dcdss.2020094

[3]

Fabio Camilli, Raul De Maio, Andrea Tosin. Transport of measures on networks. Networks & Heterogeneous Media, 2017, 12 (2) : 191-215. doi: 10.3934/nhm.2017008

[4]

Sharon M. Cameron, Ariel Cintrón-Arias. Prisoner's Dilemma on real social networks: Revisited. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1381-1398. doi: 10.3934/mbe.2013.10.1381

[5]

Zhuwei Qin, Fuxun Yu, Chenchen Liu, Xiang Chen. How convolutional neural networks see the world --- A survey of convolutional neural network visualization methods. Mathematical Foundations of Computing, 2018, 1 (2) : 149-180. doi: 10.3934/mfc.2018008

[6]

Qingyun Wang, Xia Shi, Guanrong Chen. Delay-induced synchronization transition in small-world Hodgkin-Huxley neuronal networks with channel blocking. Discrete & Continuous Dynamical Systems - B, 2011, 16 (2) : 607-621. doi: 10.3934/dcdsb.2011.16.607

[7]

C. Alonso-González, M. I. Camacho, F. Cano. Topological invariants for singularities of real vector fields in dimension three. Discrete & Continuous Dynamical Systems - A, 2008, 20 (4) : 823-847. doi: 10.3934/dcds.2008.20.823

[8]

Mingxing Zhou, Jing Liu, Shuai Wang, Shan He. A comparative study of robustness measures for cancer signaling networks. Big Data & Information Analytics, 2017, 2 (1) : 87-96. doi: 10.3934/bdia.2017011

[9]

Palle E. T. Jorgensen and Steen Pedersen. Orthogonal harmonic analysis of fractal measures. Electronic Research Announcements, 1998, 4: 35-42.

[10]

Tyrus Berry, Timothy Sauer. Consistent manifold representation for topological data analysis. Foundations of Data Science, 2019, 1 (1) : 1-38. doi: 10.3934/fods.2019001

[11]

Fabio Ancona, Laura Caravenna, Annalisa Cesaroni, Giuseppe M. Coclite, Claudio Marchi, Andrea Marson. Analysis and control on networks: Trends and perspectives. Networks & Heterogeneous Media, 2017, 12 (3) : i-ii. doi: 10.3934/nhm.201703i

[12]

Fabio Ancona, Laura Caravenna, Annalisa Cesaroni, Giuseppe M. Coclite, Claudio Marchi, Andrea Marson. Analysis and control on networks: Trends and perspectives. Networks & Heterogeneous Media, 2017, 12 (2) : i-ii. doi: 10.3934/nhm.201702i

[13]

Peter Hinow, Edward A. Rietman, Sara Ibrahim Omar, Jack A. Tuszyński. Algebraic and topological indices of molecular pathway networks in human cancers. Mathematical Biosciences & Engineering, 2015, 12 (6) : 1289-1302. doi: 10.3934/mbe.2015.12.1289

[14]

Eva Barrena, Alicia De-Los-Santos, Gilbert Laporte, Juan A. Mesa. Transferability of collective transportation line networks from a topological and passenger demand perspective. Networks & Heterogeneous Media, 2015, 10 (1) : 1-16. doi: 10.3934/nhm.2015.10.1

[15]

Zhihui Yuan. Multifractal analysis of random weak Gibbs measures. Discrete & Continuous Dynamical Systems - A, 2017, 37 (10) : 5367-5405. doi: 10.3934/dcds.2017234

[16]

Xueting Tian, Paulo Varandas. Topological entropy of level sets of empirical measures for non-uniformly expanding maps. Discrete & Continuous Dynamical Systems - A, 2017, 37 (10) : 5407-5431. doi: 10.3934/dcds.2017235

[17]

Mary Luz Mouronte, Rosa María Benito. Structural analysis and traffic flow in the transport networks of Madrid. Networks & Heterogeneous Media, 2015, 10 (1) : 127-148. doi: 10.3934/nhm.2015.10.127

[18]

Mirela Domijan, Markus Kirkilionis. Graph theory and qualitative analysis of reaction networks. Networks & Heterogeneous Media, 2008, 3 (2) : 295-322. doi: 10.3934/nhm.2008.3.295

[19]

Georges Bastin, B. Haut, Jean-Michel Coron, Brigitte d'Andréa-Novel. Lyapunov stability analysis of networks of scalar conservation laws. Networks & Heterogeneous Media, 2007, 2 (4) : 751-759. doi: 10.3934/nhm.2007.2.751

[20]

Samitha Samaranayake, Axel Parmentier, Ethan Xuan, Alexandre Bayen. A mathematical framework for delay analysis in single source networks. Networks & Heterogeneous Media, 2017, 12 (1) : 113-145. doi: 10.3934/nhm.2017005

2018 Impact Factor: 0.871

Metrics

  • PDF downloads (8)
  • HTML views (0)
  • Cited by (19)

Other articles
by authors

[Back to Top]