Skip to main content
SpringerLink
Log in

A novel centrality-based method for visual analytics of small-world networks

  • Regular Paper
  • Published:
Journal of Visualization Aims and scope Submit manuscript

Abstract

Nowadays, the network data that we need to deal with and make sense of are becoming increasingly large and complex. Small-world networks are a type of complex networks whose underling graphs have small diameter, shorter average path length between nodes, and a high degree of clustering structures and can be found in a wide range of scientific fields, including social networks, sociology, computer science, business intelligence, and biology. However, conventional visualization algorithms for small-work networks lead to a uniform clump of nodes or are restricted to a tree structure, making the network structure difficult to identify and analyze. This work provides a new visual analytical method to improve the situation. Different from previous methods based on spanning trees, this method first generates a weighted planar sub-network based on the measurement of network centrality metrics. A force-directed algorithm based on node-edge repulsion is then applied to visualize this sub-network into a proper layout for better understanding of the data. Finally, the remaining links are placed back to maintain the original network’s integrity. The experimental results show that compared to previous methods, the proposed method can be more effective in differentiating clusters and revealing relationship patterns among individual nodes and clusters in the network. Furthermore, the proposed method is applied to a data of the semiconductor wafer manufacturing industry as a case study. The work shows that this new approach allows users to gain useful insights into the data.

Graphic abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Abbasi A, Hossain L, Leydesdorff L (2012) Betweenness centrality as a driver of preferential attachment in the evolution of research collaboration networks. J Informetr 6:403–412

    Google Scholar 

  • Aleardi LC, Devillers O, Fusy É (2013) Canonical ordering for triangulations on the cylinder, with applications to periodic straight-line drawings. In: Proceedings of graph drawing, 2013. Springer, pp 376–387

  • Archambault D, Munzner T, Auber D (2011) Tugging graphs faster: efficiently modifying path-preserving hierarchies for browsing paths. IEEE Trans Vis Comput Graph 17:276–289

    Google Scholar 

  • Bassett D, Bullmore E (2017) Small-world brain networks revisited. Neuroscientist 23:499–516

    Google Scholar 

  • Bender-deMoll S, McFarland DA (2006) The art and science of dynamic network visualization. J Soc Struct 7:1–38

    Google Scholar 

  • Bertault F (2000) A force-directed algorithm that preserves edge-crossing properties. Inf Process Lett 74:7–13

    MathSciNet  MATH  Google Scholar 

  • Bertin J (1983) Semiology of graphics: diagrams, networks, maps. Esri Press, Redlands

    Google Scholar 

  • Bhandari A, Gupta A, Das D (2017) Betweenness centrality updation and community detection in streaming graphs using incremental algorithm. In: Proceedings of the 6th international conference on software and computer applications, 2017. ACM Press, pp 159–164

  • Bi C, Fu B, Chen J, Zhao Y, Yang L, Duan Y, Shi Y (2018) Machine learning based fast multi-layer liquefaction disaster assessment. World Wide Web. https://doi.org/10.1007/s11280-018-0632-8

    Google Scholar 

  • Bi CK, Yang L, Duan YL, Shi Y (2019) A survey on visualization of tensor field. J Vis 22:641–660

    Google Scholar 

  • Bonchi F, Morales GDF, Riondato M (2016) Centrality measures on big graphs: exact, approximated, and distributed algorithms. In: Proceedings of the 25th international conference companion on world wide web, 2016. ACM Press, pp 1017–1020

  • Borgatti SP, Mehra A, Brass DJ, Labianca G (2009) Network analysis in the social sciences. Science 323:892–895

    Google Scholar 

  • Boyer JM, Myrvold WJ (2004) On the cutting edge: simplified O(n) planarity by edge addition. J Graph Algorithms Appl 8:241–273

    MathSciNet  MATH  Google Scholar 

  • Brandes U (2001) A faster algorithm for betweenness centrality. J Math Sociol 25:163–177

    MATH  Google Scholar 

  • Brandes U, Indlekofer N, Mader M (2012) Visualization methods for longitudinal social networks and stochastic actor-oriented modeling. Soc Netw 34:291–308

    Google Scholar 

  • Burger M, Zelazo D, Allgower F (2013) Hierarchical clustering of dynamical networks using a saddle-point analysis. IEEE Trans Autom Control 58:113–124

    MathSciNet  MATH  Google Scholar 

  • Correa C, Crnovrsanin T, Ma K-L (2012) Visual reasoning about social networks using centrality sensitivity. IEEE Trans Vis Comput Graph 18:106–120

    Google Scholar 

  • Crnovrsanin T, Muelder CW, Faris R, Felmlee D, Ma K-L (2014) Visualization techniques for categorical analysis of social networks with multiple edge sets. Soc Netw 37:56–64

    Google Scholar 

  • Das S, Lee D, Choi W, Doppa JR, Pande PP, Chakrabarty K (2017) VFI-based power management to enhance the lifetime of high-performance 3D NoCs. ACM Trans Des Autom Electron Syst 23:1–26. https://doi.org/10.1145/3092843

    Article  Google Scholar 

  • Davidson R, Harel D (1996) Drawing graphs nicely using simulated annealing. ACM Trans Graph 15:301–331

    Google Scholar 

  • Dong J, Horvath S (2007) Understanding network concepts in modules. BMC Syst Biol 1:24

    Google Scholar 

  • Eades P (1984) A heuristics for graph drawing. Congr Numer 42:146–160

    MathSciNet  Google Scholar 

  • Fößmeier U, Kaufmann M (1996) Drawing high degree graphs with low bend numbers. In: Proceedings of graph drawing, 1996. Springer, pp 254–266

  • Freeman LC (1979) Centrality in social networks conceptual clarification. Soc Netw 1:215–239

    Google Scholar 

  • Gibson H, Vickers P (2016) Using adjacency matrices to lay out larger small-world networks. Appl Soft Comput 42:80–92

    Google Scholar 

  • Gómez D, Figueira JR, Eusébio A (2013) Modeling centrality measures in social network analysis using bi-criteria network flow optimization problems. Eur J Oper Res 226:354–365

    MathSciNet  MATH  Google Scholar 

  • Gretarsson B, O’Donovan J, Bostandjiev S, Hall C, Höllerer T (2010) Smallworlds: visualizing social recommendations. Comput Graph Forum 29:833–842

    Google Scholar 

  • Guan C, Yuen KKF (2013) Towards a hybrid approach of primitive cognitive network process and k-means clustering for social network analysis. In: Proceedings of IEEE international conference on Internet of Things (iThings/CPSCom), 2013. IEEE Press, pp 1267–1271

  • Gutwenger C, Mutzel P (1997) Grid embedding of biconnected planar graphs. Extended abstract. Max-Planck-Institut f ur Informatik, Saarbrücken

    Google Scholar 

  • Huang W, Eades P, Hong S-H, Lin C-C (2013) Improving multiple aesthetics produces better graph drawings. J Vis Lang Comput 24:262–272

    Google Scholar 

  • Huang W, Huang ML, Lin C-C (2016) Evaluating overall quality of graph visualizations based on aesthetics aggregation. Inf Sci 330:444–454

    Google Scholar 

  • Jia Y, Hoberock J, Garland M, Hart JC (2008) On the visualization of social and other scale-free networks. IEEE Trans Vis Comput Graph 14:1285–1292

    Google Scholar 

  • Jia Y, Garland M, Hart JC (2011) Social network clustering and visualization using hierarchical edge bundles. Comput Graph Forum 30:2314–2327

    Google Scholar 

  • Junger M, Leipert S, Mutzel P (1998) A note on computing a maximal planar subgraph using PQ-trees. IEEE Trans Comput Aided Des Integr Circuits Syst 17:609–612

    Google Scholar 

  • Kant G (1996) Drawing planar graphs using the canonical ordering. Algorithmica 16:4–32

    MathSciNet  MATH  Google Scholar 

  • Lee T, Kim C (2014) Statistical comparison of fault detection models for semiconductor manufacturing processes. IEEE Trans Semicond Manuf 28:80–91

    Google Scholar 

  • Lin C-C, Yen H-C (2012) A new force-directed graph drawing method based on edge–edge repulsion. J Vis Lang Comput 23:29–42

    Google Scholar 

  • Lin C-C, Huang W, Liu W-Y, Chen W-L (2018) Evaluating aesthetics for user-sketched layouts of symmetric graphs. J Vis Lang Comput 48:123–133

    Google Scholar 

  • Love M (2007) Genealogy of influence. [Online]. Available: http://mikelove.nfshost.com/genealogy/

  • Newman ME, Girvan M (2004) Finding and evaluating community structure in networks. Phys Rev E 69:026113

    Google Scholar 

  • Opsahl T, Agneessens F, Skvoretz J (2010) Node centrality in weighted networks: generalizing degree and shortest paths. Soc Netw 32:245–251

    Google Scholar 

  • Shi L et al. (2009) HiMap: adaptive visualization of large-scale online social networks. In: Proceedings of 2009 IEEE pacific visualization symposium, 2009. IEEE Press, pp 41–48

  • Shimbel A (1953) Structural parameters of communication networks. Bull Math Biophys 15:501–507

    MathSciNet  Google Scholar 

  • Sohn K, Kim D (2010) Zonal centrality measures and the neighborhood effect. Transp Res Part A: Pol Pract 44:733–743

    Google Scholar 

  • Valente TW, Foreman RK (1998) Integration and radiality: measuring the extent of an individual’s connectedness and reachability in a network. Soc Netw 20:89–105

    Google Scholar 

  • van Ham F, Wattenberg M (2008) Centrality based visualization of small world graphs. Comput Graph Forum 27:975–982

    Google Scholar 

  • Wakita K, Tsurumi T (2007) Finding community structure in mega-scale social networks: [extended abstract]. In: Proceedings of the 16th international conference on world wide web, 2007. ACM Press, pp 1275–1276

  • Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’networks. Nature 393:440–442

    MATH  Google Scholar 

  • Wong PC, Foote H, Mackey P, Chin G, Huang Z, Thomas J (2012) A space-filling visualization technique for multivariate small-world graphs. IEEE Trans Vis Comput Graph 18:797–809

    Google Scholar 

  • Yang Z, Chen W (2018) A game theoretic model for the formation of navigable small-world networks—the tradeoff between distance and reciprocity. ACM Trans Internet Technol 18:1–38

    Google Scholar 

  • Zuo X-N, Ehmke R, Mennes M, Imperati D, Castellanos FX, Sporns O, Milham MP (2012) Network centrality in the human functional connectome. Cereb Cortex 22:1862–1875

    Google Scholar 

Download references

Acknowledgements

The authors thank the anonymous referees for comments that improved the content as well as the presentation of this paper. This work has been supported in part by Ministry of Science and Technology, Taiwan, under Grants MOST 105-2628-E-009-002-MY3 and MOST 106-2221-E-009-101-MY3, and the Ministry of Education, Taiwan, under the Higher Education Sprout Project.

Author information

Authors and Affiliations

  1. Department of Industrial Engineering and Management, National Chiao Tung University, Hsinchu, 300, Taiwan

    Chun-Cheng Lin & Sheng-Feng Wu

  2. Faculty of Transdisciplinary Innovation, University of Technology Sydney, Ultimo, NSW, 2007, Australia

    Weidong Huang

  3. Department of Forestry, National Chung Hsing University, Taichung, 402, Taiwan

    Wan-Yu Liu

  4. Innovation and Development Center of Sustainable Agriculture, National Chung Hsing University, Taichung, 402, Taiwan

    Wan-Yu Liu

Authors
  1. Chun-Cheng Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Weidong Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wan-Yu Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Sheng-Feng Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wan-Yu Liu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lin, CC., Huang, W., Liu, WY. et al. A novel centrality-based method for visual analytics of small-world networks. J Vis 22, 973–990 (2019). https://doi.org/10.1007/s12650-019-00582-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12650-019-00582-5

Keywords

Search

Navigation