A complex network approach for nanoparticle agglomeration analysis in nanoscale images

  • Bruno Brandoli Machado
  • Leonardo Felipe Scabini
  • Jonatan Patrick Margarido Orue
  • Mauro Santos de Arruda
  • Diogo Nunes Goncalves
  • Wesley Nunes Goncalves
  • Raphaell Moreira
  • Jose F Rodrigues-JrEmail author
Technology and Application


Complex networks have been widely used in science and technology because of their ability to represent several systems. One of these systems is found in Biochemistry, in which the synthesis of new nanoparticles is a hot topic. However, the interpretation of experimental results in the search of new nanoparticles poses several challenges. This is due to the characteristics of nanoparticle images and due to their multiple intricate properties; one property of recurrent interest is the agglomeration of particles. Addressing this issue, this paper introduces an approach that uses complex networks to detect and describe nanoparticle agglomerates so to foster easier and more insightful analyses. In this approach, each detected particle in an image corresponds to a vertice and the distances between the particles define a criterion for creating edges. Edges are created if the distance is smaller than a radius of interest. Once this network is set, we calculate several discrete measures able to reveal the most outstanding agglomerates in a nanoparticle image. Experimental results using images of scanning tunneling microscopy (STM) of gold nanoparticles demonstrated the effectiveness of the proposed approach over several samples, as reflected by the separability between particles in three usual settings. The results also demonstrated efficacy for both convex and non-convex agglomerates.


Nanoparticle cluster Agglomeration analysis Complex networks Computer simulations 


Compliance with ethical standards

Conflict of interests

The authors declare that they have no conflict of interest.


The authors are thankful to the AG workgroup for the STM images. B. Machado and J. Rodrigues-Jr were partially supported by FAPESP under grants 2011/02918-0 and 2016/02557-0, by CNPq under grant 444985/2014-0, and by funding agency FUNDECT.


  1. A-L Barabasi ZO (2004) Network biology: understanding the cell’s functional organization. Nat Rev Genet 5(2):101–113. doi: 10.1038/nrg1272 CrossRefGoogle Scholar
  2. Antiqueira L, Oliveira-Jr O, da Fontoura Costa L, das Graças Volpe Nunes M (2009) A complex network approach to text summarization. Inf Sci 179(5):584–599. 10.1016/j.ins.2008.10.032, CrossRefGoogle Scholar
  3. B K JHS, LM G, SB L (2011) Experimental considerations on the cytotoxicity of nanoparticles. Nanomedicine 6(5):929–941. doi: 10.2217/nnm.11.77 CrossRefGoogle Scholar
  4. Barabási AL, Albert R (1999) Emergence of scaling in random networks. Science 286(5439):509–512CrossRefGoogle Scholar
  5. Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang DU (2006) Complex networks: structure and dynamics. Phys Rep 424(4):175–308CrossRefGoogle Scholar
  6. Brunelli R (2009) Template matching techniques in computer vision: theory and practice. Wiley PublishingGoogle Scholar
  7. Canny J (1986) A computational approach to edge detection. IEEE Trans Pattern Anal Mach Intell 8(6):679–698. doi: 10.1109/TPAMI.1986.4767851 CrossRefGoogle Scholar
  8. Chen S, Zhao M, Wu G, Yao C, Zhang J (2012) Recent advances in morphological cell image analysis. Comput Math Methods Med 2012:101,536:1–101,536:10. doi: 10.1155/2012/101536 Google Scholar
  9. Costa L, Rodrigues FA, Travieso G, Villas Boas PR (2007) Characterization of complex networks: a survey of measurements. Adv Phys 56(1):167–242CrossRefGoogle Scholar
  10. Ding Y, Bukkapatnam STS (2015) Challenges and needs for automating nano image processing for material characterization. Proc SPIE 9556. Nanoengineering: Fabrication, Properties, Optics, and Devices XII 9556:95,560Z–955,607. doi: 10.1117/12.2186251 Google Scholar
  11. Duda RO, Hart PE (1972) Use of the hough transformation to detect lines and curves in pictures. Commun ACM 15(1):11–15. doi: 10.1145/361237.361242 CrossRefGoogle Scholar
  12. Emin S, Singh SP, Han L, Satoh N, Islam A (2011) Colloidal quantum dot solar cells. Solar Energy 85(6):1264–1282. doi: 10.1016/j.solener.2011.02.005. CrossRefGoogle Scholar
  13. Erdos P, Renyi A (1960) On the evolution of random graphs. Publ Math Inst Hungar Acad Sci 5:17–61Google Scholar
  14. Eustace J, Wang X, Cui Y (2015) Community detection using local neighborhood in complex networks. Physica A 436:665–677. doi: 10.1016/j.physa.2015.05.044, CrossRefGoogle Scholar
  15. Fisker R, Carstensen J, Hansen M, Bødker F, Mørup S (2000) Estimation of nanoparticle size distributions by image analysis. J Nanopart Res 2(3):267–277. doi: 10.1023/A:1010023316775 CrossRefGoogle Scholar
  16. Gonçalves WN, Martinez AS, Bruno OM (2012) Complex network classification using partially self-avoiding deterministic walks. Chaos: An Interdisciplinary J Nonlinear Sci 22(3):033,139. doi: 10.1063/1.4737515 CrossRefGoogle Scholar
  17. Gonçalves WN, Machado BB, Bruno OM (2015) A complex network approach for dynamic texture recognition. Neurocomputing 153:211–220. doi: 10.1016/j.neucom.2014.11.034, CrossRefGoogle Scholar
  18. Hassellöv M, Kaegi R (2009) Analysis and characterization of manufactured nanoparticles in aquatic environments Environmental and Human Health Impacts of Nanotechnology. Wiley, pp 211–266. doi: 10.1002/9781444307504.ch6
  19. Kaue Dalmaso Peron T, da Fontoura Costa L, Rodrigues FA (2012) The structure and resilience of financial market networks. Chaos 22(1):013,117CrossRefGoogle Scholar
  20. Kim DA, Hwong AR, Stafford D, Hughes DA, O’Malley AJ, Fowler JH, Christakis NA (2015) Social network targeting to maximise population behaviour change: a cluster randomised controlled trial. The Lancet 386(9989):145–153. doi: 10.1016/S0140-6736(15)60095-2. CrossRefGoogle Scholar
  21. Larsen RJ, Marx ML (2012) An introduction to mathematical statistics and its applications, 5th ed. Prentice Hall, Boston, MAGoogle Scholar
  22. Li X, Wang L, Fan Y, Feng Q, Cui F (2012) Biocompatibility and toxicity of nanoparticles and nanotubes. J Nanomater 2012:6–6. doi: 10.1155/2012/548389 Google Scholar
  23. Liao M, Qian Zhao Y, Hua Li X, Shan Dai P, Wen Xu X, Kai Zhang J, Ji Zou B (2016) Automatic segmentation for cell images based on bottleneck detection and ellipse fitting. Neurocomputing 173(3):615–622. doi: 10.1016/j.neucom.2015.08.006, CrossRefGoogle Scholar
  24. Lorenz C, Goetz NV, Scheringer M, Wormuth M, Hungerbühler K (2011) Potential exposure of german consumers to engineered nanoparticles in cosmetics and personal care products. Nanotoxicology 5(1):12–29. doi: 10.3109/17435390.2010.484554 CrossRefGoogle Scholar
  25. MC Jones JAR (1992) Displaying the important features of large collections of similar curves. Am Stat 46(2):140–145. Google Scholar
  26. Masciangioli T, Zhang WX (2003) Peer reviewed: environmental technologies at the nanoscale. Environ Sci Technol 37(5):102A–108A. doi: 10.1021/es0323998 CrossRefGoogle Scholar
  27. Muneesawang P, Sirisathitkul C (2015) Size measurement of nanoparticle assembly using multilevel segmented tem images. J Nanomater 2015:58:58–58:58. doi: 10.1155/2015/790508 CrossRefGoogle Scholar
  28. Muneesawang P, Sirisathitkul C, Sirisathitkul Y (2015) Multi-level segmentation procedure for measuring the size distribution of nanoparticles in transmission electron microscope images. Sci Adv Mater 7(4):769–783. doi: 10.1166/sam.2015.1930 CrossRefGoogle Scholar
  29. Newman ME (2004) Who is the best connected scientist?a study of scientific coauthorship networks. In: Ben-Naim E, Frauenfelder H, Toroczkai Z (eds) Complex Networks, Lecture Notes in Physics, vol 650, Springer Berlin Heidelberg, pp 37–370. doi: 10.1007/978-3-540-44485-5_16
  30. Park C, Huang JZ, Huitink D, Kundu S, Mallick BK, Liang H, Ding Y (2012) A multi-stage, semi-automated procedure for analyzing the morphology of nanoparticles. IIE Trans 7:507–522. doi: 10.1080/0740817X.2011.587867 CrossRefGoogle Scholar
  31. Park C, Huang J, Ji J, Ding Y (2013) Segmentation, inference and classification of partially overlapping nanoparticles. IEEE Trans Pattern Anal Mach Intell 35(3):669–681. doi: 10.1109/TPAMI.2012.163 Google Scholar
  32. Porter A, Rafols I (2009) Is science becoming more interdisciplinary? measuring and mapping six research fields over time. Scientometrics 81(3):719–745. doi: 10.1007/s11192-008-2197-2 CrossRefGoogle Scholar
  33. Sugahara KN, Teesalu T, Karmali PP, Kotamraju VR, Agemy L, Girard OM, Hanahan D, Mattrey RF, Ruoslahti E (2009) Tissue-penetrating delivery of compounds and nanoparticles into tumors. Cancer Cell 16(6):510–520. doi: 10.1016/j.ccr.2009.10.013. CrossRefGoogle Scholar
  34. Tan PN, Steinbach M, Kumar V (2005) Introduction to data mining. Addison-Wesley Longman Publishing Co., Inc., BostonGoogle Scholar
  35. Tenenbaum JB, Silva Vd, Langford JC (2000) A global geometric framework for nonlinear dimensionality reduction. Science 290(5500):2319–2323. doi: 10.1126/science.290.5500.2319, CrossRefGoogle Scholar
  36. Tyler JR, Wilkinson DM, Huberman BA (2003) Communities and technologies. Kluwer, B.V., Deventer, The Netherlands, The Netherlands, pp 81–96.
  37. Van Doren EA, De Temmerman PJR, Francisco MAD, Mast J (2011) Determination of the volume-specific surface area by using transmission electron tomography for characterization and definition of nanomaterials. J Nanobiotechnol 9(1):1CrossRefGoogle Scholar
  38. Vural U, Oktay A (2014) Segmentation of fe3o4 nano particles in tem images Signal Processing and Communications Applications Conference (SIU), 2014 22nd, IEEE Computer Library, pp 1849–1852. doi: 10.1109/SIU.2014.6830613 Google Scholar
  39. Watts DJ, Strogatz SH (1998) Collective dynamics of ’small-world’ networks. Nature 393 (6684):440–442CrossRefGoogle Scholar
  40. Zhang T, Jia W, Zhu Y, Yang J (2015) Automatic tracking of neural stem cells in sequential digital images. Biocybernetics Biomed Eng 36(1):66–75. doi: 10.1016/j.bbe.2015.10.001, CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  • Bruno Brandoli Machado
    • 1
  • Leonardo Felipe Scabini
    • 1
  • Jonatan Patrick Margarido Orue
    • 1
  • Mauro Santos de Arruda
    • 1
  • Diogo Nunes Goncalves
    • 1
  • Wesley Nunes Goncalves
    • 1
  • Raphaell Moreira
    • 2
  • Jose F Rodrigues-Jr
    • 3
    Email author
  1. 1.CS DepartmentFederal University of Mato Grosso do SulPonta PoraBrazil
  2. 2.Freie Universitat BerlinTakustr 3BerlinGermany
  3. 3.CS DepartmentUniversity of Sao PauloSao CarlosBrazil

Personalised recommendations