1. Marko Samec (1), Antonio Santiago (2), Juan Pablo Cardenas (2), Rosa Maria Benito (2), Ana Maria Tarquis (3), Sacha Jon Mooney (4), Dean Korošak (1,5) (1) Faculty of Civil Engineering, University of Maribor, Maribor, Slovenia (marko.samec@gmail.com) (2) Grupo de Sistemas Complejos, Departamento de Física, Universidad Politécnica de Madrid, 28040 Madrid, Spain (3) Departamento de Matemática Aplicada, Universidad Politécnica de Madrid, 28040 Madrid, Spain (4) Environmental Sciences Section,University of Nottingham, Nottingham, UK (5) Institute of Physiology, Faculty of Medicine, University of Maribor, Maribor, Slovenia

2. SEE INTODESCRIBEQUANTIFY porous matter

3. SEE INTODESCRIBEQUANTIFY 3D X-ray CT porous matter

4. SEE INTODESCRIBEQUANTIFY complex network theory porous matter

5. SEE INTODESCRIBEQUANTIFY complexity h single parameter porous matter

6. how can one see into the porous structure of material ?

7.  part of x-rays absorbed  higher density of the matter, more X-rays are absorbed  the ones that manage to pass, create image pore space measuring cell solid space

9.  tomography image  crop and scale  contrast  threshold algorithm  binary image

10. sample average pore size [mm 2 ] perimeter [mm] porosity [%] circularity cement 0 h0,0009460,1302804,700,69937 cement 2 h0,0009450,1230512,700,72173 cement 24 h0,0009230,1270104,110,70707 clay 0 h0,0033310,2238840,830,68927 clay 2 h0,0040220,2474811,000,68024 clay 24 h0,0034970,2339201,010,66495 SC 0 days0,0042850,2418322,560,66450 SC 14 days0,0024550,1918622,890,68797 SC 28 days0,0038840,2529682,780,67895

11. how can one describe the porous structure of material ?

12.  Seven Bridges of Königsberg, Euler (1735)  sociogram, Moreno (1993)  p53 gene network, Volgestein et al. (2000)  medicine, biology, computer science, particle physics, economics, sociology, ecology, epidemology, neuroscience,...

13.  node or vertex  link or edge  direction  weight  node degree  degree distribution 110010 101010 010100 001011 110100 000100

14.  Erdos-Renyi network (random linking)  scale-free networks (preferential linking) degree distribution

15. Cumulative size distributions, determined from X-CT images of different porosity φ. All samples show scale-free behaviour of size distribution (solid line) with the exponent α=1,8-2.

16.  threshold network model (SN)  preferential attachement model (EN) the network heterogeneity can be adjusted by changing the parameters b and m

17. can one quantify different porous structure of material ?

18. correlation matrices to further explore the effect of the network parameter m on node correlations we calculated the complexity h of the pore network based on node-node link correlations

20. by combining X-ray CT and complex network models we can quantify complexity of porous structure with single parameter

21. Marko Samec (1), Antonio Santiago (2), Juan Pablo Cardenas (2), Rosa Maria Benito (2), Ana Maria Tarquis (3), Sacha Jon Mooney (4), Dean Korošak (1,5) (1) Faculty of Civil Engineering, University of Maribor, Maribor, Slovenia (marko.samec@gmail.com) (2) Grupo de Sistemas Complejos, Departamento de Física, Universidad Politécnica de Madrid, 28040 Madrid, Spain (3) Departamento de Matemática Aplicada, Universidad Politécnica de Madrid, 28040 Madrid, Spain (4) Environmental Sciences Section,University of Nottingham, Nottingham, UK (5) Institute of Physiology, Faculty of Medicine, University of Maribor, Maribor, Slovenia