**ABSTRACT**

The Nanocrystaline diamonds are very important biomedical material with variety of applications. The experimental procedures and results have been done in the Institute of Functional Nanosystems at the University Ulm, Germany. There is an existing biocompatibility of the diamond layers, selectively improved by biomimetic 3-D patterns structuring. Based on that, we have been inspired to apply the graph theory approach in analysing and defining the physical parameters within the structure of materials structure samples. Instead the parameters values, characteristic at the samples surface, we penetrate the graphs deeply in the bulk structure. These values could be only, with some probability, distributed through the micro-structure what defines not enough precious parameters values between the micro-structure constituents, grains and pores. So, we originally applied the graph theory to get defined the physical parameters at the grains and pores levels. This novelty, in our paper, we applied for thermophysical parameters, like thermoconductiviy. By graph approach we open new frontiers in controlling and defining the processes at micro-structure relations. In this way, we can easily predict and design the structure with proposed parameters.

**KEYWORDS**

PAPER SUBMITTED: 2021-04-22

PAPER REVISED: 2021-07-21

PAPER ACCEPTED: 2021-07-30

PUBLISHED ONLINE: 2021-10-10

**THERMAL SCIENCE** YEAR

**2022**, VOLUME

**26**, ISSUE

**Issue 3**, PAGES [2177 - 2186]

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