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Classification of biological neuron types and networks poses challenges to the full understanding of the brain's organisation and functioning. In this paper, we develop a novel objective classification model of biological neuronal types and networks based on the communication metrics of neurons. This presents advantages against the existing approaches since the mutual information or the delay between neurons obtained from spike trains are more abundant data compare to conventional morphological data. We firstly designed two open-access supporting computational platforms of various neuronal circuits from the Blue Brain Project realistic models, named Neurpy and Neurgen. Then we investigate how the concept of network tomography could be achieved with cortical neuronal circuits for morphological, topological and electrical classification of neurons. We extract the simulated data to many different classifiers (including SVM, Decision Trees, Random Forest, and Artificial Neuron Networks) classifying the specific cell type (and sub-group types) achieving accuracies of up to 70\%. Inference of biological network structures using network tomography reached up to 65\% of accuracy. We also analysed recall, precision and F1score of the classification of five layers, 25 cell m-types, and 14 cell e-types. Our research not only contributes to existing classification efforts but sets the road-map for future usage of cellular-scaled brain-machine interfaces for in-vivo objective classification of neurons as a sensing mechanism of the brain's structure.