The accurate prediction of cancer from microscopic biopsy images has always been a major challenge for medical practitioners and pathologists who manually observe the shape and structure of the cells from tissues under a microscope. Mathematical modelling of cell proliferation helps to predict tumour sizes and optimizes the treatment procedure. This paper introduces a cell growth estimation function that uncovers the growth behaviour of benign and malignant cells. To analyse the cellular level information from tissue images, we propose a minimized cellular graph (MCG) development method. The method extracts cells and produces different features that are useful in classifying benign and malignant tissues. The method’s graphical features enable a precise and timely exploration of huge amounts of data and can help in making predictions and informed decisions. This paper introduces an algorithm for constructing a minimized cellular graph which reduces the computational complexity. A comparative study is performed based on the state-of-the-art classifiers, SVM, decision tree, random forest, nearest neighbor, LDA, Naive Bayes, and ANN. The experimental data are obtained from the BreakHis dataset, which contains 2480 benign and 5429 malignant histopathological images. The proposed technique achieves a 97.7% classification accuracy which is 7% higher than that of the other graph feature-based classification methods. A comparative study reveals a performance improvement for breast cancer classification compared to the state-of-the-art techniques.