## 1 Introduction  
Over the past two decades, the pace at which humanity has been producing data is increasing continuously [1]. The improvement in data acquisition methods has inevitably led to the availability of high dimensional datasets, especially in applications belonging to domains like pattern recognition, data mining, and computer vision. High dimensional data, not only leads to an increase in execution time and memory requirements it also decreases the performance and restricts the applicability of machine learning methods due to the curse of dimensionality [2, 3]. To mitigate this, various methods exist for reducing features, which can be broadly categorized into two approaches, i.e., feature extraction and feature selection. In feature extraction, the feature set is transformed into a new feature set with lower dimensions. On the contrary, feature selection works on the approach of selecting a subset of features from the original feature set by eliminating redundant or irrelevant features [3]. Moreover, the feature selection approach benefits in retaining the original features of the data, which is advantageous in explaining the model. In general, feature selection is a combinatorial optimization problem [4] that has facilitated various research fields such as data comprehension and visualization [5], DNA microarray analysis [6], text classification [7], and image annotation [8]. The existing feature selection methods can be either supervised [9, 10, 11] or unsupervised [12, 13]. In supervised feature selection, class labels are known beforehand and are part of the context while predicting the label for unlabeled data points. While unsupervised feature selection has no such information at any stage of the feature selection process [14]. Moreover, other categorizations of feature selection methods could be wrapper methods, embeddedmethods, and filter methods [15]. Both wrapper and embedded methods are classifier-dependent and may lead to overfitting, while filter methods are classifier-independent and therefore have better generalization capability [16]. In filter methods, the unsupervised approach to performing feature selection is to rank the features [17; 18; 19; 20; 21; 22; 23; 24]. Rather than automatically selecting a subset of features, this approach provides the flexibility of choosing a number of highest-ranked features that fit within the memory constraints of the system. However, there is no way of knowing the exact number of features in the optimal feature subset other than trial and error. On selecting a higher number of optimal features, the method may add redundant or irrelevant features, which leads to an increase in computational requirements and noise, respectively. On the other hand, by selecting a lower number of optimal features, the method may miss out on relevant or essential features for the complete representation of the data. To determine the same, different graph approaches have been proposed for feature selection [25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37]. [PERSON] et al. [30] used Feature Association Map to present a graph-based hybrid feature selection method. While [PERSON] et al. [34] employed correlation exponential in the graph-based feature selection method. [PERSON] et al. [18] presented a feature-dependency-based unsupervised feature selection (DUFS) method that uses pairwise dependency of the features to perform feature selection. Furthermore, [PERSON] et al. [35] proposed an unsupervised feature selection method that is robust and scalable in performing feature reduction. The presented method uses dissimilarity measures along with clustering algorithms [37] and is tested on a cell imaging dataset. Moreover, [PERSON] et al. [36] proposed a feature selection method by using a bi-objective genetic algorithm with ensemble classifiers. [PERSON] et al. [26] employed the Laplacian score for feature selection (LSFS) wherein the power of locality preservation of a feature is used as a basis for ranking. Multi-cluster feature selection (MCFS), proposed by [PERSON] et al.