Graph analytics is a fast growing and significant field in the visualization and data mining community, which is applied on numerous high-impact applications such as, network security, finance, and health care, providing users with adequate knowledge across various patterns within a given system. Although a series of methods have been developed in the past years for the analysis of unstructured collections of multi-dimensional points, graph analytics has only recently been explored. Despite the significant progress that has been achieved recently, there are still many open issues in the area, concerning not only the performance of the graph mining algorithms, but also producing effective graph visualizations in order to enhance human perception.

The current thesis deals with the investigation of novel methods for graph analytics, in order to enhance data insight. Towards this direction, the current thesis proposes two methods so as to perform graph mining and visualization.

Based on previous works related to graph mining, the current thesis suggests a set of novel graph features that are particularly efficient in identifying the behavioral patterns of the nodes on the graph. The specific features proposed, are able to capture the interaction of the neighborhoods with other nodes on the graph. Moreover, unlike previous approaches, the graph features introduced herein, include information from multiple node neighborhood sizes, thus capture long-range correlations between the nodes, and are able to depict the behavioral aspects of each node with high accuracy. Experimental evaluation on multiple datasets, shows that the use of the proposed graph features for the graph mining procedure, provides better results than the use of other state-of-the-art graph features.

Thereafter, the focus is laid on the improvement of graph visualization methods towards enhanced human insight. In order to achieve this, the current thesis uses non-linear deformations so as to reduce visual clutter. Non-linear deformations have been previously used to magnify significant/cluttered regions in data or images for reducing clutter and enhancing the perception of patterns. Extending previous approaches, this work introduces a hierarchical approach for non-linear deformation that aims to reduce visual clutter by magnifying significant regions, and leading to enhanced visualizations of one/two/three-dimensional datasets. In this context, an energy function is utilized, which aims to determine the optimal deformation for every local region in the data, taking the information from multiple single-layer significance maps into consideration. The problem is subsequently transformed into an optimization problem for the minimization of the energy function under specific spatial constraints. Extended experimental evaluation provides evidence that the proposed hierarchical approach for the generation of the significance map surpasses current methods, and manages to effectively identify significant regions and deliver better results.

The thesis is concluded with a discussion outlining the major achievements of the current work, as well as some possible drawbacks and other open issues of the proposed approaches that could be addressed in future works.