Visualizing Fuzzy Overlapping Communities in Networks

Abstract

An important feature of networks for many application domains is their community structure. This is because objects within the same community usually have at least one property in common. The investigation of community structure can therefore support the understanding of object attributes from the network topology alone. In real-world systems, objects may belong to several communities at the same time, i.e., communities can overlap. Analyzing fuzzy community memberships is essential to understand to what extent objects contribute to different communities and whether some communities are highly interconnected. We developed a visualization approach that is based on node-link diagrams and supports the investigation of fuzzy communities in weighted undirected graphs at different levels of detail. Starting with the network of communities, the user can continuously drill down to the network of individual nodes and finally analyze the membership distribution of nodes of interest. Our approach uses layout strategies and further visual mappings to graphically encode the fuzzy community memberships. The usefulness of our approach is illustrated by two case studies analyzing networks of different domains: social networking and biological interactions. The case studies showed that our layout and visualization approach helps investigate fuzzy overlapping communities. Fuzzy vertices as well as the different communities to which they belong can be easily identified based on node color and position.

Improving data exploration in graphs with fuzzy logic and large-scale visualisation

“…There have also been several previous proposals on visualising fuzzy rules and data [29,30,31,32]. However, to the best of our knowledge, ours is the first attempt at applying fuzzy mechanisms in large-scale visualisation with the aim of highlighting relevant aspects, and improving the data exploration process.…”

Oriented relative fuzzy connectedness: theory, algorithms, and its applications in hybrid image segmentation methods

“…The images were taken from 20 normal subjects from both genders, in the age range from 16 to 49 years. The images were acquired with a 2T Elscint scanner and at a voxel size of 0.98×0.98×1.00 mm 3 . The cerebellum is connected to the rest of the brain through the brain stem and through its top due to partial volume.…”

“…Within this context, computational methods that make use of graphs as a basic element of study have played a key role in getting innovative solutions in various fields of knowledge, in particular in problem areas of computer vision and information visualization. Recent examples of applications that employ graph analysis in their processing pipelines are easily found in the literature such as: segmentation and classification of images via large-scale graphs [1,2], rearrangement and removal of overlaps in visual layouts, visualization and high-dimensional data clustering [3,4], among others. Thus, the modern theory of graphs is seen today as an indispensable tool to explore, analyze, and process large volumes of information, especially when it comes to digital images and high-dimensional data visualization, in view of its strong theoretical and mathematical support [5].…”

Dual Adjacency Matrix: Exploring Link Groups in Dense Networks

“…An overview of node community visualization can be found in [VRW13]. Many approaches involve node-link diagrams in which community memberships are visualized by layout [VRW13] and color [APF * 06, IMMS09].…”