ABSTRACT Reduction of Complexity: An Aspect of Network Visualization

Networks are topological structures composed of nodes and arcs. Often, networks are visualized by point symbols and lines illustrating the nodes and the arcs, respectively. As the number of the nodes and links increases, the visual representation of the network needs generalization in order to keep the visual clarity of the image. To solve the problem considered, a methodology to aggregate nodes and links into hypernodes and hyper-links is developed. The algorithm, which is based on an information theoretic approach to reorder the adjacency matrix of the network, can generate hierarchies of hyper-networks. This kind of generalization algorithm can be used to construct images which visualize the main structures of the network. Some case studies demonstrate the algorithm.

Visualization of network structure by the application of hypernodes

AbstractIn the literature several authors describe methods to construct simplified models of networks. These methods are motivated by the need to gain insight into the main properties of medium sized or large networks. The present paper contributes to this research by setting focus on weighted networks, the geographical component of networks and introducing a class of functions to model how the weights propagate from one level of abstraction to the next. Hierarchies of network models can be constructed from reordering of the adjacency matrix of the network; this is how “hypernodes” are derived in the present paper. The hypernode algorithm is explored and it is shown how it can be formulated to handle weighted networks. Weighted networks enable handling the uncertainty or the strength of the components which make up the network. The hypernode algorithm can be run in an iterative manner so that a hierarchy of simplified models of the network can be derived. Some case studies demonstrate the hypernode algorithm. In the first case the algorithm is compared with a similar implementation described in the literature. In the second case an airline dataset is analysed. This study shows that when networks are embedded in the geographical space hypernodes may relate to clusters in the spatial domain. The selection of the visual variables to illustrate the strength of the edges and nodes in a weighted network is discussed