We introduce multiforce, a force-directed layout for multiplex networks, where the nodes of the network are organized into multiple layers and both in-layer and inter-layer relationships among nodes are used to compute node coordinates. The proposed approach generalizes existing work, providing a range of intermediate layouts in-between the ones produced by known methods. Our experiments on real data show that multiforce can keep nodes well aligned across different layers without significantly affecting their internal layouts when the layers have similar or compatible topologies. As a consequence, multiforce enriches the benefits of force-directed layouts by also supporting the identification of topological correspondences between layers.
An extreme case of indirect methods, that we mention for completeness, consists in not visualizing nodes and edges at all but only indirect network properties, such as the degree of the nodes in the different layers or other summary measures @cite_3 @cite_28 @cite_2 . These approaches are complementary to graph drawing, and can also be used in combination with our proposal. Our method belongs to the slicing class, and is different from existing approaches because it allows a balancing of the effects of in-layer and inter-layer relationships.
@cite_28 @cite_3 @cite_2
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Recent studies have shown that the performance of single-image super-resolution methods can be significantly boosted by using deep convolutional neural networks. In this study, we present a novel single-image super-resolution method by introducing dense skip connections in a very deep network. In the proposed network, the feature maps of each layer are propagated into all subsequent layers, providing an effective way to combine the low-level features and high-level features to boost the reconstruction performance. In addition, the dense skip connections in the network enable short paths to be built directly from the output to each layer, alleviating the vanishing-gradient problem of very deep networks. Moreover, deconvolution layers are integrated into the network to learn the upsampling filters and to speedup the reconstruction process. Further, the proposed method substantially reduces the number of parameters, enhancing the computational efficiency. We evaluate the proposed method using images from four benchmark datasets and set a new state of the art. Recent advances in network science allows the modeling and analysis of complex inter-related entities. These entities often interact with each other in a number of different ways. Simple graphs fail to capture these multiple types of relationships requiring more sophisticated mathematical structures. One such structure is multigraph, where entities (or nodes) can be linked to each other through multiple edges. In this paper we describe a new method to manage multiple types of relationships existing in multigraphs. Our approach is based on the concept of pair of nodes (edges) and, in particular, we study how nodes on different layers interact which each other considering the edges they share. We propose a two level strategy that summarizes global local multigraph features. The global view helps us to gain knowledge related to the characteristics of layers and how they interact while the local view provides an analysis of individual layers highlighting edge properties such as cluster structure. Our proposal is complementary to standard node-link diagram and it can be coupled with such techniques in order to intelligently explore multigraphs. The proposed visualization is tested on a real world case study and the outcomes point out the ability of our proposal to discover patterns present in the data. In this paper, we develop methods to ''sample'' a small realistic graph from a large Internet topology. Despite recent activity, modeling and generation of realistic graphs resembling the Internet is still not a resolved issue. All previous work has attempted to grow such graphs from scratch. We address the complementary problem of shrinking an existing topology. In more detail, this work has three parts. First, we propose a number of reduction methods that can be categorized into three classes: (a) deletion methods, (b) contraction methods, and (c) exploration methods. We prove that some of them maintain key properties of the initial graph. We implement our methods and show that we can effectively reduce the nodes of an Internet graph by as much as 70 while maintaining its important properties. Second, we show that our reduced graphs compare favorably against construction-based generators. Finally, we successfully validate the effectiveness of our best methods in an actual performance evaluation study of multicast routing. Apart from its practical applications, the problem of graph sampling is of independent interest. We investigate the readability of node-link diagrams for directed graphs when using partially drawn links instead of showing each link explicitly in its full length. Providing the complete link information between related nodes in a graph can lead to visual clutter caused by many edge crossings. To reduce visual clutter, we draw only partial links. Then, the question arises if such diagrams are still readable, understandable, and interpretable. As a step toward answering this question, we conducted a controlled user experiment with 42 participants to uncover differences in accuracy and completion time for three different tasks: identifying the existence of a direct link, the existence of an indirect connection with one intermediate node, and the node with the largest number of outgoing edges. Furthermore, we compared tapered and traditional edge representations, three different graph sizes, and six different link lengths. In all configurations, the nodes of the graph were placed according to the force-directed layout by Fruchterman and Reingold. One result of this study is that the characteristics of completion times and error rates depend on the type of task. A general observation is that partially drawn links can lead to shorter task completion times, which occurs for nearly all graph sizes, tasks, and both tapered and traditional edge representations. In contrast, there is a tendency toward higher error rates for shorter links, which in fact is task-dependent.