Compressed Adjacency Matrices: Untangling Gene Regulatory Networks
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We present a novel technique-Compressed Adjacency Matrices-for visualizing gene regulatory networks. These directed networks have strong structural characteristics: out-degrees with a scale-free distribution, in-degrees bound by a low maximum, and few and small cycles. Standard visualization techniques, such as node-link diagrams and adjacency matrices, are impeded by these network characteristics. The scale-free distribution of out-degrees causes a high number of intersecting edges in node-link diagrams. Adjacency matrices become space-inefficient due to the low in-degrees and the resulting sparse network. Compressed adjacency matrices, however, exploit these structural characteristics. By cutting open and rearranging an adjacency matrix, we achieve a compact and neatly-arranged visualization. Compressed adjacency matrices allow for easy detection of subnetworks with a specific structure, so-called motifs, which provide important knowledge about gene regulatory networks to domain experts. We summarize motifs commonly referred to in the literature, and relate them to network analysis tasks common to the visualization domain. We show that a user can easily find the important motifs in compressed adjacency matrices, and that this is hard in standard adjacency matrix and node-link diagrams. We also demonstrate that interaction techniques for standard adjacency matrices can be used for our compressed variant. These techniques include rearrangement clustering, highlighting, and filtering.Keywords:
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In this paper the properties of node-node adjacency matrix in acyclic digraphs are considered. It is shown that topological ordering and node-node adjacency matrix are closely related. In fact, rst the one to one correspondence between upper triangularity of node-node adjacency matrix and existence of directed cycles in digraphs is proved and then with this correspondence other properties of adjacency matrix in acyclic digraphs are presented.
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In this letter, an eigenspace of network topology is introduced to increase a spatial capacity. The network topology is represented as an adjacency matrix. By an eigenvector of adjacency matrix, efficient two way transmission can be realized in wireless distributed networks. It is confirmed by numerical analysis that the scheme with an eigenvector of adjacency matrix supplies higher spatial capacity and reliability than that of conventional scheme.
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Community identification in large networks is one of the most popular Social Network Analysis applications, and many algorithms have been proposed. The visualisation of the identified structure remains a problem in large networks. The traditional graph-based visualisation does not scale well with many communities and their numerous relations among each other. In this paper, we propose a visualisation based on abstracted adjacency matrices, which scales much better, since there are no overlaps in the two-dimensional matrix. We also propose a couple of enhancements and tweaks to get the best possible user experience with this approach.
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