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Bipartite Graphs of Small Readability [chapter]

Rayan Chikhi, Vladan Jovičić, Stefan Kratsch, Paul Medvedev, Martin Milanič, Sofya Raskhodnikova, Nithin Varma
2018 Lecture Notes in Computer Science  
We show that the readability of n-vertex bipartite chain graphs is between Ω(log n) and O( √ n).  ...  One of the highlights of our techniques is the appearance of Euler's totient function in the analysis of the readability of bipartite chain graphs.  ...  This completes the proof of Lemma 6. We can now prove Theorem 5, about the readability of G m,n . We first recall the following simple observation (which follows, e.g., from [6, Theorem 4.3]).  ... 
doi:10.1007/978-3-319-94776-1_39 fatcat:57ekv2hgjbdjjjrwxhdftteyju

Readability of digraphs and bipartite graphs [article]

Vladan Jovičić
2016 arXiv   pre-print
Graphs arising in problems related to genome sequencing are of small readability, which motivates the study of graphs of small readability.  ...  The complexity of computing the readability of a given digraph (or of a given bipartite graph) is unknown.  ...  However, with fast ILP solvers, the models can be used to understand the behavior of readability of small graphs and to state hypotheses for readability in general.  ... 
arXiv:1612.07113v1 fatcat:vrikhxd6svcuvniy6ov4nt56lq

Sphere Anchored Map: A Visualization Technique for Bipartite Graphs in 3D [chapter]

Takao Ito, Kazuo Misue, Jiro Tanaka
2009 Lecture Notes in Computer Science  
However, the readability decreases when large-scale graphs are drawn.  ...  Circular anchored maps have been proposed as a drawing technique to acquire knowledge from bipartite graphs, where nodes in one set are arranged on a circumference.  ...  However, conventional visualization techniques for bipartite graphs [1] [2] [3] [4] [5] do not provide enough readability for drawing large-scale graphs.  ... 
doi:10.1007/978-3-642-02577-8_89 fatcat:xcla3tnc3bdz5oscfi3dsj4cfe

Drawing Semi-bipartite Graphs in Anchor+Matrix Style

Kazuo Misue, Qi Zhou
2011 2011 15th International Conference on Information Visualisation  
Anchored map is a graph drawing technique for bipartite graphs and provides aesthetically pleasing layouts of graphs with high readability by restricting the positions of nodes in a partition.  ...  A semi-bipartite graph is a bipartite graph with edges in one partition.  ...  Step 5: For an anchored map of a bipartite graph, each node is expressed at a point (a bullet or a small icon), and each edge is drawn in a line segment.  ... 
doi:10.1109/iv.2011.24 dblp:conf/iv/MisueZ11 fatcat:6exfh3nilvczpau67w2myjcfr4

Drawing Clustered Bipartite Graphs in Multi-circular Style

Takao Ito, Kazuo Misue, Jiro Tanaka
2010 2010 14th International Conference Information Visualisation  
In this technique, nodes in one set of the bipartite graph, which are leaves of a tree, are arranged in hierarchical multi-circular style.  ...  Bipartite graphs are often used to illustrate relationships between two sets of data, such as web pages and visitors.  ...  The relationships of a bipartite graph composed of each cluster are obtained by forming small anchored maps.  ... 
doi:10.1109/iv.2010.13 dblp:conf/iv/ItoMT10 fatcat:5av5lbhmsbbg5ad46bml4xb42a

ArchE: A graph drawing system for archaeology [chapter]

Christoph Hundack, Petra Mutzel, Igor Pouchkarev, Stefan Thome
1997 Lecture Notes in Computer Science  
Apart from archaeological applications, ArchE can be used as a general graph drawing system. * * * {hundazk, mutzel ,pouchkar, thome}©mpi-sb, mpg. de  ...  ArchE checks these data for consistency, simplifies and displays them; for each of these steps ArchE offers a number of different algorithms.  ...  Additionally ArchE includes an algorithm for finding small complete bipartite subgraphs (see [3] ) as the existing complete bipartite subgraphs often possess only few vertices.  ... 
doi:10.1007/3-540-63938-1_72 fatcat:t24acuwmcjc45affyjg3cs67ta

Anchored Map: Graph Drawing Technique to Support Network Mining

K. MISUE
2008 IEICE transactions on information and systems  
The method uses indices to decide the orders of anchors because those orders markedly affect the readability of the network diagrams.  ...  The readability of network diagrams is discussed, anchored maps are proposed, and a method for drawing anchored maps is explained.  ...  For each pair, five bipartite graphs were generated for each of the edgeoccurrence probabilities 0.1, 0.2, and 0.3 (a total of 45 bipartite graphs).  ... 
doi:10.1093/ietisy/e91-d.11.2599 fatcat:csgcs6oagzhstawlk46ojy5qti

Energy-Based Clustering of Graphs with Nonuniform Degrees [chapter]

Andreas Noack
2006 Lecture Notes in Computer Science  
Finding dense subgraphs in such graphs is of great practical interest, as these clusters may correspond to cohesive software modules, semantically related documents, and groups of friends or collaborators  ...  Widely varying node degrees occur in software dependency graphs, hyperlink structures, social networks, and many other real-world graphs.  ...  However, the cut prefers bipartitions that consist of a very small and a very large subgraph, as the following calculation shows.  ... 
doi:10.1007/11618058_28 fatcat:2yomvhdpb5bgjpa6b4if6dawl4

Visualizing Bag-of-Features Image Categorization Using Anchored Maps

Gao Yi, Hsiang-Yun Wu, Kazuo Misue, Kazuyo Mizuno, Shigeo Takahashi
2014 Proceedings of the 7th International Symposium on Visual Information Communication and Interaction - VINCI '14  
Our main idea is to associate each image with a specific number of visual words to compose a bipartite graph, and then lay out the overall set of images using anchored map representation in which the ordering  ...  This paper aims at visually rearrange the images in the projected feature space by taking advantage of a set of representative features called visual words obtained using the bag-of-features model.  ...  In our sparse representation of the bipartite graph, each image usually depends on a small number of visual words.  ... 
doi:10.1145/2636240.2636858 dblp:conf/vinci/YiWMMT14 fatcat:ql25ypcezrffnjxoypgzt6hhwe

Towards Faithful Graph Visualizations [article]

Quan Hoang Nguyen, Peter Eades
2018 arXiv   pre-print
Readability criteria have been addressed as a measurement of the quality of graph visualizations. In this paper, we argue that readability criteria are necessary but not sufficient.  ...  We propose a new kind of criteria, namely faithfulness, to evaluate the quality of graph layouts.  ...  Edge bundling methods ensure that G i is bipartite; suppose that N i = X i ∪ Y i is the bipartition of G i .  ... 
arXiv:1701.00921v2 fatcat:pn4pt56zmzdc3feyqu2bsvodma

A Structural Approach to Disentangle the Visualization of Bipartite Biological Networks

J. Garcia-Algarra, J. M. Pastor, M. L. Mouronte, J. Galeano
2018 Complexity  
These sets of interactions are complex bipartite networks.  ...  We have developed two new types of visualization which exploit the structural properties of these networks to improve readability.  ...  Acknowledgments This work was supported by Ministry of Economy and Competitiveness of Spain (MTM2015-63914-P).  ... 
doi:10.1155/2018/6204947 fatcat:hcjuoija3nee5gesgoaftmwyke

Energy Models for Graph Clustering

Andreas Noack
2007 Journal of Graph Algorithms and Applications  
The cluster structure of many real-world graphs is of great interest, as the clusters may correspond e.g. to communities in social networks or to cohesive modules in software systems.  ...  Layouts can naturally represent the cluster structure of graphs by grouping densely connected nodes and separating sparsely connected nodes.  ...  Readability The primary purpose of most energybased graph layout techniques is to produce easily readable box-and-line visualizations of graphs.  ... 
doi:10.7155/jgaa.00154 fatcat:ylwma7chwvglnghrmrdwpemdza

On the faithfulness of graph visualizations

Quan Nguyen, Peter Eades, Seok-Hee Hong
2013 2013 IEEE Pacific Visualization Symposium (PacificVis)  
Readability criteria have been commonly used to measure the quality of graph visualizations. In this paper we argue that readability criteria, while necessary, are not sufficient.  ...  We propose a new kind of criterion, generically termed faithfulness, for evaluating graph layout methods.  ...  This can be seen as a lack of not only readability but also information faithfulness.  ... 
doi:10.1109/pacificvis.2013.6596147 dblp:conf/apvis/NguyenEH13 fatcat:cadu6oh3kvf6rileinvzg7awie

Multi-document Summarization Using Bipartite Graphs

Daraksha Parveen, Michael Strube
2014 Proceedings of TextGraphs-9: the workshop on Graph-based Methods for Natural Language Processing  
We transform documents into a bipartite graph where one set of nodes represents entities and the other set of nodes represents sentences.  ...  To obtain the summary we apply a ranking technique to the bipartite graph which is followed by an optimization step.  ...  Our method computes importance on the basis of a bipartite graph.  ... 
doi:10.3115/v1/w14-3703 dblp:conf/textgraphs/ParveenS14 fatcat:ntvny3hg45apzk4k27lvwe6q6i

Exploiting the Bipartite Structure of Entity Grids for Document Coherence and Retrieval

Christina Lioma, Fabien Tarissan, Jakob Grue Simonsen, Casper Petersen, Birger Larsen
2016 Proceedings of the 2016 ACM International Conference on the Theory of Information Retrieval - ICTIR '16  
The state of the art in unsupervised coherence modelling represents documents as bipartite graphs of sentences and discourse entities, and then projects these bipartite graphs into one-mode undirected  ...  To address this we present three novel graph metrics that compute document coherence on the original bipartite graph of sentences and entities.  ...  A bipartite graph is a particular class of graph also known as two-mode graph.  ... 
doi:10.1145/2970398.2970413 dblp:conf/ictir/LiomaTSPL16 fatcat:qgqaqyfbtnf3tkzmzizolvhj54
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