An algorithm for drawing general undirected graphs
About: This article is published in Information Processing Letters.The article was published on 1989-04-12. It has received 2703 citations till now. The article focuses on the topics: Indifference graph & Chordal graph.
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01 Jan 2006
TL;DR: Platform-independent and open source igraph aims to satisfy all the requirements of a graph package while possibly remaining easy to use in interactive mode as well.
Abstract: There is no other package around that satisfies all the following requirements: •Ability to handle large graphs efficiently •Embeddable into higher level environments (like R [6] or Python [7]) •Ability to be used for quick prototyping of new algorithms (impossible with “click & play” interfaces) •Platform-independent and open source igraph aims to satisfy all these requirements while possibly remaining easy to use in interactive mode as well.
8,850 citations
TL;DR: VOSviewer’s ability to handle large maps is demonstrated by using the program to construct and display a co-citation map of 5,000 major scientific journals.
Abstract: We present VOSviewer, a freely available computer program that we have developed for constructing and viewing bibliometric maps. Unlike most computer programs that are used for bibliometric mapping, VOSviewer pays special attention to the graphical representation of bibliometric maps. The functionality of VOSviewer is especially useful for displaying large bibliometric maps in an easy-to-interpret way. The paper consists of three parts. In the first part, an overview of VOSviewer’s functionality for displaying bibliometric maps is provided. In the second part, the technical implementation of specific parts of the program is discussed. Finally, in the third part, VOSviewer’s ability to handle large maps is demonstrated by using the program to construct and display a co-citation map of 5,000 major scientific journals.
7,719 citations
Cites methods from "An algorithm for drawing general un..."
...For constructing graph-based maps, researchers in the field of bibliometrics (e.g., de Moya-Anegón et al. 2007; Leydesdorff and Rafols 2009; Vargas-Quesada and de MoyaAnegón 2007; White 2003) usually use a mapping technique developed by Kamada and Kawai (1989)....
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...The map shown in Fig. 2 is a graph-based map constructed using the Kamada‐Kawai technique ( Kamada and Kawai 1989 )....
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...Moya-Anego ´n et al. 2007; Leydesdorff and Rafols 2009; Vargas-Quesada and de Moya-Anego ´n 2007; White 2003) usually use a mapping technique developed by Kamada and Kawai (1989) ....
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...2 is a graph-based map constructed using the Kamada–Kawai technique (Kamada and Kawai 1989)....
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TL;DR: A modification of the spring‐embedder model of Eades for drawing undirected graphs with straight edges is presented, developed in analogy to forces in natural systems, for a simple, elegant, conceptually‐intuitive, and efficient algorithm.
Abstract: SUMMARY We present a modification of the spring-embedder model of Eades [ Congresses Numerantium, 42, 149–160, (1984)] for drawing undirected graphs with straight edges. Our heuristic strives for uniform edge lengths, and we develop it in analogy to forces in natural systems, for a simple, elegant, conceptuallyintuitive, and efficient algorithm.
5,242 citations
TL;DR: Network phenomena appear to be relevant to the biologic and behavioral trait of obesity, and obesity appears to spread through social ties, which has implications for clinical and public health interventions.
Abstract: Background The prevalence of obesity has increased substantially over the past 30 years. We performed a quantitative analysis of the nature and extent of the person-to-person spread of obesity as a possible factor contributing to the obesity epidemic. Methods We evaluated a densely interconnected social network of 12,067 people assessed repeatedly from 1971 to 2003 as part of the Framingham Heart Study. The bodymass index was available for all subjects. We used longitudinal statistical models to examine whether weight gain in one person was associated with weight gain in his or her friends, siblings, spouse, and neighbors. Results Discernible clusters of obese persons (body-mass index [the weight in kilograms divided by the square of the height in meters], ≥30) were present in the network at all time points, and the clusters extended to three degrees of separation. These clusters did not appear to be solely attributable to the selective formation of social ties among obese persons. A person’s chances of becoming obese increased by 57% (95% confidence interval [CI], 6 to 123) if he or she had a friend who became obese in a given interval. Among pairs of adult siblings, if one sibling became obese, the chance that the other would become obese increased by 40% (95% CI, 21 to 60). If one spouse became obese, the likelihood that the other spouse would become obese increased by 37% (95% CI, 7 to 73). These effects were not seen among neighbors in the immediate geographic location. Persons of the same sex had relatively greater influence on each other than those of the opposite sex. The spread of smoking cessation did not account for the spread of obesity in the network. Conclusions Network phenomena appear to be relevant to the biologic and behavioral trait of obesity, and obesity appears to spread through social ties. These findings have implications for clinical and public health interventions.
4,783 citations
TL;DR: A novel graph theoretic clustering algorithm, "Molecular Complex Detection" (MCODE), that detects densely connected regions in large protein-protein interaction networks that may represent molecular complexes is described.
Abstract: Recent advances in proteomics technologies such as two-hybrid, phage display and mass spectrometry have enabled us to create a detailed map of biomolecular interaction networks. Initial mapping efforts have already produced a wealth of data. As the size of the interaction set increases, databases and computational methods will be required to store, visualize and analyze the information in order to effectively aid in knowledge discovery. This paper describes a novel graph theoretic clustering algorithm, "Molecular Complex Detection" (MCODE), that detects densely connected regions in large protein-protein interaction networks that may represent molecular complexes. The method is based on vertex weighting by local neighborhood density and outward traversal from a locally dense seed protein to isolate the dense regions according to given parameters. The algorithm has the advantage over other graph clustering methods of having a directed mode that allows fine-tuning of clusters of interest without considering the rest of the network and allows examination of cluster interconnectivity, which is relevant for protein networks. Protein interaction and complex information from the yeast Saccharomyces cerevisiae was used for evaluation. Dense regions of protein interaction networks can be found, based solely on connectivity data, many of which correspond to known protein complexes. The algorithm is not affected by a known high rate of false positives in data from high-throughput interaction techniques. The program is available from ftp://ftp.mshri.on.ca/pub/BIND/Tools/MCODE
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4,599 citations
Cites methods from "An algorithm for drawing general un..."
...We use the Pajek program for large network analysis [40] with the Kamada-Kawai graph layout algorithm [ 41 ]....
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References
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TL;DR: The procedure was originally programmed in FORTRAN for the Control Data 160 desk-size computer and was limited to te t ra t ion because subroutine recursiveness in CONTROL Data 160 FORTRan has been held down to four levels in the interests of economy.
Abstract: procedure ari thmetic (a, b, c, op); in t eger a, b, c, op; ¢ o n l m e n t This procedure will perform different order ar i thmetic operations with b and c, put t ing the result in a. The order of the operation is given by op. For op = 1 addit ion is performed. For op = 2 multiplicaLion, repeated addition, is done. Beyond these the operations are non-commutat ive. For op = 3 exponentiat ion, repeated multiplication, is done, raising b to the power c. Beyond these the question of grouping is important . The innermost implied parentheses are at the right. The hyper-exponent is always c. For op = 4 te t ra t ion, repeated exponentiat ion, is done. For op = 5, 6, 7, etc., the procedure performs pentat ion, hexation, heptat ion, etc., respectively. The routine was originally programmed in FORTRAN for the Control Data 160 desk-size computer. The original program was limited to te t ra t ion because subroutine recursiveness in Control Data 160 FORTRAN has been held down to four levels in the interests of economy. The input parameter , b, c, and op, must be positive integers, not zero; b e g i n own i n t e g e r d, e, f, drop; i f o p = 1 t h e n b e g i n a := h-4c; go t o l e n d i f o p = 2 t h e n d := 0; else d := 1; e := c; drop := op 1; for f := I s t e p 1 u n t i l e do b e g i n ari thmetic (a, b, d, drop);
3,848 citations
01 Feb 1981
TL;DR: Two kinds of new methods are developed to obtain effective representations of hierarchies automatically: theoretical and heuristic methods that determine the positions of vertices in two steps to improve the readability of drawings.
Abstract: Two kinds of new methods are developed to obtain effective representations of hierarchies automatically: theoretical and heuristic methods. The methods determine the positions of vertices in two steps. First the order of the vertices in each level is determined to reduce the number of crossings of edges. Then horizontal positions of the vertices are determined to improve further the readability of drawings. The theoretical methods are useful in recognizing the nature of the problem, and the heuristic methods make it possible to enlarge the size of hierarchies with which we can deal. Performance tests of the heuristic methods and several applications are presented.
1,288 citations
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TL;DR: In this paper, the authors define nodally 3-connected graphs as simple and non-separable graphs, and show how to obtain a convex representation of such graphs without Kuratowski subgraphs.
Abstract: W E use the definitions of (11). However, in deference to some recent attempts to unify the terminology of graph theory we replace the term 'circuit' by 'polygon', and 'degree' by 'valency'. A graph G is 3-connected (nodally 3-connected) if it is simple and non-separable and satisfies the following condition; if G is the union of two proper subgraphs H and K such that HnK consists solely of two vertices u and v, then one of H and K is a link-graph (arc-graph) with ends u and v. It should be noted that the union of two proper subgraphs H and K of G can be the whole of G only if each of H and K includes at least one edge or vertex not belonging to the other. In this paper we are concerned mainly with nodally 3-connected graphs, but a specialization to 3-connected graphs is made in § 12. In § 3 we discuss conditions for a nodally 3-connected graph to be planar, and in § 5 we discuss conditions for the existence of Kuratowski subgraphs of a given graph. In §§ 6-9 we show how to obtain a convex representation of a nodally 3-connected graph, without Kuratowski subgraphs, by solving a set of linear equations. Some extensions of these results to general graphs, with a proof of Kuratowski's theorem, are given in §§ 10-11. In § 12 we discuss the representation in the plane of a pair of dual graphs, and in § 13 we draw attention to some unsolved problems.
1,124 citations
TL;DR: A bibliographic survey on algorithms whose goal is to produce aesthetically pleasing drawings of graphs is presented, a first attempt to encompass both theoretical and application-oriented papers from disparate areas.
Abstract: Several data presentation problems involve drawing graphs so that they are easy to read and understand. Examples include circuit schematics and diagrams for information systems analysis and design. In this paper we present a bibliographic survey on algorithms whose goal is to produce aesthetically pleasing drawings of graphs. Research on this topic is spread over the broad spectrum of computer science. This bibliography constitutes a first attempt to encompass both theoretical and application-oriented papers from disparate areas.
959 citations
03 Jan 1988
TL;DR: The algorithm presented draws graphs on a grid and is suitable for both undirected graphs and mixed graphs that contain as subgraphs hierarchic structures.
Abstract: The state of the art in automatic graph drawing is reviewed, with special attention to the readability of information system diagrams. Existing results in the literature are compared, and a comprehensive algorithmic approach to the problem is proposed. The algorithm presented draws graphs on a grid and is suitable for both undirected graphs and mixed graphs that contain as subgraphs hierarchic structures. Several applications of GIOTTO, a graphic tool that embodies the aforementioned facility, are shown. >
463 citations