A multilevel algorithm for force-directed graph drawing

We describe a heuristic method for drawing graphs which uses a multilevel technique combined with a force-directed placement algorithm. The multilevel process groups vertices to form clusters, uses the clusters to define a new graph and is repeated until the graph size falls below some threshold. The coarsest graph is then given an initial layout and the layout is successively refined on all the graphs starting with the coarsest and ending with the original. In this way the multilevel algorithm both accelerates and gives a more global quality to the force- directed placement. The algorithm can compute both 2 & 3 dimensional layouts and we demonstrate it on a number of examples ranging from 500 to 225,000 vertices. It is also very fast and can compute a 2D layout of a sparse graph in around 30 seconds for a 10,000 vertex graph to around 10 minutes for the largest graph. This is an order of magnitude faster than recent implementations of force-directed placement algorithms.

Statistical investigations - drawing it all together

The author's approach to teaching an integrative unit to a small group of master’s level Applied Statistics students in 2000-2001 is described. Details of the various activities such as data analysis, reading and discussion of papers, and training in consultancy skills are given, as also are details of the assessment. The students’ and lecturer’s views of the unit are discussed.

A multilevel algorithm for force-directed graph-drawing

We describe a heuristic method for drawing graphs which uses a multilevel framework combined with a force-directed placement algorithm. The multilevel technique matches and coalesces pairs of adjacent vertices to define a new graph and is repeated recursively to create a hierarchy of increasingly coarse graphs, G0, G1, …, GL. The coarsest graph, GL, is then given an initial layout and the layout is refined and extended to all the graphs starting with the coarsest and ending with the original. At each successive change of level, l, the initial layout for Gl is taken from its coarser and smaller child graph, Gl+1, and refined using force-directed placement. In this way the multilevel framework both accelerates and appears to give a more global quality to the drawing. The algorithm can compute both 2 & 3 dimensional layouts and we demonstrate it on examples ranging in size from 10 to 225,000 vertices. It is also very fast and can compute a 2D layout of a sparse graph in around 12 seconds for a 10,000 vertex graph to around 5-7 minutes for the largest graphs. This is an order of magnitude faster than recent implementations of force-directed placement algorithms.

Drawing the net: internet identification, internet use, and the image of internet users

Theory and research suggest that Internet identification may account for some of the gender divide in Internet use. Internet identification is a type of domain identification, and is inherently bound with images of those who use the Internet, a domain traditionally conceived as masculine. Combining the “draw an Internet user” test with an Internet identification scale, this study tests two hypotheses: participants drawing gender-concordant images will (i) identify with and (ii) use the Internet more than those drawing gender-discordant images. Participants were 371 students (121 males, 250 females) from three universities in the United Kingdom and Australia. The need to challenge masculinized images of the Internet is discussed.

Tono-Pen determination of intraocular pressure in patients with band keratopathy or glued cornea

Aims. To evaluate the intraocular pressure (IOP) measurements in patients with band keratopathy or glued corneas obtained from affected and non-affected areas. Methods. 15 patients with band keratopathy or glued corneas were prospectively recruited. When both eyes were affected, only the right eye was analysed. Tono-Pen readings of IOP were obtained sequentially from the affected and non-affected corneal surface. Additionally, Goldmann applanation tonometry was attempted. Results. Determination of IOP with the Tono-Pen was possible in all cases, while Goldmann tonometry was not performed in three patients because of severe corneal irregularities. The average of the Tono-Pen readings obtained from the affected cornea (34.8 (SD 14.0) mmHg) was consistently and significantly higher (p <0.001) than mean IOP obtained by the Tono-Pen from the non-affected area (14.8 (4.3) mmHg). The average of Goldmann tonometry readings (14.4 (6.1) mmHg) did not differ significantly from the Tono-Pen values obtained from the non-affected corneal area (p = 0.47) but was significantly lower than the Tono-Pen measurements obtained from the affected area (p <0.001) Conclusion. In patients with band keratopathy or glued corneas determination of IOP by Tono-Pen tonometry varies from affected to non-affected area. The Tono-Pen overestimates the level of IOP when it is applied to areas with band keratopathy or with glue.

Children drawing their own conclusions: Children’s perceptions of a ‘post-conflict’ society

In societies emerging from conflict/war, sustained occurrence of violence appears to be a common feature. In Northern Ireland, while incidents of violent deaths and injuries specifically related to the political conflict have decreased dramatically since 1998, regular riots and paramilitary activity confirm continuing division and conflict. The study described here explored children’s perceptions of their own lives and their predecessors’ lives in the country, through a draw-and-tell technique (n=179). While multiple positive elements of peace/hope were depicted by the majority of children, especially in the pictures portraying the present, negative elements and violent references mostly appeared in the pictures representing the past. Violence was more likely to be portrayed by boys, older children, and those attending segregated education.