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The Davidson-Harel layout algorithm

Description

Place vertices of a graph on the plane, according to the simulated annealing algorithm by Davidson and Harel.

Usage

layout_with_dh(graph, coords = NULL, maxiter = 10, fineiter = max(10,
  log2(vcount(graph))), cool.fact = 0.75, weight.node.dist = 1,
  weight.border = 0, weight.edge.lengths = edge_density(graph)/10,
  weight.edge.crossings = 1 - sqrt(edge_density(graph)),
  weight.node.edge.dist = 0.2 * (1 - edge_density(graph)))

with_dh(...)

Arguments

graph

The graph to lay out. Edge directions are ignored.

coords

Optional starting positions for the vertices. If this argument is not NULL then it should be an appropriate matrix of starting coordinates.

maxiter

Number of iterations to perform in the first phase.

fineiter

Number of iterations in the fine tuning phase.

cool.fact

Cooling factor.

weight.node.dist

Weight for the node-node distances component of the energy function.

weight.border

Weight for the distance from the border component of the energy function. It can be set to zero, if vertices are allowed to sit on the border.

weight.edge.lengths

Weight for the edge length component of the energy function.

weight.edge.crossings

Weight for the edge crossing component of the energy function.

weight.node.edge.dist

Weight for the node-edge distance component of the energy function.

...

Passed to layout_with_dh.

Details

This function implements the algorithm by Davidson and Harel, see Ron Davidson, David Harel: Drawing Graphs Nicely Using Simulated Annealing. ACM Transactions on Graphics 15(4), pp. 301-331, 1996.

The algorithm uses simulated annealing and a sophisticated energy function, which is unfortunately hard to parameterize for different graphs. The original publication did not disclose any parameter values, and the ones below were determined by experimentation.

The algorithm consists of two phases, an annealing phase, and a fine-tuning phase. There is no simulated annealing in the second phase.

Our implementation tries to follow the original publication, as much as possible. The only major difference is that coordinates are explicitly kept within the bounds of the rectangle of the layout.

Value

A two- or three-column matrix, each row giving the coordinates of a vertex, according to the ids of the vertex ids.

Author(s)

Gabor Csardi csardi.gabor@gmail.com

References

Ron Davidson, David Harel: Drawing Graphs Nicely Using Simulated Annealing. ACM Transactions on Graphics 15(4), pp. 301-331, 1996.

See Also

layout_with_fr, layout_with_kk for other layout algorithms.

Other graph layouts: add_layout_, component_wise, layout_as_bipartite, layout_as_star, layout_as_tree, layout_in_circle, layout_nicely, layout_on_grid, layout_on_sphere, layout_randomly, layout_with_fr, layout_with_gem, layout_with_graphopt, layout_with_kk, layout_with_lgl, layout_with_mds, layout_with_sugiyama, layout_, merge_coords, norm_coords, normalize

Examples


set.seed(42)
## Figures from the paper
g_1b <- make_star(19, mode="undirected") + path(c(2:19, 2)) +
  path(c(seq(2, 18, by=2), 2))
plot(g_1b, layout=layout_with_dh)

g_2 <- make_lattice(c(8, 3)) + edges(1,8, 9,16, 17,24)
plot(g_2, layout=layout_with_dh)

g_3 <- make_empty_graph(n=70)
plot(g_3, layout=layout_with_dh)

g_4 <- make_empty_graph(n=70, directed=FALSE) + edges(1:70)
plot(g_4, layout=layout_with_dh, vertex.size=5, vertex.label=NA)

g_5a <- make_ring(24)
plot(g_5a, layout=layout_with_dh, vertex.size=5, vertex.label=NA)

g_5b <- make_ring(40)
plot(g_5b, layout=layout_with_dh, vertex.size=5, vertex.label=NA)

g_6 <- make_lattice(c(2,2,2))
plot(g_6, layout=layout_with_dh)

g_7 <- graph_from_literal(1:3:5 -- 2:4:6)
plot(g_7, layout=layout_with_dh, vertex.label=V(g_7)$name)

g_8 <- make_ring(5) + make_ring(10) + make_ring(5) +
  edges(1,6, 2,8, 3, 10, 4,12, 5,14,
        7,16, 9,17, 11,18, 13,19, 15,20)
plot(g_8, layout=layout_with_dh, vertex.size=5, vertex.label=NA)

g_9 <- make_lattice(c(3,2,2))
plot(g_9, layout=layout_with_dh, vertex.size=5, vertex.label=NA)

g_10 <- make_lattice(c(6,6))
plot(g_10, layout=layout_with_dh, vertex.size=5, vertex.label=NA)

g_11a <- make_tree(31, 2, mode="undirected")
plot(g_11a, layout=layout_with_dh, vertex.size=5, vertex.label=NA)

g_11b <- make_tree(21, 4, mode="undirected")
plot(g_11b, layout=layout_with_dh, vertex.size=5, vertex.label=NA)

g_12 <- make_empty_graph(n=37, directed=FALSE) +
  path(1:5,10,22,31,37:33,27,16,6,1) + path(6,7,11,9,10) + path(16:22) +
  path(27:31) + path(2,7,18,28,34) + path(3,8,11,19,29,32,35) +
  path(4,9,20,30,36) + path(1,7,12,14,19,24,26,30,37) +
  path(5,9,13,15,19,23,25,28,33) + path(3,12,16,25,35,26,22,13,3)
plot(g_12,  layout=layout_with_dh, vertex.size=5, vertex.label=NA)

[Package igraph version 1.2.4.1 Index]