R igraph manual pages

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The Davidson-Harel layout algorithm


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


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)))




The graph to lay out. Edge directions are ignored.


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


Number of iterations to perform in the first phase.


Number of iterations in the fine tuning phase.


Cooling factor.


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


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 for the edge length component of the energy function.


Weight for the edge crossing component of the energy function.


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


Passed to layout_with_dh.


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.


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


Gabor Csardi csardi.gabor@gmail.com


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


## 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 Index]