wolfram mathematica - Re-layout graph after small modification while preserving features of original layout -

is there simple way following in mathematica 8?

1. construct graph, , display using graph layout.
2. modify graph (e.g. add or remove edge or vertex).
3. re-compute layout starting original layout, in such way the "shape" of object more or less preserved. e.g. re-run spring-electric layout algorithm starting coordinates of previous layout.

if graph hasn't changed between 2 displays, layout shouldn't change either (or minimally). using display of new graph or graphplot both acceptable.

edit: in essence need similar layouts similar graphs. obtain similar graphs modifying existing one, may have been laid out, generic solution acceptable.

edit 2: here's example of kind of thing useful. go http://ccl.northwestern.edu/netlogo/models/giantcomponent , click "run in browser" (requires java). click setup click go. can see graph evolve. if in mathematica, each of successive graphs different, , difficult see same graph evolving. in several applications it's quite useful able visualize small changes graph such. if many successive changes done, re-computing layout must, fading or highlighting edges not sufficient. again, example: i'm not trying use mathematica animate graph, or visualize emergence of giant component.

here 2 basic approaches altering graphs in mma 8.0. first relies on highlightgraph , in particular on graphhighlightstyle -> "dehighlighthide". second approach uses vertexcoordinates of graph in future variants of graph.

we'll discuss deletion separately addition because involve different methods.

[p.s. : made several edits answer in make clearer.]

first data:

edges={1\[undirectededge]8,1\[undirectededge]11,1\[undirectededge]18,1\[undirectededge]19,1\[undirectededge]21,1\[undirectededge]25,1\[undirectededge]26,1\[undirectededge]34,1\[undirectededge]37,1\[undirectededge]38,4\[undirectededge]11,4\[undirectededge]12,4\[undirectededge]26,4\[undirectededge]27,4\[undirectededge]47,4\[undirectededge]56,4\[undirectededge]57,4\[undirectededge]96,4\[undirectededge]117,5\[undirectededge]11,5\[undirectededge]18,7\[undirectededge]21,7\[undirectededge]25,7\[undirectededge]34,7\[undirectededge]55,7\[undirectededge]76,8\[undirectededge]11,26\[undirectededge]29,26\[undirectededge]49,26\[undirectededge]52,26\[undirectededge]111,27\[undirectededge]28,27\[undirectededge]51,42\[undirectededge]47,49\[undirectededge]97,51\[undirectededge]96} 

here initial graph:

g = graph[edges, vertexlabels -> "name", imagepadding -> 10,  imagesize -> 500] 

"deleting" graph edge without changing overall appearance of graph.

let's begin remove edge (4,11) located @ center of graph. remainingedgesandvertices contains vertices , initial edges exception of edge (4,11).

remainingedgesandvertices =   join[vertexlist[g],  complement[edgelist[g], {4 \[undirectededge] 11}]] 

let's "delete" (i.e. hide) edge (4,11):

 highlightgraph[g, remainingedgesandvertices, vertexlabels -> "name",     imagepadding -> 10, graphhighlightstyle -> "dehighlighthide",     imagesize -> 500] 

if had removed edge (4, 11) graph have radically changed appearance.

 graph[complement[edges, {4 \[undirectededge] 11}],     vertexlabels -> "name", imagepadding -> 10, imagesize -> 500] 

"adding" graph edge without changing overall appearance of graph.

adding graph edge more challenging. there 2 ways come mind. method used here works backwards. include new edge first in hidden form , uncover later. initial graph hidden, "to-be-added" edge in layout similar of graph "new" edge. reason this: in fact same graph: show different numbers of edges.

g2 = graph[append[edges, 42 \[undirectededge] 37],   vertexlabels -> "name", imagepadding -> 10, imagesize -> 500]  highlightgraph[g2,     join[complement[edgelist[g2], {42 \[undirectededge] 37}],     vertexlist[g2]], vertexlabels -> "name", imagepadding -> 10,     graphhighlightstyle -> "dehighlighthide"] 

now show graph "new edge" added.

this looks different figure 1. seems natural extension of fig. 4.

adding new vertices , edges on-the-fly

there way add edges (and vertices) while maintaining overall appearance. inspired sjoerd wrote in response.

let's reserve point {0,0} future vertex 99. add point vertexcoordinates g2:

vc = vertexcoordinates ->    append[absoluteoptions[g2, vertexcoordinates][[2]], {0, 0}] 

now let's see looks like. g3 g2 additional vertex (999) , edge (4,99).

g3 = graph[append[edgelist [g2], 4 \[undirectededge] 999], vc,    vertexlabels -> "name", imagepadding -> 10,    graphhighlightstyle -> "dehighlighthide", imagesize -> 500] 

this procedure allows add new edges , vertices move forward. trial , error needed ensure new vertices located in suitable position.

adding edge (without new vertex) easier: add new edge , use vertexcoordinates prior graph.

you should able delete edges graph using same approach (using same vertexcoordinates).