An algorithm to draw graphs without checking all pairs of vertices?

Graph drawing algorithms, such as those described here, check all the vertices two-by-two and apply additional forces if two vertices are connected by an edge. If we have a very large graph, checking all pairs of vertices would be costly. Is there any graph drawing algorithm that draws a large graph using only existing edges, not by verifying all possible pairs?

EDIT
By drawing algorithm, I meant an algorithm that assigns a 2D or 3D position to each vertex such that rendering spheres or circles (or any other shape) as vertices at their assigned positions lead to a plausible visual representation of the whole graph.

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检查这个Spring-Electrical Embedding它在O（nlog n）中。

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如果您有稀疏矩阵，您可以考虑将图形创建为邻居列表或者像顶点对那样更简单（例如（1,3）和1和3是顶点数）。

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