The enormous amount of data to be represented using large graphs exceeds in some cases the resources of a conventional computer. Edges in particular can take up a considerable amount of memory as compared to the number of nodes. However, rigorous edge storage might not always be essential to be able to draw the needed conclusions. A similar problem takes records with many variables and attempts to extract the most discernible features. It is said that the ``dimension'' of this data is reduced. Following an approach with the same objective in mind, we can map a graph representation to a $k$-dimensional space and answer queries of neighboring nodes mainly by measuring Euclidean distances. The accuracy of our answers would decrease but would be compensated for by fuzzy logic which gives an idea about the likelihood of error. This method allows for reasonable representation in memory while maintaining a fair amount of useful information, and allows for concise embedding in $k$-dimensional Euclidean space as well as solving some problems without having to decompress the graph. Of particular interest is the case where $k=2$. Promising highly accurate experimental results are obtained and reported.

翻译：使用大型图表示海量数据在某些情况下会超出常规计算机的资源限制。与节点数量相比，边尤其会占用大量内存。然而，严格的边存储并非总是得出所需结论的必要条件。类似的问题也出现在处理包含多个变量的记录时，需要提取最显著的特征。这被称为数据的“维度”降低。遵循相同目标的思路，我们可以将图的表示映射到$k$维空间，主要通过测量欧几里得距离来回答关于邻近节点的查询。答案的准确性会降低，但可通过模糊逻辑进行补偿，从而给出误差可能性的概念。该方法在内存中实现合理表示，同时保留相当数量的有用信息，并允许在$k$维欧几里得空间中进行简明嵌入，以及无需解压图即可解决某些问题。特别值得关注的是$k=2$的情况。本文报告了通过实验获得的高精度结果。