最近，有许多关注于顶点集为群的图，其定义基于群结构。（交换图，其中两个元素如果交换则相连，是最早和最著名的例子。）本文的目的在于研究将此类图的定义扩展到一般代数（在普遍代数意义上）的可行性。似乎很难为交换图或其他如 nilpotency 和 Engel 图制定这样的定义。然而，对于定义依赖于由子集生成的子群或子代数的图，现有的定义无需更改即可使用。这些图包括几个已被深入研究的例子：幂图、增强幂图、生成图、独立图和秩图。在这些情况下，一些关于群的结果可以扩展到任意代数而无需更改，但其他结果则需要群的特定性质，并对研究者提出了挑战。在接下来的两节中，我将描述一些扩展到有向图（定向幂图和内射有向图）和到简单复形（独立和强独立复形）的情况。最后一节给出独立代数上所有这些对象的显式描述。
英文摘要：
There has been a great deal of attention recently to graphs whose vertex set is a group, defined using the group structure. (The commuting graph, where two elements are joined if they commute, is the oldest and most famous example.)
The purpose of this paper is to investigate extending the definitions of such graphs to general algebras (in the sense of universal algebra). It seems unlikely that such a definition can be made for the commuting graph, or for various others such as the nilpotency and Engel graphs. However, for graphs whose definition depends on the notion of subgroup or subalgebra generated by a subset, the existing definitions work without change. These graphs include several well-studied examples: the power graph, enhanced power graph, generating graph, independence graph, and rank graph. In these cases, some results about groups extend to arbitrary algebras unchanged, but others require specific properties of groups, and pose a challenge to researchers.
In the next two sections, I will describe some extensions to directed graphs (the directed power graph and the endomorphism digraph) and to simplicial complexes (the independence and strong independence complexes). The final section gives explicit descriptions of all of these objects for independence algebras.
