Typed metagraphs are defined as hypergraphs with types assigned to hyperedges and their targets, and the potential to have targets of hyperedges connect to whole links as well as targets. Directed typed metagraphs (DTMGs) are introduced via partitioning the targets of each edge in a typed metagraph into input, output and lateral sets; one can then look at "metapaths" in which edges' output-sets are linked to other edges' input-sets. An initial algebra approach to DTMGs is presented, including introduction of constructors for building up DTMGs and laws regarding relationships among multiple ways of using these constructors. A menagerie of useful morphism types is then defined on DTMGs (catamorphisms, anamorphisms, histomorphisms, futumorphisms, hylomorphisms, chronomorphisms, metamorphisms and metachronomorphisms), providing a general abstract framework for formulating a broad variety of metagraph operations. Deterministic and stochastic processes on typed metagraphs are represented in terms of forests of DTMGs defined over a common TMG, where the various morphisms can be straightforwardly extended to these forests. The framework outlined can be applied to realistic metagraphs involving complexities like dependent and probabilistic types, multidimensional values and dynamic processing including insertion and deletion of edges.

翻译：类型元体被定义为具有指定用于高科技及其目标的类型的超光谱及其目标,以及具有将高科技目标与整个链接和目标连接在一起的高级目标的可能性。 定向打字元体(DTMGs)通过在输入、输出和横向组合中将每个边缘的目标分隔成一个输入、 输出和横向元体; 然后可以查看“ 元虫”,其中边缘输出群与其他边缘输入群相联系。 介绍了对DTMGs的初步代数法方法,包括引入构建DTMGs的构件和关于使用这些构建器的多种方式之间关系的法律。 定向打字元体元体(DTMGs) 通过在输入、输出和横向组合中区分每个边缘的目标; 然后可以查看“ 元体”, 边缘输出群与其他边缘的输入群连接。 对DMGsmalimal Form Form, 包括直流型MGMG 格式定义的磁体和直立型结构框架, 可以在这些直态的森林中, 将这些直态型型型变形变法化和直态的图状框架的图解过程加以扩展。