  Adjacency between two vertices in graphs or hypergraphs is a pairwise
relationship. It is redefined in this article as 2-adjacency. In general
hypergraphs, hyperedges hold for $n$-adic relationship. To keep the $n$-adic
relationship the concepts of $k$-adjacency and e-adjacency are defined. In
graphs 2-adjacency and e-adjacency concepts match, just as $k$-adjacency and
e-adjacency do for $k$-uniform hypergraphs. For general hypergraphs these
concepts are different. This paper also contributes in a uniformization process
of a general hypergraph to allow the definition of an e-adjacency tensor,
viewed as a hypermatrix, reflecting the general hypergraph structure. This
symmetric e-adjacency hypermatrix allows to capture not only the degree of the
vertices and the cardinality of the hyperedges but also makes a full separation
of the different layers of a hypergraph.
