  In this paper, as a new notion, we define a transitive system to be a set
system $(V, {\mathcal C}\subseteq 2^V)$ on a finite set $V$ of elements such
that every three sets $X,Y,Z\in{\mathcal C}$ with $Z\subseteq X\cap Y$ implies
$X\cup Y\in{\mathcal C}$, where we call a set $C\in {\mathcal C}$ a component.
We assume that two oracles $\mathrm{L}_1$ and $\mathrm{L}_2$ are available,
where given two subsets $X,Y\subseteq V$, $\mathrm{L}_1$ returns a maximal
component $C\in {\mathcal C}$ with $X\subseteq C\subseteq Y$; and given a set
$Y\subseteq V$, $\mathrm{L}_2$ returns all maximal components $C\in {\mathcal
C}$ with $C\subseteq Y$. Given a set $I$ of attributes and a function
$\sigma:V\to 2^I$ in a transitive system, a component $C\in {\mathcal C}$ is
called a solution if the set of common attributes in $C$ is inclusively
maximal; i.e., $\bigcap_{v\in C}\sigma(v)\supsetneq \bigcap_{v\in X}\sigma(v)$
for any component $X\in{\mathcal C}$ with $C\subsetneq X$. We prove that there
exists an algorithm of enumerating all solutions in delay bounded by a
polynomial with respect to the input size and the running times of the oracles.
The proposed algorithm yields the first polynomial-delay algorithms for
enumerating connectors in an attributed graph and for enumerating all subgraphs
with various types of connectivities such as all $k$-edge/vertex-connected
induced subgraphs and all $k$-edge/vertex-connected spanning subgraphs in a
given undirected/directed graph for a fixed $k$.
