  Eisenstein-Jacobi (EJ) networks were proposed as an efficient interconnection
network topology for parallel and distributed systems. They are based on
Eisenstein-Jacobi integers modulo $a = a+b\rho$, where $0 \leq a \leq b$, and
they are 6-regular symmetric networks and considered as a generalization of
hexagonal networks. Most of the interconnection networks are modeled as graphs
where the applications and functions of graph theory could be applied to. The
cycles in a graph are one type of communications in interconnection networks
that are considered as a factor to measure the efficiency and reliability of
the networks' topology. The network is said to be panconnected if there are
cycles of length $l$ for all $l = D(u, v), D(u, v)+1, D(u, v)+2, \dots, n-1$
where $D(u, v)$ is the shortest distance between nodes $u$ and $v$ in a given
network. In this paper, we investigate the panconnectivity problem in
Eisenstein-Jacobi networks. The proposed algorithm constructs and proves the
panconnectivity of a given Eisenstein-Jacobi network and its complexity is
$O(n^4)$. Simulation results are given to support the correctness of this work.
