I am not a mathematician and I have a difficulty to formulate a problem in my work in robotics using rigorous mathematical terms.
I have a system which generally consists of $l$ points, $m$ rigid bodies, and $n$ cables. We can write the set of points as $\mathcal{P} = \{p_1, \, p_2, \, \ldots, \, p_l \big\}$ the set of bodies as $\mathcal{B} = \{B_1, \, B_2, \, \ldots, \, B_m \big\}$, and the set of cables as $\mathcal{C} = \{C_1, \, C_2, \, \ldots, \, C_n \big\}$.
A subset $\mathcal{P}_j \subset \mathcal{P}$ defines the points that are attached to body $B_j$, $j \in \{1, \, 2, \, \ldots, \, m \big\}$. The cable $C_k$ is defined by a sequence of points $(p_k)$ and $p_k \in \mathcal{P}$. The points in $(p_k)$ do not have a particular order and may be repeated again in the sequence and also points in two different cables is possible. A cable segment is defined by two consecutive points on a cable.
We have to do operations on point level, body level, cable level, and on segment level.
What is the best structure that can represent the above described system?
colored graph?