Implement a Graph: Add/Remove Nodes & Edges, Path Search, Cycle Detection

Question

## Problem

Implement a graph supporting `addNode`, `removeNode`, `addEdge`, `removeEdge`, `hasPath(a, b)`, and `hasCycle()`.

## Example
```
addEdge(A,B); addEdge(B,C); hasPath(A,C) -> true; addEdge(C,A); hasCycle() -> true
```

## Constraints
- Directed graph; handle removal of nodes with incident edges

## What Palantir looks for
Clean API and data model; correct DFS for path/cycle. Expect probing on time/space complexity and design choices.