  Multi-qubit graph states generated by the action of controlled phase shift
operators on a separable quantum state of a system, in which all the qubits are
in arbitrary identical states, are examined. The geometric measure of
entanglement of a qubit with other qubits is found for the graph states
represented by arbitrary graphs. The entanglement depends on the degree of the
vertex representing the qubit, the absolute values of the parameter of the
phase shift gate, and the parameter of state the gate is acting on. Also, the
geometric measure of entanglement of the graph states is quantified on the
quantum computer $\textrm{ibmq\_athens}$. The results obtained on the quantum
device are in good agreement with analytical ones.
