How is electromagnetic induction analogous to gravitational frame dragging? This wiki says: https://en.wikipedia.org/wiki/Frame-dragging

Qualitatively, frame-dragging can be viewed as the gravitational
analog of electromagnetic induction.

I was wondering what exactly this means, and the wiki for electromagnetic induction doesn't seem to go into it. I wasn't able to Google anything that shed light on this analogy either.
What does this sentence mean exactly? How is gravitational frame dragging, analogous to electromagnetic induction?
 A: The common factor is that the complete interaction includes velocity-dependent effects.
In the case of electromagnetism: the Lorentz force is velocity-dependent.

Newtonian gravity is purely position dependent, and that has implications for what has to be assumed about the speed of gravity.
A theory of gravity in which gravity is purely position dependent, and with a finite speed of gravity, is a theory that does not comply with the principle of conservation of momentum. (The problem is often referred to as 'force aberration'; with a finite speed of propagation (and pure position dependence) the force does not point instantaneously to the point where the attracting body is.)

Maxwell's equations for the electromagnetic field imply a particular speed for the propagation of the electromagnetic interaction: the speed of light.
Given that it was recognized that electromagnetic interaction propagates at a finite speed physicists began to explore possibilities of formulating a theory of gravity with a finite speed for the propagation of the gravitatitional interaction.
The physicists of the time recognized that a theory of gravity with a finite speed of propagation would have the potential of accounting for the anomalous precession of Mercury.
In order for such a theory to comply with conservation of momentum the interaction must include velocity-dependent effects, in just the right way.
The constraint of compliance with the principle of conservation of momentum narrows down the possibilities. In that sense it is very much a guiding constraint.
Einstein's 1915 General Relativity rendered all previous attempts at formulating finite-speed theory of gravity obsolete.
For more information:
1999 article by Steve Carlip:
'Aberration and the speed of Gravity'
Carlip discusses the interconnections between speed of propagation of an interaction, velocity-dependent effects of the interaction, and the emission of waves.
A: The easiest way to access the idea behind this analogy is to think in 4-vector, we know that the electric and magnetic fields can be represented in one being  $A^{\mu}=(\phi/c, \vec{A})$ with $ \vec{B}=\vec{\nabla}\times\vec{A}\;\;,\vec{E}=-\vec{\nabla}\phi-\frac{\partial\vec{A}}{ \partial t} $
If we replace the electric field by the gravitational field ($\vec{g}=-\vec{\nabla}\Phi)$, we need to complete the 4D "representation" for this scalar field by a vector field which is the analog of the vector $\vec{A} $ that is related to the magnetic field.
The analogy and explanations here  : https://en.wikipedia.org/wiki/Gravitoelectromagnetism
