compare to other colleagues and feel insulted.
The other two answers are good - but this confuses me. When I've done stakeholder analysis, the process has been open and participatory. There shouldn't be any value judgement. Power and influence are closely related to budget and participation. If a given stakeholder feels that the graph shows them as less powerful or less influential, that is an opportunity to discuss their involvement. If they want to be perceived as more powerful, I'd welcome their budgetary contributions. If they want to be more influential, I'd be happy to forward the invitation to the Integrated Project Team.
If the real issue is just ego stroking - where person x wants to be shown as more important than person Y, then I'll offer to escalate that to the project sponsor and ask the project sponsor to formally declare which of the people is more important to the project and which of them is a more concerned about their own ego than the business.
But the whole point of doing stakeholder mapping is to escalate these conflicts and make them transparent. If there are two stakeholders who are trying to control the direction of the project, then you want to identify that and resolve that conflict early. Better to have that conversation before they start spiking one another's participation in the configuration control board.
Projects thrive when they have clear vision shared by all participants. Part of establishing that vision is communication.
Sometimes (unfortunately) communication involves telling stakeholder X that Stakeholder Y has more control of this project - that budgetary or business reasons mandate that the project will address stakeholder Y's interests. In such a condition, I'd do my best to identify the lowest common denominator, but give stakeholder X the opportunity to solve the problem their own way (with their own project). I would hope that someone senior in the enterprise would deconflict the divergent interests, but I will serve my stakeholders.
Like I said, the other two answers are good -but I wanted to provide an alternative perspective.
@DavidEspina has managed to express everything I said above in a more pithy quote:
Transparency would be my go to all the way up until I can't.
I suggest less emotionally laden labels for the boxes; I don't mind being invited to monitor a project, but I think being labelled as an "Apathetic" is likely to generate unwelcome management attention. There are multiple variations of this graph - here is one I found that I think might generate less bruised egos