1) Your Follower Map – this is a pretty graphic showing where your followers come from, what countries, and what distribution.
2) Your Ranking – now this is a killer feature. It allows you to select how much weight various factors (e.g. engagement!) have, and creates a ranking chart based on those weighted criteria. This kind of openness in ranking systems is just what we need – and the start of transparent, effective social network analysis.
What makes a weighted, custom ranking so special? It allows you to identify community leaders, not just popular idols. And that's something that, until now, has not been transparent through closed, proprietary ranking schemas. That said, there are a few things I'd like to see that would make this type of analysis even more valuable – and become a much more valuable resource for monitoring your own presence as well as topping what the 'What's hot' charts present:
1) Your rank in the custom ranking that you create.
2) An influence chart – a zoomable bubblechart of your circles would be fine, with distance indicating how closely you and a particular person/page interact, and size indicating the rank of that person.
3) Adding number of unique commentors / plussers / sharers as a metric (as opposed to total numbers)
4) Topical charts – given my custom ranking and a particular topical keyword, create a chart of top people.
Generate your own ranking for Google+
You can define a special ranking for Google+ with defining the weight of the parameter that should be taken into account. Try it out!