The kinds of diagram you're talking about each do slightly different things.
I'll go through each of the types you mention and try to talk a bit more about what they're good for. Which is better for visualizing the data depends very much on what you're trying to find or show in the data.
1 - Chord diagram
and they're good at showing how things relate, but not so good at showing strengths of each relationship if there are a lot of them to show. They can also end up masking clusters of related things if the relationships are complex and leave a mess of lines all over the place. If they get too busy then they can be hard to follow.
2 - Many strong links in middle
I don't know what I'd call this one, but you'd probably get something very similar to it by working with #3 anyway...
3 - Force-directed layout
There are various implementations of these out there. My understanding is that, by default, they make all lengths the same... but most of the implementations have a means to change that. For example, the d3.js implementation lets you set a link distance for each relationship which sets the optimal length of that line. You could determine the link distance for each relationship based on the strength of the relationship. This would cause the strongly related things to clump together and the weakly related things to pull apart.
I've also seen versions where a higher number of relations to a node causes that node to be rendered at a larger size - which could have a similar effect.
There are a lot of off-the-shelf tools for force-directed layouts out there which could probably bear the brunt of a lot of the required coding effort. d3 would be my start point if I had to make a library recommendation, but that's just because it's well known and widely used.
4 - Geography based
This idea is the only place where you mention geography in the entire question. Is the geography important enough to base the visualization on? If you do use this kind of visualization then you're limited in how you can show the strength of relationships, and clusters are going to be harder to see.
5 - ???
I have no idea how that would work, so can't really comment on it further.
My Recommendation
If you're trying to make it easy to see relationships between people AND to see how people group, I'd strongly suggest a force directed layout. With the number of nodes you're suggesting, performance could be an issue, but I think that would be the approach I'd start with.
If you're trying to see geographic clusters, then #4 could work - and I'd suggest a mix of line weight and line opacity to indicate the strength of each relationship.