Two different ways to make interconnected dots and lines. 
In this video, I take a look I've seen a lot in videos and break down how to achieve a connected network or nexus of points / dots which vibrate slowly. A lot of people have asked how to do this sort of effect and the usual answer on forums is the Plexus plugin. While that's obviously an option for some, if you don't have the spare money there are a couple of other ways which yield similar results. 
For the first approach I use Shapes on a single shape layer and the createPath expression to link them all together and while the expression is complex, once you have it it's easy to add more and more dots. The second technique uses Video Copilot Element 3D and its distortion options to create the network of lines then a point cloud to create the dots.
Wiggle expression:
X = wiggle(effect("Frequency")("Slider"),thisComp.width*effect("X amplitude")("Slider")/100)[0];
Y = wiggle(effect("Frequency")("Slider"),thisComp.height*effect("Y amplitude")("Slider")/100)[1];
Shape 1's expression
var points = [];
for (var i = 1; i < content("Shape 1").propertyIndex-1; i++) {
    points[i-1] = content("Ellipse "+i).transform.position;
createPath(points = points, inTangents = [], outTangents = [], isClosed = true)

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