trouble in understanding outliers' influence on K-means 
When outliers are present, the resulting cluster centroids may not be as representative as they otherwise would be and thus, the SSE will be higher as well.

However, I don't understand this sentence.
Look at the following picture. The original centroid is marked as "A" and the outlier is marked as red. It is clear that the original centroid "A" is better than the outlier when considering SSE. Thank you !

 A: Imagine we have a dataset containing 2 clusters that are nice, Gaussian point clouds. We want to find 2 clusters in the data using K-means. However, say there's also a single outlier, located very far from either of the 'true' clusters. Maybe millions of times further away from any other point than any other points are to each other. If we chose the centroids to be the centers of the true clusters (the best 'representative' configuration), the value of the loss function would be very high. The loss function is the sum of squared distances from each point to its assigned cluster centroid. It would be high because the outlier is so far from the nearest centroid. Therefore, K-means would reduce the loss function by choosing the outlier itself to be one of centroids, and placing the other centroid somewhere in the middle of the remaining data. This configuration is clearly not representative of the the underlying distribution, but a pathological situation caused by the presence of a single outlier.
A: Here is a new paper on this topic:
http://www.math.uconn.edu/~gan/ggpaper/gan2017kmor.pdf
I think this is very relevant for people who might like to use a proper outlier treatment.
