Analyzing the Erasmus mobility network, we illustrate typical problems and approaches in analyzing weighted networks. We propose alternative exploratory views on the network "Erasmus+ learning mobility flows since 2014". The network has 35 nodes (countries), is very dense, and the range of link weights (number of visits) is huge (from 1 to 217003). An increasing transformation is used to reduce the range. The traditional graph-based visualization is unreadable. To gain insight into the structure of a dense network, it can be reduced to a skeleton by removing less essential links and/or nodes. We have determined the 1-neighbors and 2-neighbors subnetworks. The 1-neighbors skeleton highlights Spain as the main attractor in the network. The 2-neighbors skeleton shows the dominant role of Spain, Germany, France, and Italy. The hubs and authorities, Pathfinder and Ps cores methods confirm these observations. Using the "right" order of the nodes in a matrix representation can reveal the network structure as block patterns in the displayed matrix. The clustering of network nodes based on corrected Salton dissimilarity again shows the dominant role of Spain, Germany, France, and Italy, but also two main clusters of the division into developed/less developed countries. The Balassa normalization (log(measured/expected) visits) matrix shows that most visits within the two main clusters are above expected, while most visits between them are below expected; within the clusters of Balkan countries, Baltic countries, {SK, CZ, HU}, {IS, DK, NO} visits are much above expected, etc.