Measuring Tie Strength in Implicit Social Networks
  Given a set of people and a set of events they attend, we address the problem of measuring connectedness or tie strength between each pair of persons given that attendance at mutual events gives an implicit social network between people. We take an axiomatic approach to this problem. Starting from a list of axioms that a measure of tie strength must satisfy, we characterize functions that satisfy all the axioms and show that there is a range of measures that satisfy this characterization. A measure of tie strength induces a ranking on the edges (and on the set of neighbors for every person). We show that for applications where the ranking, and not the absolute value of the tie strength, is the important thing about the measure, the axioms are equivalent to a natural partial order. Also, to settle on a particular measure, we must make a non-obvious decision about extending this partial order to a total order, and that this decision is best left to particular applications. We classify measures found in prior literature according to the axioms that they satisfy. In our experiments, we measure tie strength and the coverage of our axioms in several datasets. Also, for each dataset, we bound the maximum Kendall's Tau divergence (which measures the number of pairwise disagreements between two lists) between all measures that satisfy the axioms using the partial order. This informs us if particular datasets are well behaved where we do not have to worry about which measure to choose, or we have to be careful about the exact choice of measure we make. 
Mangesh Gupte and Tina Eliassi-Rad
cs.SI physics.soc-ph