  The structure of personal networks reflects how we organise and maintain
social relationships. The distribution of tie strengths in personal networks is
heterogeneous, with a few close, emotionally intense relationships and a larger
number of weaker ties. Recent results indicate this feature is universal across
communication channels. Within this general pattern, there is a substantial and
persistent inter-individual variation that is also similarly distributed among
channels. The reason for the observed universality is yet unclear -- one
possibility is that people's traits determine their personal network features
on any channel. To address this hypothesis, we need to compare an individual's
personal networks across channels, which is a non-trivial task: while we are
interested in measuring the differences in tie strength heterogeneity, personal
network size is also expected to vary a lot across channels. Therefore, for any
measure that compares personal networks, one needs to understand the
sensitivity with respect to network size. Here, we study different measures of
personal network similarity and show that a recently introduced
alter-preferentiality parameter and the Gini coefficient are equally suitable
measures for tie strength heterogeneity, as they are fairly insensitive to
differences in network size. With these measures, we show that the earlier
observed individual-level persistence of personal network structure cannot be
attributed to network size stability alone, but that the tie strength
heterogeneity is persistent too. We also demonstrate the effectiveness of the
two measures on multichannel data, where tie strength heterogeneity in personal
networks is seen to moderately correlate for the same users across two
communication channels (calls and text messages).
