Capturing User Friendship in WLAN Traces

Most of recent research works on analyzing wireless LAN (WLAN) traces focused on individual user behaviors [1], [2], [3]. These previous works provide good understandings on WLAN users, and have made vast amount of WLAN traces available to the research community (e.g. from [1], [2], [3], [6]). However, we know from daily lives that we do not make random movement decisions. Usually, WLAN users show preferences in their visits to a small set of the campus. As a result, mobile nodes (MNs1) in WLAN traces are in fact not uniformly distributed across campus, and users with similar preferences show up at the same access point (AP) more frequently. We look into this issue and try to identify the closeness (i.e. friendship) between node pairs, and understand its influences on network connectivity if we make connections between nodes based on their friendship. Specifically, we give several intuitive definitions about friendship between MNs, utilizing traces about their association to APs in a WLAN. These friendship indexes capture the observed closeness between the involved MNs from the trace. Although such closeness may or may not reflect friendship in social context, it reveals the closeness between wireless devices as displayed in their association patterns. Empirical distribution of these friendship indexes mostly follow exponential distribution, with few node pairs showing high friendship index. We further utilize the Small World model [4] to understand the characteristics of the encounter-relationship graphs (ER graphs) formed by WLAN users, in which two nodes are connected by a link if they ever associate with the same AP during overlapped time intervals. We find that WLAN users form connected Small World graphs via encounters. Furthermore, we investigate the issue of how friendship influence the characteristics of ER graphs. We find that if nodes with high friendship indexes are used in ER graph, the resultant graph displays higher clustering coefficient and average path length. In other words, it is more inclined toward a regular graph. On the other hand, if we use nodes with low friendship index in ER graph, it displays lower clustering coefficient and average path length. This finding points out, similar to social networks, close friends in WLANs often form cliques and random friends are keys to wide-reached connectivity in a network.