One of the key concerns with location-aware Ad-hoc Wireless Sensor Networks (AWSNs) is how sensor nodes determine their position. The inherent power limitations of an AWSN along with the requirement for long network lifetimes makes achieving fast and power-efficient localization vital. This research examines the cost (in terms of power) of network irregularities on communications and localization in an AWSN. The number of data bits transmitted and received are significantly affected by varying levels of mobility, node degree, and network shape. The concurrent localization approach, used by the APS-Euclidean algorithm, has significantly more accurate position estimates with a higher percentage of nodes localized, while requiring 50% less data communications overhead, than the Map-Growing algorithm. Analytical power models capable of estimating the power required to localize are derived. The average amount of data communications required by either of these algorithms in a highly mobile network with a relatively high degree consumes less than 2.0% of the power capacity of an average 560mA-hr battery. This is less than expected and contrary to the common perception that localization algorithms consume a significant amount of a node\u27s power
