Abstract
Network connections have been shown to be correlated with structural or external attributes of the network vertices in a variety of cases. Given the prevalence of this phenomenon network scientists have developed metrics to quantify its extent. In particular, the assortativity coefficient is used to capture the level of correlation between a single-dimensional attribute (categorical or scalar) of the network nodes and the observed connections, i.e., the edges. Nevertheless, in many cases a multi-dimensional, i.e., vector feature of the nodes is of interest. Similar attributes can describe complex behavioral patterns (e.g., mobility) of the network entities. To date little attention has been given to this setting and there has not been a general and formal treatment of this problem. In this study we develop a metric, the vector assortativity index (VA-index for short), based on network randomization and (empirical) statistical hypothesis testing that is able to quantify the assortativity patterns of a network with respect to a vector attribute. Our extensive experimental results on synthetic network data show that the VA-index outperforms a baseline extension of the assortativity coefficient, which has been used in the literature to cope with similar cases. Furthermore, the VA-index can be calibrated (in terms of parameters) fairly easy, while its benefits increase with the (co-)variance of the vector elements, where the baseline systematically over(under)estimate the true mixing patterns of the network.
Highlights
Assortativity mixing is a network phenomenon that describes the tendency of nodes to attach to others with similar characteristics
We compare our system with a baseline extension of the assortativity coefficient
Given that in our synthetic data we know the actual assortativity patterns of the network our evaluation metric is the Root Mean Square Error (RMSE) of the assortativity values obtained from the VA-index and the baseline
Summary
Assortativity mixing is a network phenomenon that describes the tendency of nodes to attach to others with similar characteristics. The mixing patterns are important in complex network theory since they can have many implications depending on the type of network examined. Degree assortativity, that is, assortativity with respect to the node degree, is closely related with the resilience of a network to targeted attacks [1]. In the realm of social networks assortativity mixing with respect to external nodal attributes, usually termed as homophily [2], can reveal important information for the mechanisms that lead to friendship creation. Studies of high school friendships have revealed a high degree of PLOS ONE | DOI:10.1371/journal.pone.0146188. Studies of high school friendships have revealed a high degree of PLOS ONE | DOI:10.1371/journal.pone.0146188 January 27, 2016
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