Are technological and social networks really different?

Abstract

The use of the Pearson coefficient (denoted r) to characterize graph assortativity has been applied to networks from a variety of domains. Often, the graphs being compared are vastly different, as measured by their size (i.e., number of nodes and arcs) as well as their aggregate connectivity (i.e., degree sequence D). Although the hypothetical range for the Pearson coefficient is [ −1, +1], we show by systematically rewiring 38 example networks while preserving simplicity and connectedness that the actual lower limit may be far from −1 and also that when restricting attention to graphs that are connected and simple, the upper limit is often very far from +1. As a result, when interpreting the r-values of two different graphs it is important to consider not just their direct comparison but their values relative to the possible ranges for each respectively. Furthermore, network domain (”social” or ”technological”) is not a reliable predictor of the sign of r. Collectively, we find that in many cases of practical interest, an observed value of r may be explained simply by the constraints imposed by its D, and empirically such constraints are often the case for observed r < 0. In other cases, most often for r > 0, other explanations must be sought.