## 1 Introduction  
The revealed comparative advantage (RCA) index, also called Balassa index as it was first proposed by [PERSON] in 1965 [1], is an important metric for quantifying the relative strength of a country in producing a product vis-a-vis its trading partners. While it has been widely used in empirical studies, the RCA index has also been further studied theoretically. Those works mainly focus on the statistical features of the RCA index, and can be roughly classified into two groups. One group is somewhat traditional, with emphasis on clarifying the statistical characteristics of the RCA index across sectors or countries. In many applications, it is desirable to have a normally distributed RCA index, so that it can reliably measure a country's revealed comparative advantage [2]. However, in the majority of empirical studies, a non-Gaussian distribution of the RCA index has been observed. The non-Gaussianity has made the RCA index to suffer from many disturbing properties such as unstable distribution and poor ordinal ranking property [3], the unstable mean [4, 5], asymmetric distributional shape [2], and skewness and variable upper bound [6, 7]. These features of the RCA index have made its interpretation difficult [3, 4, 8, 9, 10], and thus have motivated a lot of researchers to develop alternative indices of the RCA index so that the new indices can be more normally distributed [3, 4, 5, 11, 12, 13, 14, 15]. These efforts are not very successful, however. To understand why the RCA index and its alternatives may not follow Gaussian distributions, [PERSON] and [PERSON] systematically analyzed the distribution characteristics of the RCA index cross sectors and countries [16]. They find that the RCA index in the majority of the situations cannot be normally distributed, since it is the ratio of two distributions, one following an exponentially truncated Zipf-Mandelbrot's law, the other being a permutation of the truncated Zipf-Mandelbrot's law [16]. Only occasionally can a normally distributed RCA index be observed--it may emerge with about 1% chance. The significance of a normally distributed RCA index has not yet been explained, however. The other group of the work on the theoretical aspects of the RCA index mainly employs matrix and complex network theory by constructing the country-product bipartite network, where countries are connected to the products they export. The bipartite network is an 0-1 adjacency matrix constructed according to the value of the RCA index (the element is 1 if the corresponding RCA \(\geq\) 1 and 0 otherwise). By developing the Method of Reflections to interpret an export bipartite network, [PERSON] and [PERSON] proposed the Economic Complexity Index (ECI) and Product Complexity Index (PCI) [17; 18]. [PERSON] and [PERSON]'s approach has been proven to be equivalent to a spectral clustering algorithm that partitions a similarity graph into two parts [19]. Although, the ECI may offer a good description of global macroeconomic relations, technological trends, and growth dynamics [20], and could be used to measure the gap in the economic development between countries [21], the approach suffers from a number of conceptual and practical problems [22; 23; 24; 25; 26]. To overcome these problems, the Fitness Index (FI) and some other variants of the ECI have been developed [22; 23; 24; 27; 28]. The ECI and its variants have been widely used to study the impact of economic structures on economic development [18; 20; 29; 40; 41; 42]. Fundamentally speaking, however, the FI and the other new variants of the ECI are not very different from the ECI, since the ECI and FI (or log FI) are strongly positively correlated [37; 38; 39; 40; 41], and both metrics have almost the same skill in predicting economic growth [42]. This raises an important question as to which of the neglected aspects of the RCA index by the network based approach should be reinstated so that characterization of economic complexity can be fundamentally improved.