Network Analysis Process

1 Introduction

There are many types network, such as Co-Authorship Network, Gene Co-expression Network, and Transportation Network. Here we only introduce the common analysis methods for world trade network.

2 Analysis Process

Commonly we follow the following step to analysis a trade network.

2.1 Weighted Network

The weighted matrix $W$ is defined as
\[w^t_{ij}=\frac{e^t_{ij}}{GDP^t_i}\]
where $e^t_{ij}$ is the exports from country $i$ to country $j$ in year $t$. $GDP^t_i$ is the total exports of country $i$ in year $t$.
We also employ the convention of dividing all entries in $W$ by their maximum value, make $w^i_{ij} \in [0,1]$ for all $(i,j)$ and $t$.

2.2 Symmetric Analysis

In order to testify a network whether is a symmetric network, we need to observe the correlation of in-degree and out-degree, correlation of in-strength and out-strength. The symmetric index S must be calculated. If it is more close to 0, the network can be taken as a symmetric network.

2.3 Network Connectivity Analysis

We can analysis the network connectivity from the following aspects.

• Explore the distributions of ND (number of partners or degree of the network) and NS (interaction intensity or strength of the network), including the average varies through time and the varies in some fixed time.
• Explore the degree-strength correlation over time.

2.4 Network Assortativity Analysis

Countries holding many links only trade with poorly-connected countries (we call such a network “disassortative”). Conversely, it may be the case that better connected countries also tend to trade with other well-connected countries (an “assortative” network).

We can analysis the network assortativity from the following aspects.

• Explore the population average ANND (average nearest-neighbor degree ), ANNS (average nearest-neighbor strength) and WANND (weighted average nearest-
  neighbor degree) over time.

• Explore the above metrics (ANND,ANNS,WANND) correlation with other network statistics, such as degree and strength.

2.5 Network Clustering Analysis

We can analysis the network clustering from the following aspects.

• Explore the population average clustering coefficients over time.
• Explore the clustering coefficients-degree/strength correlation varies over time.
• Explore the relationship between pcGDP (per capita GDP) and clustering coefficients

2.6 Network Centrality Analysis

If a network has a core-periphery structure, we can analysis the network centrality from the following aspects.

• Explore the distribution of RWBC (random-walk betweenness centrality).
• Explore the varies of the first few bigger value, corresponding the core countries varies.
• Explore the relationship between pcGDP (per capita GDP) and RWBC.

2.7 Network Robustness Analysis

For weighted network, we need to check the weight robustness. We explore the above analysis varies by dividing the trade flow by the GDP of the importer country (j's GDP, in the
above example).