1. Empirical analysis of Chinese airport network as a complex weighted network
Methodology Section
Presented by Di Li

2. Outline Introduction Purpose of the study Methodology Datasets Tools
Conclusion

3. Introduce Topological properties of WAN, ANI, USFN etc. Small-world
Scale free power-law degree distribution
Correlation on degree-degree, clustering-degree, centrality-degree relationships
Nonlinear weight-degree relationship

4. Goals Calculate basic airport network metrics
Identify the similarities and differences with others
Modeling the Chinese airport network
Compare the preferential ingredients
Observe the robustness of CAN
Detect the critical airports in various criteria

5. Dataset Collection Transport Database: contains throughput of airports1
Airport Database: contains over 10,000 airports
Name | City | Country | IATA| Latitude | Longitude | Altitude | TZ 2
Air Route Database: contains routes between 3209 airports
Airline | Airline ID | Src_Airport | S_ID | Dest_Airport | D_ID | Code Share | Stops 3
Transport Database: contains throughput of airports
Passenger Traffic
Cargo and Mail

6. Dataset Collection Cont.4
Source: China Statistical Yearbook published by China Statistic Press
Urban population
The value of cities’ economy
The transport of railway and road

7. Data Preparation Step1: Filter out CAN data2
Step2: Manual organization of data

8. The basic airport network metrics
Vertices : Airports
Edges: Flights
Weight: Routes and Distance
Strength: Airport throughput, Population and Economy
Metrics
Nodes
Edges
Average Degree
Average shortest path length
Diameter
Clustering coefficient
Cumulative degree distribution and the power-law

9. Assortative Mixing Correlations
Degree-degree correlation
Preference of nodes inter-connection
The average degree of all neighboring nodes of nodes with degree k
Pearson correlation 𝑟= 𝑀 −1 𝑖 𝑗 𝑖 𝑘 𝑖 − 𝑀 −1 𝑖 𝑗 𝑖 + 𝑘 𝑖 𝑀 −1 𝑖 𝑗 𝑖 2 + 𝑘 𝑖 2 − 𝑀 −1 𝑖 𝑗 𝑖 + 𝑘 𝑖 2
Implemented by Gephi or stand-alone programming

10. Degree-degree correlation
Preference of nodes inter-connection
The average degree of all neighboring nodes of nodes with degree k
Pearson correlation 𝑟= 𝑀 −1 𝑖 𝑗 𝑖 𝑘 𝑖 − 𝑀 −1 𝑖 𝑗 𝑖 + 𝑘 𝑖 𝑀 −1 𝑖 𝑗 𝑖 2 + 𝑘 𝑖 2 − 𝑀 −1 𝑖 𝑗 𝑖 + 𝑘 𝑖 2
Implemented by Gephi or stand-alone programming

11. Assortative Mixing Correlations
Implement the following with Gephi and Matlab
Degree-strength correlation
Strength-weight correlation
Betweenness-degree correlation
Betweenness-strength correlation
Clustering-degree correlation

12. Modeling the airport network1
Generate the degree distribution of actual CAN
Use preferential attachment with prescribed probability to generate random graph 2
Compare the random graph and actual network graph in terms of degree distribution 3

13. Results Comparison b) Random 1 degree distribution
a) the real network degree distribution
c) Random 2 degree distribution

14. Simulate by Distance Preferential attachment simulation
Generate scale-free networks
Probability of creating a link between new node 𝑗 and existing node 𝑖 is Π 𝑗 ∝ 𝑘 𝑗 𝐹 𝑑 𝑖𝑗
Probability of creating a link between two existing nodes 𝑖 and 𝑗 is Π 𝑖𝑗 ∝ 𝑘 𝑖 𝑘 𝑗 𝐹 𝑑 𝑖𝑗
𝐹( 𝑑 𝑖𝑗 ) is an increasing function of distance between 𝑖 and 𝑗

15. Simulate by Distance(Continued)
Power-law dependence on distance, i.e.
𝐹 𝑑 = 𝑑 𝑟
Exponential dependence on distance, i.e.
𝐹 𝑑 =exp⁡( 𝑑 𝑑 𝑥 )
where 𝑑 𝑥 is a fixed constant.

16. Simulate by other factors
Distance as a factor has certain limitations
A real-network can’t evolution by a well-designed function
The complex function difficult to express the actual meaning
Introduce more related indicators
Population
Economy

17. Why is the tertiary Industry?
“The tertiary sector or service sector is the third of the three economic sectors of the three-sector theory. Services may involve the transport, distribution and sale of goods from producer to a consumer, as may happen in wholesaling and retailing, or may involve the provision of a service, such as in pest control or entertainment.”
Wikipedia

18. CAN traffic vs Tertiary
x – Annual CAN traffic, y – Annual Tertiary
𝑟 𝑥𝑦 = (𝑥 𝑖 − 𝑥 ) (𝑦 𝑖 − 𝑦 ) (𝑥 𝑖 − 𝑥 ) 2 (𝑦 𝑖 − 𝑦 ) 2
𝑟 𝑥𝑦 >0, positive correlation
𝑟 𝑥𝑦 =0, zero correlation (i.e. uncorrelated)
𝑟 𝑥𝑦 <0, negative correlation

19. Robustness of CAN Random attack to network Targeted attack to network
Select a number of random airports to isolate from the network and calculate the resulting giant component fraction
Targeted attack to network
Select a number of targeted airports (according to certain metrics, e.g. degree, centrality etc.) to isolate from the network and calculate the resulting giant component fraction

20. Conclusion Three research questions Four expected results
Structural properties; Connection mechanism; Robustness
Four expected results
Basic airport network metrics; Assortative Mixing Correlations; Preferential attachment Simulation and Critical cities/airports
Five dimension datasets
Airports/Cities, Routes, Traffic, Population and Economy