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

Outline Introduction Purpose of the study Methodology Datasets Tools Conclusion

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

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

Dataset Collection Transport Database: contains throughput of airports 1 Airport Database: contains over 10,000 airports Name | City | Country | IATA| Latitude | Longitude | Altitude | TZ 2 Air Route Database: contains 59036 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

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

Data Preparation Step1: Filter out CAN data 2 Step2: Manual organization of data

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

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 1 2 𝑗 𝑖 + 𝑘 𝑖 2 𝑀 −1 𝑖 1 2 𝑗 𝑖 2 + 𝑘 𝑖 2 − 𝑀 −1 𝑖 1 2 𝑗 𝑖 + 𝑘 𝑖 2 Implemented by Gephi or stand-alone programming

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 1 2 𝑗 𝑖 + 𝑘 𝑖 2 𝑀 −1 𝑖 1 2 𝑗 𝑖 2 + 𝑘 𝑖 2 − 𝑀 −1 𝑖 1 2 𝑗 𝑖 + 𝑘 𝑖 2 Implemented by Gephi or stand-alone programming

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

Modeling the airport network 1 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

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

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

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.

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

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

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

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

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