Iteration 3: Graph Visualisation Analysis (IP)

The above Iteration 2 provided us with initial structural insights for the three mobile broadband operator networks at IP granularity, while also indicating, based on the general, edge and vertex metrics, that the structuring likely followed a Scale-Free

Network model. As a result of this learning, we wanted to know more about the structural

properties of the three operator networks, while also gaining insight into connectivity importance of certain vertices that might indicate structural bottlenecks (given the apparent Scale-Free Network nature) for providing upstream internetworking features of the three mobile broadband operator networks. Therefore, exploring the first two network models (Small-World and Scale-Free) of the Graph Visualisation Analysis (and simulation of Scale-Free Network models) at IP granularity in this Iteration 3 aimed to better understand the structural properties of the three mobile broadband operator networks. The Small-World Network features were therefore analysed using the Kleinberg (2000) algorithm (see section 3.4.3 above), while the Barabási-Albert Models (Standard Model, Model A and Model B, see Barabásilabs (2013)) were used to simulate the Scale-Free Network nature of the operator networks. Computing the k-core

decomposition algorithm and graph visualisation using R (2016) upon the work of

Alvarez-Hamelin et al. (2006) was then chosen to reveal those vertices, indicating potential structural internetworking bottlenecks. Hence, this section starts by describing the steps to generate the Small-World Network Model below, followed by the Barabási- Albert Scale-Free Network Models and lastly the k-core decomposition. The outcomes of Iteration 3 were reported in section 4.2.6.

Small-World Network Model

To generate the Small-World graph visualisations, we first re-opened Gephi (2016), activated the Complex Generators plugin and created a new project. Next, we imported our previously generated raw data *.csv files as edge tables (e.g. ‘ AS38266_for_gephi.csv’ for Vodafone) and started the Kleinberg algorithm by following ‘File > Generate > Kleinberg Small World Model’ in Gephi (2016). The graph visualisation layout was set at the Layered Layout by Kuchar (2012), which we had to download (from the Gephi Marketplace) and install prior to usage. Before visualising the graph, we computed the Weighted Average Clustering Coefficient measurements in the statistics section of Gephi (2016). Next, we chose the Weighted Average Clustering

Coefficient as distance parameter in the Layered Layout graph visualisation. Once the

the edges ‘blue’ and exported the resulting visualisations as *.png files while saving the models (e.g. as ‘AS38266_Kleinberg_blue.gephi’ for Vodafone). Lastly, we reported our findings alongside the utilised graph visualisation parameters. These were set in the Open Source Network Exploration Tool Gephi (2016) as:

• The calculated Weighted Clustering Coefficient. • Layer Distance of 1250.

• Edge-thickness of 0.5, whereas due to readability purposes, we visualised the

G_{òjôöõjúù} with a smaller edge-thickness of 0.25.

• Size of lattice: 10.

• Lattice distance to local contacts: 2. • Long range contacts: 2

• Clustering exponent: 0. • ‘Black’ vertex colouring. • ‘Light blue’ edge colouring. Scale-Free Network Model

Obtaining the Barabási-Albert Scale-Free graph visualisations followed a somewhat similar approach. Here, we opened Gephi (2016) again and activated the Complex Generators plugin. Next, we started and saved a new project as *.gephi file (e.g. ‘AS55831_BAModel.gephi’ for Aircel) and imported the raw data *.csv file (e.g. ‘AS38266_for_gephi.csv’ for Vodafone) as edge table. We started the BA Standard Model algorithm by following ‘File > Generate > Barabási Albert Scale-Free Model’. Prior to this generation, we had to obtain the number of unique vertices for the graph. This information is found by opening ‘Window > Context’. The number of unique vertices was then included as ‘N Number of nodes in generated network’ (nodes is a synonym for vertices) in the settings of the Barabási-Albert Scale-Free Network algorithm. ‘M, the number of edges coming with every new node’ and ‘m0, number of nodes at the start time’ remained at ‘1’. Furthermore, we ticked the box to consider the existing vertices, representing the existing IP addresses or Autonomous Systems in the given three mobile broadband operator networks. Once the algorithm event finished the calculations, we generated the graph visualisations using the Force Atlas 2 Layout. To make the visualisation more readable, we made use of a specific set of graph layout parameters. Moreover, we changed the visualisation background colour again to ‘white’ and the colour of the edges to ‘blue’. Once the graph visualisations were generated, we

explored its components by setting a ‘k-core parameter’ as ‘topology query’. The respective graph visualisations were then exported as *.png files (e.g. ‘AS55831_BAModel_blue.png’ for Aircel). Next, we followed similar steps to generate the graph visualisations of the Barabási-Albert Model A and the Barabási-Albert Model B. Hence, we created and saved two new projects as *.gephi files (e.g. ‘AS45609_BAModel_nogrowth_blue.gephi’ and ‘AS45609_BAModel_uniformattach ment_blue.gephi’ for Bharti Airtel).

We then launched the BA-model algorithm without growth by following ‘File > Generate > Barabási Albert Scale-Free Model B (no growth)’ and the BA-model algorithm without preferential attachment by following ‘File > Generate > Barabási Albert Scale-Free Model A (uniform attachment)’. For both models, we chose the number of unique vertices for ‘N Number of nodes in generated network’, obtained as stated above. Once the networks were generated, we again utilised the Force Atlas 2 Layout to visualise the generated graphs and exported the files in the *.png formats (e.g. ‘AS45609_BAModel_nogrowth_blue.png’ and ‘AS45609_BAModel_uniformattachme nt_blue.png’ for Bharti Airtel). Alongside their respective descriptions, the graph visualisations were then reported in section 4.2.6 of Chapter 4, where we also stated the following visualisation parameters to ensure comparability between the mobile broadband operator graph visualisations:

• Edge weight of 1 represents a normal edge influence.

• Fixed visualisation scale of 20 provides the graph visualisation with less repulsion.

• Normal gravity attraction of 1 assures that vertices are not leaving the two- dimensional Euclidean space.

• ‘Black’ vertex colouring. • ‘Light-blue’ edge colouring. k-core decomposition

Due to a lack of a suitable Gephi (2016) plugins, we modelled the computation and visualisation of the k-core decomposition as proposed by Alvarez-Hamelin et al. (2008) by using the Statistical Computing Tool R (2016). Hence, we installed the Network Analysis and Visualisation package ‘igraph’ by entering ‘>install.packages(“igraph“)’ in the R (2016) console. Once this package was installed, we wrote a R-script (see script in

Appendices), on the basis of Casas-Roma (2015), for computing and visualising the three mobile broadband operator networks’ k-core decompositions. For readability purposes, we included comments (marked with a hashtag) in the script (see script in Appendices) below. However, this script only functions once the imported *.csv is cleaned from any header rows and identifier columns. These files were saved e.g. as ‘AS45609_Bharti_for_R.csv’ for Bharti Airtel. Having imported the respective *.csv files, R (2016) then calculated the k-core decomposition utilising the elaborated script, a task which needed significant computing resources. The resulting graph visualisations for the three Tamil Nadu mobile broadband operator networks were then exported and saved (e.g. as ‘BhartiAirtel_kcore_decomposition.png’ for Bharti Airtel). The exploration of the findings, alongside a comparison with the previous graph visualisations, was then also reported in section 4.2.6 of Chapter 4.