Class 10: Introduction to CINET Using CINET for network analysis and visualization Network Science: Introduction to CINET 2015 Prof. Boleslaw K. Szymanski Konstantin Kuzmin

CINET Hands-on Labs Overview Exercise 1 Review different random graph generators available in CINET Generate ER random graphs Exercise 2 Experiment with random graph generation facility of CINET Find the smallest probability value to satisfy a given property Exercise 3 Compare the structural measures of an Erdős-Renyi (ER) random network with those of a Barabasi-Albert (preferential attachment based) scale-free (SF) network Exercise 4 Compare the structural properties of a network with its shuffled version Network Science: Introduction to CINET

CINET Links Useful links Main CINET page Granite page Stanford Network Analysis Project Network Science: Introduction to CINET

CINET Hands-on Labs Exercise 1 Objectives In this exercise Review random graph models available in CINET Practice random graph generation Generate three random graphs using the Erdős-Renyi (ER) model with different probability values. For each of the three graphs, compute three network measures. Fill in the following table: Network Science: Introduction to CINET

CINET Hands-on Labs Exercise 1 Procedure Follow these steps Under the “Network Generators” tab, CINET has a “+ New Network Generator” button which allows a user to specify the generator name and select a generator from the list. For this exercise please use the “G(n, p) random graph” choice that generates an ER model random undirected graph with a specified number of nodes (n) and edge probability (p). After you generate a random graph, you need to add it to the CINET repository of graphs so that you can use CINET to compute all the required measures: a)Click on its “View Report” link to see the output files generated. b)Download and unzip the output. c)Rename the output.out file as output.nx. (The extension “.nx” indicates a file that can be processed by CINET using NetworkX. d)Use the “+New Network” tab (in the “Networks” tab of Granite) to upload the generated network and do the following: Select the option “Directly upload a file”. Click on “Done”. Choose the file (output.nx) to upload. Provide the requested details for the network (e.g., name, type) and select the Visible option as “Only Me”. (This will make the network private to you.) Click on “Save”. The uploaded network will be seen in the “Networks” list. Now, use the “Network Analysis” button to compute each necessary measure for the added network. Network Science: Introduction to CINET

CINET Hands-on Labs Exercise 1 Outcome Exercise review What random graph models are available in CINET? What parameters are available for ER networks? How do they affect the networks to be generated? Network Science: Introduction to CINET

Experiment with random graph generation facility of CINET Consider random graphs generated using the Erdős-Renyi model on 1,000 nodes. As we increase the edge probability p, the number of edges in the generated graph increases. The goal of this exercise is to experiment with various probability values and find the smallest probability value at which the generated graph has a certain property. Perform the exercise for three properties and fill in the following table: CINET Hands-on Labs Exercise 2 Objectives In this exercise Network Science: Introduction to CINET PropertyProbability p The graph has a giant component with at least 900 nodes The graph is connected The graph has no bridge edges

CINET Hands-on Labs Exercise 2 Procedure Follow these steps First choose a graph property; let us call it P. You need to try various edge probability values and find the smallest value. (If you are familiar with binary search, you can do this in a systematic manner.) For each probability value p, you need to carry out the following steps. 1.Generate the random graph with edge probability p. 2.Add it to the list of networks in CINET. 3.Compute the measure corresponding to property P. Depending on the value of the measure obtained in Step 3 above, you must increase or decrease the value of p appropriately for the next attempt. Network Science: Introduction to CINET

CINET Hands-on Labs Exercise 3 Objectives In this exercise Compare the structural measures of an Erdős-Renyi (ER) random network with those of a Barabasi-Albert (preferential attachment based) scale-free (SF) network Network Science: Introduction to CINET

CINET Hands-on Labs Exercise 3 Procedure Follow these steps Choose the same number of nodes (say, 1,000) in both graphs. Choose the parameters (probability of each edge for the ER model and the number of edges attached to each new node for the SF model) so that both graphs have (approximately) the same number of edges. Generate two graphs using CINET and upload them. (We will use G1 and G2 to the ER graph and the SF graph respectively.) Compute and compare the degree distributions of G1 and G2. Compute and compare the clustering coefficient distributions of G1 and G2. Compute and compare the numbers of articulation points of G1 and G2. Compute and compare the numbers of bridge edges of G1 and G2. Network Science: Introduction to CINET

CINET Hands-on Labs Exercise 4 Objectives In this exercise Compare the structural properties of a network with its shuffled version We will indicate how a shuffled network can be generated for one value of the fraction f of the number of edges. You can try different values of f. Network Science: Introduction to CINET

CINET Hands-on Labs Exercise 4 Procedure Follow these steps Choose a network from the list of available networks in CINET. (Let G1 denote this network.) In the “Measures” tab of CINET, choose “Shuffle (switch) edges”. When you start the analysis (by clicking on the “Analyze” button), the system will ask you to input the fraction f of the number of edges to be switched. To begin with, choose the fraction 0.1. (You can repeat all of the steps for other values of f.) Generate the shuffled version G2 of G1 and upload G2 to CINET. Compute and compare the degree distributions of G1 and G2. Compute and compare the clustering coefficient distributions of G1 and G2. Compute and compare the numbers of articulation points of G1 and G2. Compute and compare the numbers of bridge edges of G1 and G2. Network Science: Introduction to CINET