1. For this exercise, choose an undirected network from any online repository with more than 1000 nodes. Some things to pay attention: Provide the appropriate reference for the dataset. There are some repositories linked on the module's Blackboard page, but you are free to choose networks from other repositories. When choosing your network, it is a good idea to first read the exercises and seek for a network that will be appropriate for the required analysis. a) Describe the nature of the network by explicitly indicating what kind of objects are its nodes and their number, what kind of relation the links represent and their number, and what actual function does the network represent. b) s) Using the maximum likelihood method, adjust a power law distribution to the degree distribution of your network and test the quality of the result by calculating the root mean square error between the estimated and the actual degree distribution. Write down explicitly the expression for the adjusted power law. c) ) Calculate the root mean square error obtained by estimating the degree distribution of your network using a Poisson approximation of a G(N,p) model with the appropriated parameter obtained from your data. ) Plot the original degree distribution, the adjusted power law and the Poisson estimate in the same graph for the sake of comparison. Interpret your results by comparing the shape of the distributions and their root mean square errors. Indicate which of the latter two approximates better the actual distribution of the network and justify whether it makes sense for the kind of network you have d) { 1. For this exercise, choose an undirected network from any online repository with more than 1000 nodes. Some things to pay attention: Provide the appropriate reference for the dataset. There are some repositories linked on the module's Blackboard page, but you are free to choose networks from other repositories. When choosing your network, it is a good idea to first read the exercises and seek for a network that will be appropriate for the required analysis. a) Describe the nature of the network by explicitly indicating what kind of objects are its nodes and their number, what kind of relation the links represent and their number, and what actual function does the network represent. b) s) Using the maximum likelihood method, adjust a power law distribution to the degree distribution of your network and test the quality of the result by calculating the root mean square error between the estimated and the actual degree distribution. Write down explicitly the expression for the adjusted power law. c) ) Calculate the root mean square error obtained by estimating the degree distribution of your network using a Poisson approximation of a G(N,p) model with the appropriated parameter obtained from your data. ) Plot the original degree distribution, the adjusted power law and the Poisson estimate in the same graph for the sake of comparison. Interpret your results by comparing the shape of the distributions and their root mean square errors. Indicate which of the latter two approximates better the actual distribution of the network and justify whether it makes sense for the kind of network you have d) {