Analysis and simulation of small-world and scale-free network

Kam, Michael (2013) Analysis and simulation of small-world and scale-free network. Bachelor thesis, Universitas Pelita Harapan.

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Abstract

Real networks are complex, not ordered, and yet not fully random graph. Several approaches had been done to model real networks. Two of the approaches to model real networks are small-world and scale-free. The small-world term was coined by Stanley Milgram and had been developed mathematically mainly by Watts and Strogatz. Meanwhile, scale-free is the term given by the Barabási and Albert for the model they found. Small-world can be developed using edges rewiring, edges adding, and hotspots adding. On the other hand, scale-free network is built using growth and preferential attachment. This thesis begins by giving theoretical basics of graph theory and smallworld and scale-free theories. Thereafter, the simulation and analysis of smallworld and scale-free networks using MATLAB will be discussed. Afterwards, nodes isolation analysis for small-world Watts-Strogatz’s model will become the focus. The effects of the isolation to characteristic path length of the network are the purpose of the analysis. The simulation of small-world and scale-free models yield networks with low characteristic path length. The clustering coefficients in the small-world models are relatively high while the clustering coefficients in the scale-free model is low. However, there are two ways to increase the clustering coefficient in scale-free network: by increasing the initial number of nodes m0 and or by increasing the new node’s connections m. Another problem discussed in this thesis is the nodes isolation of WattsStrogatz’s small-world network. The purpose of the isolation is to increase the chacteristic path length of the network to some level. For number of nodes n = 1000 and number of initial connections k = 10, the nodes isolation successfully increases the characteristic path length L passing the L(0) for random probability p = 0:01 and p = 0:02. For p = 0:03 to p = 0:06 with the same n and k, L was not able to pass L(0) but able to increase to five times or more of L(p). For n = 2000 and k = 20, the nodes isolation process does not increase L to L(0) for all p. However, for p = 0:01 and p = 0:02, L of the network increased to five times or more of L(p) in the nodes isolation process.

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