Closeness Centrality and Epidemic Spreading in Networks

This thesis is about the relation between the closeness centrality of the first infected node in the network and each of the total infection time that needs to infect all nodes in that network ,the infection rate for spreading epidemics in that network ,which measures the fraction of nodes those infected per unit time and the infection spreading power of that node ,that measures the power for each node to spread the epidemic to other uninfected nodes in that network. In this thesis, I deal with four types of networks ,unweight small and large networks and weighted small and large networks and study that relation in these four types. The importance of this work is when we find the closeness centrality and the infection spreading power of any node that help us understand which weakness or advantages this node has for maintenance or blocking dangers at the right time. In this work, I made some development in the SI model for the epidemic network in which most of authors consider the infection rate in that model assumed and constant. In this work I found that this infection rate is not constant but it depends on the closeness centrality of the first infected node in the network ,hence I suggest to replace the infection rate in the SI model by the closeness centrality of the first infected node in the network. The results obtained from this work show that each of the total infection time, the infection rate and the infection spreading power when any node infected first in the network depend on the closeness centrality for that node.