%0 Journal Article
	%A Yilun Shang
	%D 2011
	%J International Journal of Mathematical and Computational Sciences
	%B World Academy of Science, Engineering and Technology
	%I Open Science Index 52, 2011
	%T The Giant Component in a Random Subgraph of a Weak Expander
	%U https://publications.waset.org/pdf/8522
	%V 52
	%X In this paper, we investigate the appearance of the giant component in random subgraphs G(p) of a given large finite graph family Gn = (Vn, En) in which each edge is present independently with probability p. We show that if the graph Gn satisfies a weak isoperimetric inequality and has bounded degree, then the probability p under which G(p) has a giant component of linear order with some constant probability is bounded away from zero and one. In addition, we prove the probability of abnormally large order of the giant component decays exponentially. When a contact graph is modeled as Gn, our result is of special interest in the study of the spread of infectious diseases or the identification of community in various social networks.

	%P 698 - 702