%0 Journal Article %1 Molloy_1998 %A Molloy, Michael %A Reed, Bruce %D 1998 %K degree_distributions giant_component, networks, %P 295–305 %T The Size of the Giant Component of a Random Graph with a Given Degree Sequence %V 7 %X Given a sequence of nonnegative real numbers λ0 , λ1 , . . . that sum to 1, we consider a random graph having approximately λi n vertices of degree i. In 12 the authors essentially show that if i(i − 2)λi > 0 then the graph a.s. has a giant component, while if i(i − 2)λi < 0 then a.s. all components in the graph are small. In this paper we analyse the size of the giant component in the former case, and the structure of the graph formed by deleting that component. We determine , λ0 , λ1 . . . such that a.s. the giant component, C, has n + o(n) vertices, and the structure of the graph remaining after deleting C is basically that of a random graph with n = n − |C| vertices, and with λi n of them of degree i.

@article{Molloy_1998, abstract = {Given a sequence of nonnegative real numbers λ0 , λ1 , . . . that sum to 1, we consider a random graph having approximately λi n vertices of degree i. In [12] the authors essentially show that if i(i − 2)λi > 0 then the graph a.s. has a giant component, while if i(i − 2)λi < 0 then a.s. all components in the graph are small. In this paper we analyse the size of the giant component in the former case, and the structure of the graph formed by deleting that component. We determine , λ0 , λ1 . . . such that a.s. the giant component, C, has n + o(n) vertices, and the structure of the graph remaining after deleting C is basically that of a random graph with n = n − |C| vertices, and with λi n of them of degree i.}, added-at = {2010-05-10T08:12:01.000+0200}, author = {Molloy, Michael and Reed, Bruce}, biburl = {https://www.bibsonomy.org/bibtex/27ad42dd3f2903fbd701b68a165671d4a/dhruvbansal}, file = {/home/dhruv/projects/work/papers/papers/Molloy_1998.pdf}, interhash = {cc8fb979967f02b082c80253494038a3}, intrahash = {7ad42dd3f2903fbd701b68a165671d4a}, keywords = {degree_distributions giant_component, networks,}, month = {November}, pages = {295–305}, read = {nil}, timestamp = {2010-05-10T08:12:05.000+0200}, title = {The Size of the Giant Component of a Random Graph with a Given Degree Sequence}, volume = 7, year = 1998 }