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For large graph with single machine i.e. limitedspace , We can use Map/ Reduce systems and Key/ value stores.

Store the adjacency list for each vertex in a different machine.

Store the adjacency list for each vertex in a separate machine,

Adj list, but in following way:
Distributed hash map.
A key is either a node or pair of nodes.
If it is a node, a value is a pair that consists of key node and the first node in adjacency list.
If it is a pair. The key consists of node for who the adjacency list and the current node in adj list. A value consists of node for who the adjacency list and the next node in adj list.

Group the Nodes ( n1,n2,n3,n5,......) and store them to different Machine.
now mark the different machines as node of graph(N1,N2,N3,N4, ....).

and store a Adjacency list which keep trace of major nodes.

(1) Use Adjacency Matrix and create submatrix (as per node capacity).
(2) Create Adjacency Matrix for Vertices identifiers for finding out index of edge.
(3) Create Vertices identifiers and servers map to find out from which server to fetch submatrix.

Hadoop is best option for such kind of system

What kind of system should it be? Should it require high performance online access or Should it be used for data warehouse analytics batch processing? I would initially suggest Cassandra for the first and Hadoop for the latter.

Use adjacency matrix, divide the matrix across machines.

Use Bulk-Synchronous-Parallel (BSP) algorithm.

Bulk-Synchronous-Parallel (BSP) algorithm.

actually which graph r u talking about its 1 rupee graph or 2 rupees graph. i know better that 2 rupee graph is bigger in size