# Giant Component in Random Graph

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A random graph is a graph with nodes where the probability of finding an edge between two nodes is . When tends to a constant (as grows), the graph will almost surely contain a "giant" connected component, absorbing a considerably large fraction of the nodes. This phenomenon is often mentioned as an example of emergence in random graph behavior.

Contributed by: Tommaso Bolognesi (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The emergence of a giant connected component plays a crucial role in the theory of autocatalytic chemical networks, which attempts to explain the appearance of life in the universe ("abiogenesis") as a self-organization phenomenon occurring within chemical systems. The idea was first proposed by Stuart Kauffman in 1995.

See the actual graph growth process at Giant Component.

S. Kauffman, *At Home in the Universe: The Search for the Laws of Self-Organization and Complexity*, Oxford: Oxford Univ. Press, 1995.

## Permanent Citation

"Giant Component in Random Graph"

http://demonstrations.wolfram.com/GiantComponentInRandomGraph/

Wolfram Demonstrations Project

Published: March 7 2011