An adjacency matrix of an Erdős–Rényi random graph: an undirected graph is chosen uniformly at random from the set of all symmetric graphs with a fixed number of nodes and edges. For example:
julia> matrixdepot("erdrey", 5, 3) # an undirected graph with 5 nodes and 3 edges. 5x5 sparse matrix with 6 Float64 entries: [3, 1] = 1.0 [3, 2] = 1.0 [1, 3] = 1.0 [2, 3] = 1.0 [5, 4] = 1.0 [4, 5] = 1.0
- An adjacency matrix of a Gilbert random graph: each possible edge occurs independently with a given probability.
Motivated by the small world model proposed by Watts and Strogatz [wast98], we proposed a random graph model by adding shortcuts to a kth nearest neighbor ring (node \(i\) and \(j\) are connected iff \(|i-j| \leq k\) or \(|n - |i-j|| \leq k\)).
[wast98] D.J. Watts and S. H. Strogatz. Collective Dynamics of Small World Networks, Nature 393 (1998), pp. 440-442.