Table 2 Random network models

Network science aims to build models that reproduce the properties of real networks. Here, we describe broadly used three random network models.

1. Erdös - Rènyi(ER) network: ER characterizes random graphs and depicts that many of the properties of such networks can be calculated analytically. Construction of an ER random graph with parameter 0≤p≤1 and N nodes is by connecting every pair of nodes with probability p.

2. Small-world (SW) network: This model is characterized by small-world phenomenon of social networks that suggests we are all linked by short chains of acquaintances. Watts and Strogatz SW model is purely built on ER graphs and comprise of properties of high clustering coefficient and short average path (Watts and Strogatz 1998). Friendship networks in social media and gene regulatory networks follow small-world phenomena.

3. Scale-free (SF) network: This model is characterized by an important property of real world networks that most network nodes have a few links to other nodes, however a small number of nodes are highly connected and have a huge number of links to other nodes. This leads to the observation that these networks do not have nodes with a typical number of neighbors, and in this sense these networks are scale-free. Degree distribution of SF follows power law and the power law exponent lies between 2 and 3. Widely used SF generation algorithm is Barabási-Albert (BA) model of preferential attachment (Barabási and Albert 1999). Real-world network such as PPI, transport network follow scale-free behavior (Przulj et al. 2004).