Beta Index
Measures the level of connectivity in a graph and is expressed by the relationship between the number of links (e) over the number of nodes (v). Trees and simple networks have Beta value of less than one. A connected network with one cycle has a value of 1. More complex networks have a value greater than 1. In a network with a fixed number of nodes, the higher the number of links, the higher the number of paths possible in the network. Complex networks have a high value of Beta. The rich-club coefficient is the Beta index applied to relations among larger order (degree) nodes; it verifies whether the connectivity is higher among larger degree nodes than for the whole network. These above four graphs are of growing connectivity. Graph A and B are not fully connected and their Beta value is lower than 1. Graph C is connected and has a Beta value of 1. Graph D is even more connected with a Beta value of 1.25.