We show here that co-occurrence networks are characterized by scale-free topology and hierarchical modularity.
In this manner, the emergence of the short-cut path can explain the origin of several structural features: heterogeneous connectivity, network motifs (modules), and hierarchical modularity.
In particular, several striking structural properties have recently been found such as heterogeneous connectivity [ 9], small-worlds [ 10, 11], and hierarchical modularity [ 12].
The statistical study of biological networks has led to important novel biological insights, such as the presence of hubs and hierarchical modularity.
We first present mathematical solutions of this model using mean-field approximation, and demonstrate that this model can reproduce structural properties, such as heterogeneous connectivity and hierarchical modularity, in real metabolic networks both qualitatively and quantitatively.
Here, we investigate the topological properties of co-occurrence networks derived from published gene expression signatures and show that co-occurrence networks are characterized by scale-free topology and hierarchical modularity.
This observation may be related to a recent finding that, in a complex network, the large-scale topological organization (characterized by the degree exponents of the scale-free and hierarchical modularity) and the variable counts of the different motif topologies can define each other [ 28, 29].
The clustering coefficient C(k) depending on the link k can be approximated with a power law formula as follows: where w = scaling exponent of the network The value of scaling exponent w is close to -1 that indicates that the hierarchical modularity and both cancer and normal samples tend to have a hierarchical modular structure.
In addition, normal brain networks display hierarchical modularity, and a connectivity backbone that consists of interconnected hub nodes.
