arXiv subjects

M. Kanehisa

Publications and source records attributed to M. Kanehisa.

3 recordsLinked to original sources

arXiv2005

Two complementary representations of a scale-free network

Several studies on real complex networks from different fields as biology, economy, or sociology have shown that the degree of nodes (number of edges connected to each node) follows a scale-free power-law distribution like $P(k)\approx k^{-γ}$, where $P(k)$ denotes the frequency of the nodes that are connected to $k$ other nodes. Here we have carried out a study on scale-free networks, where a line graph transformation (i.e., edges in an initial network are transformed into nodes) is applied to a power-law distribution. Our results indicate that a power-law distribution as $P(k)\approx k^{-γ+1}$ is found for the transformed network together with a peak for low-degree nodes. In the present work we show a parametrization of this behaviour and discuss its application to real networks as metabolic networks, protein-protein interaction network and World Wide Web.

physics.bio-ph↗

arXiv2004

Flexible construction of hierarchical scale-free networks with general exponent

Extensive studies have been done to understand the principles behind architectures of real networks. Recently, evidences for hierarchical organization in many real networks have also been reported. Here, we present a new hierarchical model which reproduces the main experimental properties observed in real networks: scale-free of degree distribution $P(k)$ (frequency of the nodes that are connected to $k$ other nodes decays as a power-law $P(k)\sim k^{-γ}$) and power-law scaling of the clustering coefficient $C(k)\sim k^{-1}$. The major novelties of our model can be summarized as follows: {\it (a)} The model generates networks with scale-free distribution for the degree of nodes with general exponent $γ> 2$, and arbitrarily close to any specified value, being able to reproduce most of the observed hierarchical scale-free topologies. In contrast, previous models can not obtain values of $γ> 2.58$. {\it (b)} Our model has structural flexibility because {\it (i)} it can incorporate various types of basic building blocks (e.g., triangles, tetrahedrons and, in general, fully connected clusters of $n$ nodes) and {\it (ii)} it allows a large variety of configurations (i.e., the model can use more than $n-1$ copies of basic blocks of $n$ nodes). The structural features of our proposed model might lead to a better understanding of architectures of biological and non-biological networks.

cond-mat.other↗

arXiv2004

Clustering under the line graph transformation: Application to reaction network

Many real networks can be understood as two complementary networks with two kind of nodes. This is the case of metabolic networks where the first network has chemical compounds as nodes and the second one has nodes as reactions. The second network can be related to the first one by a technique called line graph transformation (i.e., edges in an initial network are transformed into nodes). Recently, the main topological properties of the metabolic networks have been properly described by means of a hierarchical model. In our work, we apply the line graph transformation to a hierarchical network and the clustering coefficient $C(k)$ is calculated for the transformed network, where $k$ is the node degree. While $C(k)$ follows the scaling law $C(k)\sim k^{-1.1}$ for the initial hierarchical network, $C(k)$ scales weakly as $k^{0.08}$ for the transformed network. These results indicate that the reaction network can be identified as a degree-independent clustering network.

q-bio.MN↗