Network Science
Explore the metrics and layouts that BeGraph offers

Network Metrics

Metrics in BeGraph are mathematical operations based on Graph Theory used to characterize the network. They can provide insights on the centrality of the nodes, the most transited links, cohesion properties, network clustering, and topology. Usually, their result is a new node/link property. So far, BeGraph offers a variety of useful network metrics listed below. Click on each metric for detailed information.

Spatial Layouts

A Layout is a spatial arrangement of the network that helps to understand its topology and structure. Note that the exact positions in space of the nodes are completely irrelevant for this purpose, only their relative location and grouping have meaning. BeGraph provides several layout algorithms: Fruchterman-Reingold, Kamada-Kawai, Force Atlas and a node property based layout (scatter plot):

Force Atlas Layout

This is a layout algorithm based on a force directed system (a more sophisticated version of Fruchterman-Reingold), optimized for dealing with large networks and highly configurable. There are many forces acting on the nodes: repulsion on every pair of nodes depending on their degree, attraction on linked nodes, central gravity, outer attraction and more.

Two examples of Force Atlas results applied on two social networks. We can observe how the nodes group together in clusters around some important nodes. Node color correspond to the Louvain community detection algorithm.

Fruchterman-Reingold Layout

It is a layout algorithm based on an attraction-repulsion force system. All nodes suffer repulsion forces from every other node and attraction to those who are linked. The total energy of the system is minimized using simulated annealing, finding a state with force equilibrium. The intensity of the attraction force can be influenced by any numerical link property, reflecting the strength of the link. This layout is recommended for small and medium-size networks (10.000 nodes max.) due to the bad scaling with the number of nodes.

Two examples of this layout results applied on two social networks. Node color correspond to the Louvain community detection algorithm.
These plots shows the effect of the expansion factor [e.f.] on the same network:

Layered Force Atlas Layout

It is a layout very similar to the standard Force Atlas Layout , with the exception that the z coordinate [called layer] is provided as a node property. It is recommended for bipartite networks, where each bipartite group lays on a layer. It presents the same options as the Force Atlas layout with the exception of a new parameter.

forceatlaslayered

Kamada-Kawai Layout

Layout algorithm based on a physical spring force system. Each node is connected with all the remaining nodes with a spring, and each spring has a constant and equilibrium length related to the distance in the network between the two nodes. The closer the nodes are in the network, the stronger the spring is and the shorter its equilibrium length. Reaching the equilibrium force requires a very expensive computation, so this layout is only recommended for small networks (~1000 nodes), although it may produce beautiful network disposals

Plots of a 2D and 3D layout of a gene network (yeast). Node size corresponds to its degree and its color identifies its community.

Scatter Layout

In this layout, the positions of the nodes are given by two or three node properties. It is possible to normalize the properties to values between 0 and 1. Can be used to look for correlations between the network topology and numerical properties of the nodes. This layout is also a way to draw and navigate in big scatter plots, without network structure. 

Two plots showing a visualization of the vertices of an OBJ file (which include the vertex positions). All nodes have transparency, and the darker regions indicate an accumulation of nodes. In total, the figure has more than 66000 nodes.

References

Albert-Lázsló Barabási’s book on Network Science (excellent introduction)
M.E.J. Newman, Networks, an introduction, Oxford University Press, 2010, ISBN: 978-0-19-920665-0, sec. 10.3.3.