Structural distance and evolutionary relationship of networks

Evolutionary mechanism in a self-organized system cause some functional changes that force to adapt new conformation of the interaction pattern between the components of that system. Measuring the structural differences one can retrace the evolutionary relation between two systems. We present a method to quantify the topological distance between two networks of different sizes, finding that the architectures of the networks are more similar within the same class than the outside of their class. With 43 cellular networks of different species, we show that the evolutionary relationship can be elucidated from the structural distances.

💡 Research Summary

The paper introduces a novel quantitative framework for comparing the topology of networks of differing sizes and for inferring their evolutionary relationships. The authors base their approach on the normalized graph Laplacian, a well‑studied operator defined on undirected, unweighted graphs. For a graph Γ with N vertices, the Laplacian Δ is defined as Δv(i)=v(i)−(1/ni)∑_{j∼i}v(j), where ni is the degree of vertex i. Its spectrum consists of N real eigenvalues lying in the interval