Galatasaray Üniversitesi Matematik Bölümü Seminerleri
Entropy, Assortativity, and Hierarchical Structures in Networks
Türker Bıyıkoğlu
Izmir Institute of Technology, Türkiye
I will connect several notions relating the structural and dynamical properties of a graph. Among them are the topological entropy, the spectral radius of the graph’s adjacency matrix, the Randi\'c index, and the degree assortativity. We will see that a hierarchical structure; namely, satisfies a breadth-first search ordering with decreasing degrees is a necessary structure for the extremal graphs that maximize these properties.
