Urban Hierarchy and the Rank-Size Distribution

Agents with Dycotomic Goals Which Generate a Rank-size Distribution

Mono-Size Distribution Index (MSDI): A new criterion for the quantitative description of size distribution

Graphical size distribution is widely used in different fields of science and studies related to powders, droplets, bubbles, and pores. However, in some condition it may also be necessary to express the size distribution quantitatively. In spite of there being several suggested ways to quantify size distribution in the literature, some of these approaches are not applicable for many methods and...

Degree Distribution, Rank-size Distribution, and Leadership Persistence in Mediation-Driven Attachment Networks

We investigate the growth of a class of networks in which a new node first picks a mediator at random and connects with m randomly chosen neighbors of the mediator at each time step. We show that degree distribution in such a mediation-driven attachment (MDA) network exhibits power-law P (k) ∼ k with a spectrum of exponents depending on m. To appreciate the contrast between MDA and Barabási-Alb...

Hierarchy Size and Environmental Uncertainty

We examine how a firm’s changing environment and the information constraints of its managers interact as determinants of the size of the firm’s administration. Following the recent decentralized information processing literature, we assume that it takes individual managers time to process information. A consequence is that it takes time for a firm to aggregate information, even when this task i...

The rank and size of graphs

We show that the number of points with pairwise different sets of neighbors in a graph is O(2) where r is the rank of the adjacency matrix. We also give an example that achieves this bound.