Complex network zeta function and Dimension of Complex Network
(O. Shanker)
I work at Hewlett-Packard, and one of my research interests is complex networks (others include the Riemann zeta zeros and the related physics). In this page I provide a brief description and links to my work. Defining Dimension of Complex Network
One usually thinks of dimension for a set which is dense, like the points on a line, for example. Dimension makes sense in a discrete setting, like for graphs, only in the large system limit, as the size tends to infinity. For example, in Statistical Mechanics, one considers discrete points which are located on regular lattices of different dimensions. Such studies have been extended to arbitrary networks, and it is interesting to consider how the definition of dimension can be extended to cover these cases. Application of zeta function to Text Analysis
The graph zeta function is also useful in other contexts, such as Text Analysis. The plot below (based on my work with my colleague Giovanni Motta) shows how the function can be used to separate texts belonging to different languages. Further details regarding the definition of dimension using complex network zeta functions are given in my publication list. O. Shanker Email: oshanker.AT.gmail.com Thanks for your visit to the page! The files describing my work are pdf files, and need the Acrobat or similar pdf reader. If you wish to search for citations to my work, the best keyword to use is O. Shanker (Some people use the keywords Oruganti Shanker, Oruganti U. Shanker, or Oruganti Uma Shanker, and these searches should lead to my Software page). |