Fractal Dimension On Networks - Other Definitions For Network Dimensions

Other Definitions For Network Dimensions

The best definition of dimension for a complex network or graph depends on the application. For example, metric dimension is defined in terms of the resolving set for a graph. Definitions based on the scaling property of the "mass" as defined above with distance, or based on the complex network zeta function have also been studied.

For networks embedded in real space, one can define a dimension that characterize the number of nodes that can be reached with an average Euclidean distance.

Read more about this topic:  Fractal Dimension On Networks

Famous quotes containing the words definitions, network and/or dimensions:

    The loosening, for some people, of rigid role definitions for men and women has shown that dads can be great at calming babies—if they take the time and make the effort to learn how. It’s that time and effort that not only teaches the dad how to calm the babies, but also turns him into a parent, just as the time and effort the mother puts into the babies turns her into a parent.
    Pamela Patrick Novotny (20th century)

    How have I been able to live so long outside Nature without identifying myself with it? Everything lives, moves, everything corresponds; the magnetic rays, emanating either from myself or from others, cross the limitless chain of created things unimpeded; it is a transparent network that covers the world, and its slender threads communicate themselves by degrees to the planets and stars. Captive now upon earth, I commune with the chorus of the stars who share in my joys and sorrows.
    Gérard De Nerval (1808–1855)

    Words are finite organs of the infinite mind. They cannot cover the dimensions of what is in truth. They break, chop, and impoverish it.
    Ralph Waldo Emerson (1803–1882)