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)
“A culture may be conceived as a network of beliefs and purposes in which any string in the net pulls and is pulled by the others, thus perpetually changing the configuration of the whole. If the cultural element called morals takes on a new shape, we must ask what other strings have pulled it out of line. It cannot be one solitary string, nor even the strings nearby, for the network is three-dimensional at least.”
—Jacques Barzun (b. 1907)
“It seems to me that we do not know nearly enough about ourselves; that we do not often enough wonder if our lives, or some events and times in our lives, may not be analogues or metaphors or echoes of evolvements and happenings going on in other people?—or animals?—even forests or oceans or rocks?—in this world of ours or, even, in worlds or dimensions elsewhere.”
—Doris Lessing (b. 1919)