2 research outputs found
Transtemporal edges and crosslayer edges in incompressible high-order networks
This work presents some outcomes of a theoretical investigation of
incompressible high-order networks defined by a generalized graph
representation. We study some of their network topological properties and how
these may be related to real-world complex networks. We show that these
networks have very short diameter, high k-connectivity, degrees of the order of
half of the network size within a strong-asymptotically dominated standard
deviation, and rigidity with respect to automorphisms. In addition, we
demonstrate that incompressible dynamic (or dynamic multilayered) networks have
transtemporal (or crosslayer) edges and, thus, a snapshot-like representation
of dynamic networks is inaccurate for capturing the presence of such edges that
compose underlying structures of some real-world networks.Comment: Accepted extended abstract in
http://csbc2019.sbc.org.br/eventos/4etc/ The results of this paper are also
contained in arXiv:1812.0117
On incompressible multidimensional networks
In order to deal with multidimensional structure representations of
real-world networks, as well as with their worst-case irreducible information
content analysis, the demand for new graph abstractions increases. This article
presents an investigation of incompressible multidimensional networks defined
by generalized graph representations. In particular, we mathematically study
the lossless incompressibility of snapshot-dynamic networks and multiplex
networks in comparison to the lossless incompressibility of more general forms
of dynamic networks and multilayer networks, from which snapshot-dynamic
networks or multiplex networks are particular cases. We show that
incompressible snapshot-dynamic (or multiplex) networks carry an amount of
algorithmic information that is linearly dominated by the size of the set of
time instants (or layers). This contrasts with the algorithmic information
carried by incompressible general dynamic (or multilayer) networks that is of
the quadratic order of the size of the set of time instants (or layers).
Furthermore, we prove that incompressible general multidimensional networks
have edges linking vertices at non-sequential time instants (layers or, in
general, elements of a node dimension). Thus, representational
incompressibility implies a necessary underlying constraint in the
multidimensional network topology