61,111 research outputs found
Modular Decomposition and the Reconstruction Conjecture
We prove that a large family of graphs which are decomposable with respect to
the modular decomposition can be reconstructed from their collection of
vertex-deleted subgraphs.Comment: 9 pages, 2 figure
Size reconstructibility of graphs
The deck of a graph is given by the multiset of (unlabelled) subgraphs
. The subgraphs are referred to as the cards of .
Brown and Fenner recently showed that, for , the number of edges of a
graph can be computed from any deck missing 2 cards. We show that, for
sufficiently large , the number of edges can be computed from any deck
missing at most cards.Comment: 15 page
Reconstruction of Directed Networks from Consensus Dynamics
This paper addresses the problem of identifying the topology of an unknown,
weighted, directed network running a consensus dynamics. We propose a
methodology to reconstruct the network topology from the dynamic response when
the system is stimulated by a wide-sense stationary noise of unknown power
spectral density. The method is based on a node-knockout, or grounding,
procedure wherein the grounded node broadcasts zero without being eliminated
from the network. In this direction, we measure the empirical cross-power
spectral densities of the outputs between every pair of nodes for both grounded
and ungrounded consensus to reconstruct the unknown topology of the network. We
also establish that in the special cases of undirected or purely unidirectional
networks, the reconstruction does not need grounding. Finally, we extend our
results to the case of a directed network assuming a general dynamics, and
prove that the developed method can detect edges and their direction.Comment: 6 page
- …