1,830 research outputs found
Structural patterns in complex networks through spectral analysis
The study of some structural properties of networks is introduced from a graph spectral perspective. First, subgraph centrality of nodes is defined and used to classify essential proteins in a proteomic map. This index is then used to produce a method that allows the identification of superhomogeneous networks. At the same time this method classify non-homogeneous network into three universal classes of structure. We give examples of these classes from networks in different real-world scenarios. Finally, a communicability function is studied and showed as an alternative for defining communities in complex networks. Using this approach a community is unambiguously defined and an algorithm for its identification is proposed and exemplified in a real-world network
Communicability in temporal networks
A first-principles approach to quantify the communicability between pairs of nodes in temporal networks is proposed. It corresponds to the imaginary-time propagator of a quantum random walk in the temporal network, which accounts for unique structural and temporal characteristics of both streaming and nonstreaming temporal networks. The influence of the system's temperature on the perdurability of information and how the communicability identifies patterns of communication hidden in the temporal and topological structure of the networks are also studied for synthetic and real-world systems
Spectral Scaling in Complex Networks
A complex network is said to show topological isotropy if the topological
structure around a particular node looks the same in all directions of the
whole network. Topologically anisotropic networks are those where the local
neighborhood around a node is not reproduced at large scale for the whole
network. The existence of topological isotropy is investigated by the existence
of a power-law scaling between a local and a global topological characteristic
of complex networks obtained from graph spectra. We investigate this structural
characteristic of complex networks and its consequences for 32 real-world
networks representing informational, technological, biological, social and
ecological systems.Comment: 9 pages, 3 figure
Metaplex networks: influence of the exo-endo structure of complex systems on diffusion
In a complex system the interplay between the internal structure of its
entities and their interconnection may play a fundamental role in the global
functioning of the system. Here, we define the concept of metaplex, which
describes such trade-off between internal structure of entities and their
interconnections. We then define a dynamical system on a metaplex and study
diffusive processes on them. We provide analytical and computational evidences
about the role played by the size of the nodes, the location of the internal
coupling areas, and the strength and range of the coupling between the nodes on
the global dynamics of metaplexes. Finally, we extend our analysis to two
real-world metaplexes: a landscape and a brain metaplex. We corroborate that
the internal structure of the nodes in a metaplex may dominate the global
dynamics (brain metaplex) or play a regulatory role (landscape metaplex) to the
influence of the interconnection between nodes.Comment: 28 pages, 19 figure
Communicability Angles Reveal Critical Edges for Network Consensus Dynamics
We consider the question of determining how the topological structure
influences a consensus dynamical process taking place on a network. By
considering a large dataset of real-world networks we first determine that the
removal of edges according to their communicability angle -an angle between
position vectors of the nodes in an Euclidean communicability space- increases
the average time of consensus by a factor of 5.68 in real-world networks. The
edge betweenness centrality also identifies -in a smaller proportion- those
critical edges for the consensus dynamics, i.e., its removal increases the time
of consensus by a factor of 3.70. We justify theoretically these findings on
the basis of the role played by the algebraic connectivity and the
isoperimetric number of networks on the dynamical process studied, and their
connections with the properties mentioned before. Finally, we study the role
played by global topological parameters of networks on the consensus dynamics.
We determine that the network density and the average distance-sum -an
analogous of the node degree for shortest-path distances, account for more than
80% of the variance of the average time of consensus in the real-world networks
studied.Comment: 15 pages, 2 figure
Returnability in complex directed networks (digraphs)
The concept of returnability is proposed for complex directed networks (digraphs). It can be seen as a generalization of the concept of reciprocity. Two measures of the returnability are introduced. We establish closed formulas for the calculation of the returnability measures, which are also related to the digraph spectrum. The two measures are calculated for simple examples of digraphs as well as for real-world complex directed networks and are compared with the reciprocity
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