495,837 research outputs found
k-core organization of complex networks
We analytically describe the architecture of randomly damaged uncorrelated
networks as a set of successively enclosed substructures -- k-cores. The k-core
is the largest subgraph where vertices have at least k interconnections. We
find the structure of k-cores, their sizes, and their birth points -- the
bootstrap percolation thresholds. We show that in networks with a finite mean
number z_2 of the second-nearest neighbors, the emergence of a k-core is a
hybrid phase transition. In contrast, if z_2 diverges, the networks contain an
infinite sequence of k-cores which are ultra-robust against random damage.Comment: 5 pages, 3 figure
Deciphering the global organization of clustering in real complex networks
We uncover the global organization of clustering in real complex networks. To this end, we ask whether triangles in real networks organize as in maximally random graphs with given degree and clustering distributions, or as in maximally ordered graph models where triangles are forced into modules. The answer comes by way of exploring m-core landscapes, where the m-core is defined, akin to the k-core, as the maximal subgraph with edges participating in at least m triangles. This property defines a set of nested subgraphs that, contrarily to k-cores, is able to distinguish between hierarchical and modular architectures. We find that the clustering organization in real networks is neither completely random nor ordered although, surprisingly, it is more random than modular. This supports the idea that the structure of real networks may in fact be the outcome of self-organized processes based on local optimization rules, in contrast to global optimization principles.Fil: Colomer de Simón, Pol. Universidad de Barcelona; EspañaFil: Serrano, María de Los Angeles. Universidad de Barcelona; EspañaFil: Beiro, Mariano Gastón. Universidad de Buenos Aires. Facultad de Ingenieria. Departamento de Electronica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Tecnologías y Ciencias de la Ingeniería; ArgentinaFil: Alvarez Hamelin, Jose Ignacio. Universidad de Buenos Aires. Facultad de Ingenieria. Departamento de Electronica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Tecnologías y Ciencias de la Ingeniería; ArgentinaFil: Boguñá, Marián. Universidad de Barcelona; Españ
Network centrality: an introduction
Centrality is a key property of complex networks that influences the behavior
of dynamical processes, like synchronization and epidemic spreading, and can
bring important information about the organization of complex systems, like our
brain and society. There are many metrics to quantify the node centrality in
networks. Here, we review the main centrality measures and discuss their main
features and limitations. The influence of network centrality on epidemic
spreading and synchronization is also pointed out in this chapter. Moreover, we
present the application of centrality measures to understand the function of
complex systems, including biological and cortical networks. Finally, we
discuss some perspectives and challenges to generalize centrality measures for
multilayer and temporal networks.Comment: Book Chapter in "From nonlinear dynamics to complex systems: A
Mathematical modeling approach" by Springe
Detection of the elite structure in a virtual multiplex social system by means of a generalized -core
Elites are subgroups of individuals within a society that have the ability
and means to influence, lead, govern, and shape societies. Members of elites
are often well connected individuals, which enables them to impose their
influence to many and to quickly gather, process, and spread information. Here
we argue that elites are not only composed of highly connected individuals, but
also of intermediaries connecting hubs to form a cohesive and structured
elite-subgroup at the core of a social network. For this purpose we present a
generalization of the -core algorithm that allows to identify a social core
that is composed of well-connected hubs together with their `connectors'. We
show the validity of the idea in the framework of a virtual world defined by a
massive multiplayer online game, on which we have complete information of
various social networks. Exploiting this multiplex structure, we find that the
hubs of the generalized -core identify those individuals that are high
social performers in terms of a series of indicators that are available in the
game. In addition, using a combined strategy which involves the generalized
-core and the recently introduced -core, the elites of the different
'nations' present in the game are perfectly identified as modules of the
generalized -core. Interesting sudden shifts in the composition of the elite
cores are observed at deep levels. We show that elite detection with the
traditional -core is not possible in a reliable way. The proposed method
might be useful in a series of more general applications, such as community
detection.Comment: 13 figures, 3 tables, 19 pages. Accepted for publication in PLoS ON
Large-scale network organization in the avian forebrain: a connectivity matrix and theoretical analysis
Many species of birds, including pigeons, possess demonstrable cognitive capacities, and some are capable of cognitive feats matching those of apes. Since mammalian cortex is laminar while the avian telencephalon is nucleated, it is natural to ask whether the brains of these two cognitively capable taxa, despite their apparent anatomical dissimilarities, might exhibit common principles of organisation on some level. Complementing recent investigations of macro-scale brain connectivity in mammals, including humans and macaques, we here present the first large-scale wiring diagram for the forebrain of a bird. Using graph theory, we show that the pigeon telencephalon is organised along similar lines to that of a mammal. Both are modular, small-world networks with a connective core of hub nodes that includes prefrontal-like and hippocampal structures. These hub nodes are, topologically speaking, the most central regions of the pigeon's brain, as well as being the most richly connected, implying a crucial role in information flow. Overall, our analysis suggests that indeed, despite the absence of cortical layers and close to 300 million years of separate evolution, the connectivity of the avian brain conforms to the same organisational principles as the mammalian brain
Clustering Algorithms for Scale-free Networks and Applications to Cloud Resource Management
In this paper we introduce algorithms for the construction of scale-free
networks and for clustering around the nerve centers, nodes with a high
connectivity in a scale-free networks. We argue that such overlay networks
could support self-organization in a complex system like a cloud computing
infrastructure and allow the implementation of optimal resource management
policies.Comment: 14 pages, 8 Figurs, Journa
The Impact of Network Flows on Community Formation in Models of Opinion Dynamics
We study dynamics of opinion formation in a network of coupled agents. As the
network evolves to a steady state, opinions of agents within the same community
converge faster than those of other agents. This framework allows us to study
how network topology and network flow, which mediates the transfer of opinions
between agents, both affect the formation of communities. In traditional models
of opinion dynamics, agents are coupled via conservative flows, which result in
one-to-one opinion transfer. However, social interactions are often
non-conservative, resulting in one-to-many transfer of opinions. We study
opinion formation in networks using one-to-one and one-to-many interactions and
show that they lead to different community structure within the same network.Comment: accepted for publication in The Journal of Mathematical Sociology.
arXiv admin note: text overlap with arXiv:1201.238
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