6,695 research outputs found
Optimizing and controlling functions of complex networks by manipulating rich-club connections
Traditionally, there is no evidence suggesting that there are strong ties
between the rich-club property and the function of complex networks. In this
study, we find that whether a very small portion of rich nodes connected to
each other or not can strongly affect the frequency of occurrence of basic
building blocks (motif) within networks, and therefore the function, of a
heterogeneous network. Conversely whether a homogeneous network has a rich-club
property or not generally has no significant effect on its structure and
function. These findings open the possibility to optimize and control the
function of complex networks by manipulating rich-club connections.
Furthermore, based on the subgraph ratio profile, we develop a more rigorous
approach to judge whether a network has a rich-club or not. The new method does
not calculate how many links there are among rich nodes but depends on how the
links among rich nodes can affect the overall structure as well as function of
a given network. These results can also help us to understand the evolution of
dynamical networks and design new models for characterizing real-world
networks.Comment: 6 pages, 3 figure
Beyond clustering: mean-field dynamics on networks with arbitrary subgraph composition
Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of triangles, and this has led to the principle of constructing networks from such building blocks. This approach has been generalised to networks being constructed from a set of more exotic subgraphs. As long as these are fully connected, it is then possible to derive mean-field models that approximate epidemic dynamics well. However, there are virtually no results for non-fully connected subgraphs. In this paper, we provide a general and automated approach to deriving a set of ordinary differential equations, or mean-field model, that describes, to a high degree of accuracy, the expected values of system-level quantities, such as the prevalence of infection. Our approach offers a previously unattainable degree of control over the arrangement of subgraphs and network characteristics such as classical node degree, variance and clustering. The combination of these features makes it possible to generate families of networks with different subgraph compositions while keeping classical network metrics constant. Using our approach, we show that higher-order structure realised either through the introduction of loops of different sizes or by generating networks based on different subgraphs but with identical degree distribution and clustering, leads to non-negligible differences in epidemic dynamics
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