42,763 research outputs found
Linear work generation of R-MAT graphs
R-MAT (for Recursive MATrix) is a simple, widely used model for generating graphs with a power law degree distribution, a small diameter, and communitys structure. It is particularly attractive for generating very large graphs because edges can be generated independently by an arbitrary number of processors. However, current R-MAT generators need time logarithmic in the number of nodes for generating an edge— constant time for generating one bit at a time for node IDs of the connected nodes. We achieve constant time per edge by precomputing pieces of node IDs of logarithmic length. Using an alias table data structure, these pieces can then be sampled in constant time. This simple technique leads to practical improvements by an order of magnitude. This further pushes the limits of attainable graph size and makes generation overhead negligible in most situations
Discrete Scale Invariance in Scale Free Graphs
In this work we introduce an energy function in order to study finite scale
free graphs generated with different models. The energy distribution has a
fractal pattern and presents log periodic oscillations for high energies. This
oscillations are related to a discrete scale invariance of certain graphs, that
is, there are preferred scaling ratios suggesting a hierarchical distribution
of node degrees. On the other hand, small energies correspond to graphs with
evenly distributed degrees.Comment: 13 pages, 12 figure
Power Grid Network Evolutions for Local Energy Trading
The shift towards an energy Grid dominated by prosumers (consumers and
producers of energy) will inevitably have repercussions on the distribution
infrastructure. Today it is a hierarchical one designed to deliver energy from
large scale facilities to end-users. Tomorrow it will be a capillary
infrastructure at the medium and Low Voltage levels that will support local
energy trading among prosumers. In our previous work, we analyzed the Dutch
Power Grid and made an initial analysis of the economic impact topological
properties have on decentralized energy trading. In this paper, we go one step
further and investigate how different networks topologies and growth models
facilitate the emergence of a decentralized market. In particular, we show how
the connectivity plays an important role in improving the properties of
reliability and path-cost reduction. From the economic point of view, we
estimate how the topological evolutions facilitate local electricity
distribution, taking into account the main cost ingredient required for
increasing network connectivity, i.e., the price of cabling
Emergent relativistic-like Kinematics and Dynamical Mass Generation for a Lifshitz-type Yukawa model
We study the Infra Red (IR) limit of dispersion relations for scalar and
fermion fields in a Lifshitz-type Yukawa model, after dressing by quantum
fluctuations. Relativistic-like dispersion relations emerge dynamically in the
IR regime of the model, after quantum corrections are taken into account. In
this regime, dynamical mass generation also takes place, but in such a way that
the particle excitations remain massive, even if the bare masses vanish. The
group velocities of the corresponding massive particles of course are smaller
than the speed of light, in a way consistent with the IR regime where the
analysis is performed. We also comment on possible extensions of the model
where the fermions are coupled to an Abelian gauge field
An extensive English language bibliography on graph theory and its applications, supplement 1
Graph theory and its applications - bibliography, supplement
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