3 research outputs found
Sampling properties of directed networks
For many real-world networks only a small "sampled" version of the original
network may be investigated; those results are then used to draw conclusions
about the actual system. Variants of breadth-first search (BFS) sampling, which
are based on epidemic processes, are widely used. Although it is well
established that BFS sampling fails, in most cases, to capture the
IN-component(s) of directed networks, a description of the effects of BFS
sampling on other topological properties are all but absent from the
literature. To systematically study the effects of sampling biases on directed
networks, we compare BFS sampling to random sampling on complete large-scale
directed networks. We present new results and a thorough analysis of the
topological properties of seven different complete directed networks (prior to
sampling), including three versions of Wikipedia, three different sources of
sampled World Wide Web data, and an Internet-based social network. We detail
the differences that sampling method and coverage can make to the structural
properties of sampled versions of these seven networks. Most notably, we find
that sampling method and coverage affect both the bow-tie structure, as well as
the number and structure of strongly connected components in sampled networks.
In addition, at low sampling coverage (i.e. less than 40%), the values of
average degree, variance of out-degree, degree auto-correlation, and link
reciprocity are overestimated by 30% or more in BFS-sampled networks, and only
attain values within 10% of the corresponding values in the complete networks
when sampling coverage is in excess of 65%. These results may cause us to
rethink what we know about the structure, function, and evolution of real-world
directed networks.Comment: 21 pages, 11 figure
A Novel Approach to Discontinuous Bond Percolation Transition
We introduce a bond percolation procedure on a -dimensional lattice where
two neighbouring sites are connected by channels, each operated by valves
at both ends. Out of a total of , randomly chosen valves are open at
every site. A bond is said to connect two sites if there is at least one
channel between them, which has open valves at both ends. We show analytically
that in all spatial dimensions, this system undergoes a discontinuous
percolation transition in the limit when
crosses a threshold. It must be emphasized
that, in contrast to the ordinary percolation models, here the transition
occurs even in one dimensional systems, albeit discontinuously. We also show
that a special kind of discontinuous percolation occurs only in one dimension
when depends on the system size.Comment: 6 pages, 6 eps figure
Exact solutions for mass-dependent irreversible aggregations
We consider the mass-dependent aggregation process (k + 1) X -> X, given a fixed number of unit mass particles in the initial state. One cluster is chosen proportional to its mass and is merged into one, either with k neighbors in one dimension, or-in the well-mixed case-with k other clusters picked randomly. We find the same combinatorial exact solutions for the probability to find any given configuration of particles on a ring or line, and in the well-mixed case. The mass distribution of a single cluster exhibits scaling laws and the finite-size scaling form is given. The relation to the classical sum kernel of irreversible aggregation is discussed