794 research outputs found
Why social networks are different from other types of networks
We argue that social networks differ from most other types of networks,
including technological and biological networks, in two important ways. First,
they have non-trivial clustering or network transitivity, and second, they show
positive correlations, also called assortative mixing, between the degrees of
adjacent vertices. Social networks are often divided into groups or
communities, and it has recently been suggested that this division could
account for the observed clustering. We demonstrate that group structure in
networks can also account for degree correlations. We show using a simple model
that we should expect assortative mixing in such networks whenever there is
variation in the sizes of the groups and that the predicted level of
assortative mixing compares well with that observed in real-world networks.Comment: 9 pages, 2 figure
Percolation and epidemics in a two-dimensional small world
Percolation on two-dimensional small-world networks has been proposed as a
model for the spread of plant diseases. In this paper we give an analytic
solution of this model using a combination of generating function methods and
high-order series expansion. Our solution gives accurate predictions for
quantities such as the position of the percolation threshold and the typical
size of disease outbreaks as a function of the density of "shortcuts" in the
small-world network. Our results agree with scaling hypotheses and numerical
simulations for the same model.Comment: 7 pages, 3 figures, 2 table
Renormalization group analysis of the small-world network model
We study the small-world network model, which mimics the transition between
regular-lattice and random-lattice behavior in social networks of increasing
size. We contend that the model displays a normal continuous phase transition
with a divergent correlation length as the degree of randomness tends to zero.
We propose a real-space renormalization group transformation for the model and
demonstrate that the transformation is exact in the limit of large system size.
We use this result to calculate the exact value of the single critical exponent
for the system, and to derive the scaling form for the average number of
"degrees of separation" between two nodes on the network as a function of the
three independent variables. We confirm our results by extensive numerical
simulation.Comment: 4 pages including 3 postscript figure
An analysis of the fixation probability of a mutant on special classes of non-directed graphs
There is a growing interest in the study of evolutionary dynamics on populations with some non-homogeneous structure. In this paper we follow the model of Lieberman et al. (Lieberman et al. 2005 Nature 433, 312–316) of evolutionary dynamics on a graph. We investigate the case of non-directed equally weighted graphs and find solutions for the fixation probability of a single mutant in two classes of simple graphs. We further demonstrate that finding similar solutions on graphs outside these classes is far more complex. Finally, we investigate our chosen classes numerically and discuss a number of features of the graphs; for example, we find the fixation probabilities for different initial starting positions and observe that average fixation probabilities are always increased for advantageous mutants as compared with those of unstructured populations
Graph Metrics for Temporal Networks
Temporal networks, i.e., networks in which the interactions among a set of
elementary units change over time, can be modelled in terms of time-varying
graphs, which are time-ordered sequences of graphs over a set of nodes. In such
graphs, the concepts of node adjacency and reachability crucially depend on the
exact temporal ordering of the links. Consequently, all the concepts and
metrics proposed and used for the characterisation of static complex networks
have to be redefined or appropriately extended to time-varying graphs, in order
to take into account the effects of time ordering on causality. In this chapter
we discuss how to represent temporal networks and we review the definitions of
walks, paths, connectedness and connected components valid for graphs in which
the links fluctuate over time. We then focus on temporal node-node distance,
and we discuss how to characterise link persistence and the temporal
small-world behaviour in this class of networks. Finally, we discuss the
extension of classic centrality measures, including closeness, betweenness and
spectral centrality, to the case of time-varying graphs, and we review the work
on temporal motifs analysis and the definition of modularity for temporal
graphs.Comment: 26 pages, 5 figures, Chapter in Temporal Networks (Petter Holme and
Jari Saram\"aki editors). Springer. Berlin, Heidelberg 201
Edge overload breakdown in evolving networks
We investigate growing networks based on Barabasi and Albert's algorithm for
generating scale-free networks, but with edges sensitive to overload breakdown.
the load is defined through edge betweenness centrality. We focus on the
situation where the average number of connections per vertex is, as the number
of vertices, linearly increasing in time. After an initial stage of growth, the
network undergoes avalanching breakdowns to a fragmented state from which it
never recovers. This breakdown is much less violent if the growth is by random
rather than preferential attachment (as defines the Barabasi and Albert model).
We briefly discuss the case where the average number of connections per vertex
is constant. In this case no breakdown avalanches occur. Implications to the
growth of real-world communication networks are discussed.Comment: To appear in Phys. Rev.
Analysis of Computer Science Communities Based on DBLP
It is popular nowadays to bring techniques from bibliometrics and
scientometrics into the world of digital libraries to analyze the collaboration
patterns and explore mechanisms which underlie community development. In this
paper we use the DBLP data to investigate the author's scientific career and
provide an in-depth exploration of some of the computer science communities. We
compare them in terms of productivity, population stability and collaboration
trends.Besides we use these features to compare the sets of topranked
conferences with their lower ranked counterparts.Comment: 9 pages, 7 figures, 6 table
Cross-over behaviour in a communication network
We address the problem of message transfer in a communication network. The
network consists of nodes and links, with the nodes lying on a two dimensional
lattice. Each node has connections with its nearest neighbours, whereas some
special nodes, which are designated as hubs, have connections to all the sites
within a certain area of influence. The degree distribution for this network is
bimodal in nature and has finite variance. The distribution of travel times
between two sites situated at a fixed distance on this lattice shows fat
fractal behaviour as a function of hub-density. If extra assortative
connections are now introduced between the hubs so that each hub is connected
to two or three other hubs, the distribution crosses over to power-law
behaviour. Cross-over behaviour is also seen if end-to-end short cuts are
introduced between hubs whose areas of influence overlap, but this is much
milder in nature. In yet another information transmission process, namely, the
spread of infection on the network with assortative connections, we again
observed cross-over behaviour of another type, viz. from one power-law to
another for the threshold values of disease transmission probability. Our
results are relevant for the understanding of the role of network topology in
information spread processes.Comment: 12 figure
Citation Networks in High Energy Physics
The citation network constituted by the SPIRES data base is investigated
empirically. The probability that a given paper in the SPIRES data base has
citations is well described by simple power laws, ,
with for less than 50 citations and for 50 or more citations. Two models are presented that both represent the
data well, one which generates power laws and one which generates a stretched
exponential. It is not possible to discriminate between these models on the
present empirical basis. A consideration of citation distribution by subfield
shows that the citation patterns of high energy physics form a remarkably
homogeneous network. Further, we utilize the knowledge of the citation
distributions to demonstrate the extreme improbability that the citation
records of selected individuals and institutions have been obtained by a random
draw on the resulting distribution.Comment: 9 pages, 6 figures, 2 table
Scaling Properties of Random Walks on Small-World Networks
Using both numerical simulations and scaling arguments, we study the behavior
of a random walker on a one-dimensional small-world network. For the properties
we study, we find that the random walk obeys a characteristic scaling form.
These properties include the average number of distinct sites visited by the
random walker, the mean-square displacement of the walker, and the distribution
of first-return times. The scaling form has three characteristic time regimes.
At short times, the walker does not see the small-world shortcuts and
effectively probes an ordinary Euclidean network in -dimensions. At
intermediate times, the properties of the walker shows scaling behavior
characteristic of an infinite small-world network. Finally, at long times, the
finite size of the network becomes important, and many of the properties of the
walker saturate. We propose general analytical forms for the scaling properties
in all three regimes, and show that these analytical forms are consistent with
our numerical simulations.Comment: 7 pages, 8 figures, two-column format. Submitted to PR
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