2,750 research outputs found
Clustering in complex networks. II. Percolation properties
The percolation properties of clustered networks are analyzed in detail. In
the case of weak clustering, we present an analytical approach that allows to
find the critical threshold and the size of the giant component. Numerical
simulations confirm the accuracy of our results. In more general terms, we show
that weak clustering hinders the onset of the giant component whereas strong
clustering favors its appearance. This is a direct consequence of the
differences in the -core structure of the networks, which are found to be
totally different depending on the level of clustering. An empirical analysis
of a real social network confirms our predictions.Comment: Updated reference lis
Random acyclic networks
Directed acyclic graphs are a fundamental class of networks that includes
citation networks, food webs, and family trees, among others. Here we define a
random graph model for directed acyclic graphs and give solutions for a number
of the model's properties, including connection probabilities and component
sizes, as well as a fast algorithm for simulating the model on a computer. We
compare the predictions of the model to a real-world network of citations
between physics papers and find surprisingly good agreement, suggesting that
the structure of the real network may be quite well described by the random
graph.Comment: 4 pages, 2 figure
A dissemination strategy for immunizing scale-free networks
We consider the problem of distributing a vaccine for immunizing a scale-free
network against a given virus or worm. We introduce a new method, based on
vaccine dissemination, that seems to reflect more accurately what is expected
to occur in real-world networks. Also, since the dissemination is performed
using only local information, the method can be easily employed in practice.
Using a random-graph framework, we analyze our method both mathematically and
by means of simulations. We demonstrate its efficacy regarding the trade-off
between the expected number of nodes that receive the vaccine and the network's
resulting vulnerability to develop an epidemic as the virus or worm attempts to
infect one of its nodes. For some scenarios, the new method is seen to render
the network practically invulnerable to attacks while requiring only a small
fraction of the nodes to receive the vaccine
Properties of Random Graphs with Hidden Color
We investigate in some detail a recently suggested general class of ensembles
of sparse undirected random graphs based on a hidden stub-coloring, with or
without the restriction to nondegenerate graphs. The calculability of local and
global structural properties of graphs from the resulting ensembles is
demonstrated. Cluster size statistics are derived with generating function
techniques, yielding a well-defined percolation threshold. Explicit rules are
derived for the enumeration of small subgraphs. Duality and redundancy is
discussed, and subclasses corresponding to commonly studied models are
identified.Comment: 14 pages, LaTeX, no figure
The role of clustering and gridlike ordering in epidemic spreading
The spreading of an epidemic is determined by the connectiviy patterns which
underlie the population. While it has been noted that a virus spreads more
easily on a network in which global distances are small, it remains a great
challenge to find approaches that unravel the precise role of local
interconnectedness. Such topological properties enter very naturally in the
framework of our two-timestep description, also providing a novel approach to
tract a probabilistic system. The method is elaborated for SIS-type epidemic
processes, leading to a quantitative interpretation of the role of loops up to
length 4 in the onset of an epidemic.Comment: Submitted to Phys. Rev. E; 15 pages, 11 figures, 5 table
A weighted configuration model and inhomogeneous epidemics
A random graph model with prescribed degree distribution and degree dependent
edge weights is introduced. Each vertex is independently equipped with a random
number of half-edges and each half-edge is assigned an integer valued weight
according to a distribution that is allowed to depend on the degree of its
vertex. Half-edges with the same weight are then paired randomly to create
edges. An expression for the threshold for the appearance of a giant component
in the resulting graph is derived using results on multi-type branching
processes. The same technique also gives an expression for the basic
reproduction number for an epidemic on the graph where the probability that a
certain edge is used for transmission is a function of the edge weight. It is
demonstrated that, if vertices with large degree tend to have large (small)
weights on their edges and if the transmission probability increases with the
edge weight, then it is easier (harder) for the epidemic to take off compared
to a randomized epidemic with the same degree and weight distribution. A recipe
for calculating the probability of a large outbreak in the epidemic and the
size of such an outbreak is also given. Finally, the model is fitted to three
empirical weighted networks of importance for the spread of contagious diseases
and it is shown that can be substantially over- or underestimated if the
correlation between degree and weight is not taken into account
A General Formalism for Inhomogeneous Random Graphs
We present and investigate an extension of the classical random graph to a
general class of inhomogeneous random graph models, where vertices come in
different types, and the probability of realizing an edge depends on the types
of its terminal vertices. This approach provides a general framework for the
analysis of a large class of models. The generic phase structure is derived
using generating function techniques, and relations to other classes of models
are pointed out.Comment: 7 pages, no figures. To appear in Phys. Rev.
Emergence of Clusters in Growing Networks with Aging
We study numerically a model of nonequilibrium networks where nodes and links
are added at each time step with aging of nodes and connectivity- and
age-dependent attachment of links. By varying the effects of age in the
attachment probability we find, with numerical simulations and scaling
arguments, that a giant cluster emerges at a first-order critical point and
that the problem is in the universality class of one dimensional percolation.
This transition is followed by a change in the giant cluster's topology from
tree-like to quasi-linear, as inferred from measurements of the average
shortest-path length, which scales logarithmically with system size in one
phase and linearly in the other.Comment: 8 pages, 6 figures, accepted for publication in JSTA
How technology shapes assessment design: findings from a study of university teachers
A wide range of technologies has been developed to enhance assessment, but adoption has been inconsistent. This is despite assessment being critical to student learning and certification. To understand why this is the case and how it can be addressed, we need to explore the perspectives of academics responsible for designing and implementing technology-supported assessment strategies. This paper reports on the experience of designing technology-supported assessment based on interviews with 33 Australian university teachers. The findings reveal the desire to achieve greater efficiencies and to be contemporary and innovative as key drivers of technology adoption for assessment. Participants sought to shape student behaviors through their designs and made adaptations in response to positive feedback and undesirable outcomes. Many designs required modification because of a lack of appropriate support, leading to compromise and, in some cases, abandonment. These findings highlight the challenges to effective technology-supported assessment design and demonstrate the difficulties university teachers face when attempting to negotiate mixed messages within institutions and the demands of design work. We use these findings to suggest opportunities to improve support by offering pedagogical guidance and technical help at critical stages of the design process and encouraging an iterative approach to design
What makes for effective feedback: staff and student perspectives
Since the early 2010s the literature has shifted to view feedback as a process that students do where they make sense of information about work they have done, and use it to improve the quality of their subsequent work. In this view, effective feedback needs to demonstrate effects. However, it is unclear if educators and students share this understanding of feedback. This paper reports a qualitative investigation of what educators and students think the purpose of feedback is, and what they think makes feedback effective. We administered a survey on feedback that was completed by 406 staff and 4514 students from two Australian universities. Inductive thematic analysis was conducted on data from a sample of 323 staff with assessment responsibilities and 400 students. Staff and students largely thought the purpose of feedback was improvement. With respect to what makes feedback effective, staff mostly discussed feedback design matters like timing, modalities and connected tasks. In contrast, students mostly wrote that high-quality feedback comments make feedback effective – especially comments that are usable, detailed, considerate of affect and personalised to the student’s own work. This study may assist researchers, educators and academic developers in refocusing their efforts in improving feedbac
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