1,517 research outputs found
Modeling self-organization of communication and topology in social networks
This paper introduces a model of self-organization between communication and
topology in social networks, with a feedback between different communication
habits and the topology. To study this feedback, we let agents communicate to
build a perception of a network and use this information to create strategic
links. We observe a narrow distribution of links when the communication is low
and a system with a broad distribution of links when the communication is high.
We also analyze the outcome of chatting, cheating, and lying, as strategies to
get better access to information in the network. Chatting, although only
adopted by a few agents, gives a global gain in the system. Contrary, a global
loss is inevitable in a system with too many liarsComment: 6 pages 7 figures, Java simulation available at
http://cmol.nbi.dk/models/inforew/inforew.htm
Spectral centrality measures in complex networks
Complex networks are characterized by heterogeneous distributions of the
degree of nodes, which produce a large diversification of the roles of the
nodes within the network. Several centrality measures have been introduced to
rank nodes based on their topological importance within a graph. Here we review
and compare centrality measures based on spectral properties of graph matrices.
We shall focus on PageRank, eigenvector centrality and the hub/authority scores
of HITS. We derive simple relations between the measures and the (in)degree of
the nodes, in some limits. We also compare the rankings obtained with different
centrality measures.Comment: 11 pages, 10 figures, 5 tables. Final version published in Physical
Review
Superlinear Scaling for Innovation in Cities
Superlinear scaling in cities, which appears in sociological quantities such
as economic productivity and creative output relative to urban population size,
has been observed but not been given a satisfactory theoretical explanation.
Here we provide a network model for the superlinear relationship between
population size and innovation found in cities, with a reasonable range for the
exponent.Comment: 5 pages, 5 figures, 1 table, submitted to Phys. Rev. E; references
corrected; figures corrected, references and brief discussion adde
Paradoxes in Fair Computer-Aided Decision Making
Computer-aided decision making--where a human decision-maker is aided by a
computational classifier in making a decision--is becoming increasingly
prevalent. For instance, judges in at least nine states make use of algorithmic
tools meant to determine "recidivism risk scores" for criminal defendants in
sentencing, parole, or bail decisions. A subject of much recent debate is
whether such algorithmic tools are "fair" in the sense that they do not
discriminate against certain groups (e.g., races) of people.
Our main result shows that for "non-trivial" computer-aided decision making,
either the classifier must be discriminatory, or a rational decision-maker
using the output of the classifier is forced to be discriminatory. We further
provide a complete characterization of situations where fair computer-aided
decision making is possible
Solution for the properties of a clustered network
We study Strauss's model of a network with clustering and present an analytic
mean-field solution which is exact in the limit of large network size. Previous
computer simulations have revealed a degenerate region in the model's parameter
space in which triangles of adjacent edges clump together to form
unrealistically dense subgraphs, and perturbation calculations have been found
to break down in this region at all orders. Our analytic solution shows that
this region corresponds to a classic symmetry-broken phase and that the onset
of the degeneracy corresponds to a first-order phase transition in the density
of the network.Comment: 5 pages, 2 figure
Exact solutions for models of evolving networks with addition and deletion of nodes
There has been considerable recent interest in the properties of networks,
such as citation networks and the worldwide web, that grow by the addition of
vertices, and a number of simple solvable models of network growth have been
studied. In the real world, however, many networks, including the web, not only
add vertices but also lose them. Here we formulate models of the time evolution
of such networks and give exact solutions for a number of cases of particular
interest. For the case of net growth and so-called preferential attachment --
in which newly appearing vertices attach to previously existing ones in
proportion to vertex degree -- we show that the resulting networks have
power-law degree distributions, but with an exponent that diverges as the
growth rate vanishes. We conjecture that the low exponent values observed in
real-world networks are thus the result of vigorous growth in which the rate of
addition of vertices far exceeds the rate of removal. Were growth to slow in
the future, for instance in a more mature future version of the web, we would
expect to see exponents increase, potentially without bound.Comment: 9 pages, 3 figure
Degree Distribution of Competition-Induced Preferential Attachment Graphs
We introduce a family of one-dimensional geometric growth models, constructed
iteratively by locally optimizing the tradeoffs between two competing metrics,
and show that this family is equivalent to a family of preferential attachment
random graph models with upper cutoffs. This is the first explanation of how
preferential attachment can arise from a more basic underlying mechanism of
local competition. We rigorously determine the degree distribution for the
family of random graph models, showing that it obeys a power law up to a finite
threshold and decays exponentially above this threshold.
We also rigorously analyze a generalized version of our graph process, with
two natural parameters, one corresponding to the cutoff and the other a
``fertility'' parameter. We prove that the general model has a power-law degree
distribution up to a cutoff, and establish monotonicity of the power as a
function of the two parameters. Limiting cases of the general model include the
standard preferential attachment model without cutoff and the uniform
attachment model.Comment: 24 pages, one figure. To appear in the journal: Combinatorics,
Probability and Computing. Note, this is a long version, with complete
proofs, of the paper "Competition-Induced Preferential Attachment"
(cond-mat/0402268
Finding local community structure in networks
Although the inference of global community structure in networks has recently
become a topic of great interest in the physics community, all such algorithms
require that the graph be completely known. Here, we define both a measure of
local community structure and an algorithm that infers the hierarchy of
communities that enclose a given vertex by exploring the graph one vertex at a
time. This algorithm runs in time O(d*k^2) for general graphs when is the
mean degree and k is the number of vertices to be explored. For graphs where
exploring a new vertex is time-consuming, the running time is linear, O(k). We
show that on computer-generated graphs this technique compares favorably to
algorithms that require global knowledge. We also use this algorithm to extract
meaningful local clustering information in the large recommender network of an
online retailer and show the existence of mesoscopic structure.Comment: 7 pages, 6 figure
Fusing Data with Correlations
Many applications rely on Web data and extraction systems to accomplish
knowledge-driven tasks. Web information is not curated, so many sources provide
inaccurate, or conflicting information. Moreover, extraction systems introduce
additional noise to the data. We wish to automatically distinguish correct data
and erroneous data for creating a cleaner set of integrated data. Previous work
has shown that a na\"ive voting strategy that trusts data provided by the
majority or at least a certain number of sources may not work well in the
presence of copying between the sources. However, correlation between sources
can be much broader than copying: sources may provide data from complementary
domains (\emph{negative correlation}), extractors may focus on different types
of information (\emph{negative correlation}), and extractors may apply common
rules in extraction (\emph{positive correlation, without copying}). In this
paper we present novel techniques modeling correlations between sources and
applying it in truth finding.Comment: Sigmod'201
Modeling Dynamics of Information Networks
We propose an information-based model for network dynamics in which imperfect
information leads to networks where the different vertices have widely
different number of edges to other vertices, and where the topology has
hierarchical features. The possibility to observe scale free networks is linked
to a minimally connected system where hubs remain dynamic.Comment: 4 pages, 5 figures; changed content and new fig
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