2,057 research outputs found

### 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

### 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

### 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

### Kronecker Graphs: An Approach to Modeling Networks

How can we model networks with a mathematically tractable model that allows
for rigorous analysis of network properties? Networks exhibit a long list of
surprising properties: heavy tails for the degree distribution; small
diameters; and densification and shrinking diameters over time. Most present
network models either fail to match several of the above properties, are
complicated to analyze mathematically, or both. In this paper we propose a
generative model for networks that is both mathematically tractable and can
generate networks that have the above mentioned properties. Our main idea is to
use the Kronecker product to generate graphs that we refer to as "Kronecker
graphs".
First, we prove that Kronecker graphs naturally obey common network
properties. We also provide empirical evidence showing that Kronecker graphs
can effectively model the structure of real networks.
We then present KronFit, a fast and scalable algorithm for fitting the
Kronecker graph generation model to large real networks. A naive approach to
fitting would take super- exponential time. In contrast, KronFit takes linear
time, by exploiting the structure of Kronecker matrix multiplication and by
using statistical simulation techniques.
Experiments on large real and synthetic networks show that KronFit finds
accurate parameters that indeed very well mimic the properties of target
networks. Once fitted, the model parameters can be used to gain insights about
the network structure, and the resulting synthetic graphs can be used for null-
models, anonymization, extrapolations, and graph summarization

### Scale-free network growth by ranking

Network growth is currently explained through mechanisms that rely on node
prestige measures, such as degree or fitness. In many real networks those who
create and connect nodes do not know the prestige values of existing nodes, but
only their ranking by prestige. We propose a criterion of network growth that
explicitly relies on the ranking of the nodes according to any prestige
measure, be it topological or not. The resulting network has a scale-free
degree distribution when the probability to link a target node is any power law
function of its rank, even when one has only partial information of node ranks.
Our criterion may explain the frequency and robustness of scale-free degree
distributions in real networks, as illustrated by the special case of the Web
graph.Comment: 4 pages, 2 figures. We extended the model to account for ranking by
arbitrarily distributed fitness. Final version to appear on Physical Review
Letter

### Sequential item pricing for unlimited supply

We investigate the extent to which price updates can increase the revenue of
a seller with little prior information on demand. We study prior-free revenue
maximization for a seller with unlimited supply of n item types facing m myopic
buyers present for k < log n days. For the static (k = 1) case, Balcan et al.
[2] show that one random item price (the same on each item) yields revenue
within a \Theta(log m + log n) factor of optimum and this factor is tight. We
define the hereditary maximizers property of buyer valuations (satisfied by any
multi-unit or gross substitutes valuation) that is sufficient for a significant
improvement of the approximation factor in the dynamic (k > 1) setting. Our
main result is a non-increasing, randomized, schedule of k equal item prices
with expected revenue within a O((log m + log n) / k) factor of optimum for
private valuations with hereditary maximizers. This factor is almost tight: we
show that any pricing scheme over k days has a revenue approximation factor of
at least (log m + log n) / (3k). We obtain analogous matching lower and upper
bounds of \Theta((log n) / k) if all valuations have the same maximum. We
expect our upper bound technique to be of broader interest; for example, it can
significantly improve the result of Akhlaghpour et al. [1]. We also initiate
the study of revenue maximization given allocative externalities (i.e.
influences) between buyers with combinatorial valuations. We provide a rather
general model of positive influence of others' ownership of items on a buyer's
valuation. For affine, submodular externalities and valuations with hereditary
maximizers we present an influence-and-exploit (Hartline et al. [13]) marketing
strategy based on our algorithm for private valuations. This strategy preserves
our approximation factor, despite an affine increase (due to externalities) in
the optimum revenue.Comment: 18 pages, 1 figur

### 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

### 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

### 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

### Social Ranking Techniques for the Web

The proliferation of social media has the potential for changing the
structure and organization of the web. In the past, scientists have looked at
the web as a large connected component to understand how the topology of
hyperlinks correlates with the quality of information contained in the page and
they proposed techniques to rank information contained in web pages. We argue
that information from web pages and network data on social relationships can be
combined to create a personalized and socially connected web. In this paper, we
look at the web as a composition of two networks, one consisting of information
in web pages and the other of personal data shared on social media web sites.
Together, they allow us to analyze how social media tunnels the flow of
information from person to person and how to use the structure of the social
network to rank, deliver, and organize information specifically for each
individual user. We validate our social ranking concepts through a ranking
experiment conducted on web pages that users shared on Google Buzz and Twitter.Comment: 7 pages, ASONAM 201

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