1,451 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
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
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
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
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
Activity ageing in growing networks
We present a model for growing information networks where the ageing of a
node depends on the time at which it entered the network and on the last time
it was cited. The model is shown to undergo a transition from a small-world to
large-world network. The degree distribution may exhibit very different shapes
depending on the model parameters, e.g. delta-peaked, exponential or power-law
tailed distributions.Comment: 9 pages, 2 figure
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
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
Greedy Connectivity of Geographically Embedded Graphs
We introduce a measure of {\em greedy connectivity} for geographical networks
(graphs embedded in space) and where the search for connecting paths relies
only on local information, such as a node's location and that of its neighbors.
Constraints of this type are common in everyday life applications. Greedy
connectivity accounts also for imperfect transmission across established links
and is larger the higher the proportion of nodes that can be reached from other
nodes with a high probability. Greedy connectivity can be used as a criterion
for optimal network design
- …