44,814 research outputs found
Improving controllability of complex networks by rewiring links regularly
Network science have constantly been in the focus of research for the last
decade, with considerable advances in the controllability of their structural.
However, much less effort has been devoted to study that how to improve the
controllability of complex networks. In this paper, a new algorithm is proposed
to improve the controllability of complex networks by rewiring links regularly
which transforms the network structure. Then it is demonstrated that our
algorithm is very effective after numerical simulation experiment on typical
network models (Erd\"os-R\'enyi and scale-free network). We find that our
algorithm is mainly determined by the average degree and positive correlation
of in-degree and out-degree of network and it has nothing to do with the
network size. Furthermore, we analyze and discuss the correlation between
controllability of complex networks and degree distribution index: power-law
exponent and heterogeneit
Relation between Financial Market Structure and the Real Economy: Comparison between Clustering Methods
We quantify the amount of information filtered by different hierarchical
clustering methods on correlations between stock returns comparing it with the
underlying industrial activity structure. Specifically, we apply, for the first
time to financial data, a novel hierarchical clustering approach, the Directed
Bubble Hierarchical Tree and we compare it with other methods including the
Linkage and k-medoids. In particular, by taking the industrial sector
classification of stocks as a benchmark partition, we evaluate how the
different methods retrieve this classification. The results show that the
Directed Bubble Hierarchical Tree can outperform other methods, being able to
retrieve more information with fewer clusters. Moreover, we show that the
economic information is hidden at different levels of the hierarchical
structures depending on the clustering method. The dynamical analysis on a
rolling window also reveals that the different methods show different degrees
of sensitivity to events affecting financial markets, like crises. These
results can be of interest for all the applications of clustering methods to
portfolio optimization and risk hedging.Comment: 31 pages, 17 figure
Centrality metrics and localization in core-periphery networks
Two concepts of centrality have been defined in complex networks. The first
considers the centrality of a node and many different metrics for it has been
defined (e.g. eigenvector centrality, PageRank, non-backtracking centrality,
etc). The second is related to a large scale organization of the network, the
core-periphery structure, composed by a dense core plus an outlying and
loosely-connected periphery. In this paper we investigate the relation between
these two concepts. We consider networks generated via the Stochastic Block
Model, or its degree corrected version, with a strong core-periphery structure
and we investigate the centrality properties of the core nodes and the ability
of several centrality metrics to identify them. We find that the three measures
with the best performance are marginals obtained with belief propagation,
PageRank, and degree centrality, while non-backtracking and eigenvector
centrality (or MINRES}, showed to be equivalent to the latter in the large
network limit) perform worse in the investigated networks.Comment: 15 pages, 8 figure
FROST -- Fast row-stochastic optimization with uncoordinated step-sizes
In this paper, we discuss distributed optimization over directed graphs,
where doubly-stochastic weights cannot be constructed. Most of the existing
algorithms overcome this issue by applying push-sum consensus, which utilizes
column-stochastic weights. The formulation of column-stochastic weights
requires each agent to know (at least) its out-degree, which may be impractical
in e.g., broadcast-based communication protocols. In contrast, we describe
FROST (Fast Row-stochastic-Optimization with uncoordinated STep-sizes), an
optimization algorithm applicable to directed graphs that does not require the
knowledge of out-degrees; the implementation of which is straightforward as
each agent locally assigns weights to the incoming information and locally
chooses a suitable step-size. We show that FROST converges linearly to the
optimal solution for smooth and strongly-convex functions given that the
largest step-size is positive and sufficiently small.Comment: Submitted for journal publication, currently under revie
Any-k: Anytime Top-k Tree Pattern Retrieval in Labeled Graphs
Many problems in areas as diverse as recommendation systems, social network
analysis, semantic search, and distributed root cause analysis can be modeled
as pattern search on labeled graphs (also called "heterogeneous information
networks" or HINs). Given a large graph and a query pattern with node and edge
label constraints, a fundamental challenge is to nd the top-k matches ac-
cording to a ranking function over edge and node weights. For users, it is di
cult to select value k . We therefore propose the novel notion of an any-k
ranking algorithm: for a given time budget, re- turn as many of the top-ranked
results as possible. Then, given additional time, produce the next lower-ranked
results quickly as well. It can be stopped anytime, but may have to continues
until all results are returned. This paper focuses on acyclic patterns over
arbitrary labeled graphs. We are interested in practical algorithms that
effectively exploit (1) properties of heterogeneous networks, in particular
selective constraints on labels, and (2) that the users often explore only a
fraction of the top-ranked results. Our solution, KARPET, carefully integrates
aggressive pruning that leverages the acyclic nature of the query, and
incremental guided search. It enables us to prove strong non-trivial time and
space guarantees, which is generally considered very hard for this type of
graph search problem. Through experimental studies we show that KARPET achieves
running times in the order of milliseconds for tree patterns on large networks
with millions of nodes and edges.Comment: To appear in WWW 201
Hierarchy measure for complex networks
Nature, technology and society are full of complexity arising from the
intricate web of the interactions among the units of the related systems (e.g.,
proteins, computers, people). Consequently, one of the most successful recent
approaches to capturing the fundamental features of the structure and dynamics
of complex systems has been the investigation of the networks associated with
the above units (nodes) together with their relations (edges). Most complex
systems have an inherently hierarchical organization and, correspondingly, the
networks behind them also exhibit hierarchical features. Indeed, several papers
have been devoted to describing this essential aspect of networks, however,
without resulting in a widely accepted, converging concept concerning the
quantitative characterization of the level of their hierarchy. Here we develop
an approach and propose a quantity (measure) which is simple enough to be
widely applicable, reveals a number of universal features of the organization
of real-world networks and, as we demonstrate, is capable of capturing the
essential features of the structure and the degree of hierarchy in a complex
network. The measure we introduce is based on a generalization of the m-reach
centrality, which we first extend to directed/partially directed graphs. Then,
we define the global reaching centrality (GRC), which is the difference between
the maximum and the average value of the generalized reach centralities over
the network. We investigate the behavior of the GRC considering both a
synthetic model with an adjustable level of hierarchy and real networks.
Results for real networks show that our hierarchy measure is related to the
controllability of the given system. We also propose a visualization procedure
for large complex networks that can be used to obtain an overall qualitative
picture about the nature of their hierarchical structure.Comment: 29 pages, 9 figures, 4 table
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