3,570 research outputs found
Detecting Core-Periphery Structures by Surprise
Detecting the presence of mesoscale structures in complex networks is of
primary importance. This is especially true for financial networks, whose
structural organization deeply affects their resilience to events like default
cascades, shocks propagation, etc. Several methods have been proposed, so far,
to detect communities, i.e. groups of nodes whose connectivity is significantly
large. Communities, however do not represent the only kind of mesoscale
structures characterizing real-world networks: other examples are provided by
bow-tie structures, core-periphery structures and bipartite structures. Here we
propose a novel method to detect statistically-signifcant bimodular structures,
i.e. either bipartite or core-periphery ones. It is based on a modification of
the surprise, recently proposed for detecting communities. Our variant allows
for bimodular nodes partitions to be revealed, by letting links to be placed
either 1) within the core part and between the core and the periphery parts or
2) just between the (empty) layers of a bipartite network. From a technical
point of view, this is achieved by employing a multinomial hypergeometric
distribution instead of the traditional (binomial) hypergeometric one; as in
the latter case, this allows a p-value to be assigned to any given
(bi)partition of the nodes. To illustrate the performance of our method, we
report the results of its application to several real-world networks, including
social, economic and financial ones.Comment: 11 pages, 10 figures. Python code freely available at
https://github.com/jeroenvldj/bimodular_surpris
Minimum Cuts in Geometric Intersection Graphs
Let be a set of disks in the plane. The disk graph
for is the undirected graph with vertex set
in which two disks are joined by an edge if and only if they
intersect. The directed transmission graph for
is the directed graph with vertex set in which
there is an edge from a disk to a disk if and only if contains the center of .
Given and two non-intersecting disks , we
show that a minimum - vertex cut in or in
can be found in
expected time. To obtain our result, we combine an algorithm for the maximum
flow problem in general graphs with dynamic geometric data structures to
manipulate the disks.
As an application, we consider the barrier resilience problem in a
rectangular domain. In this problem, we have a vertical strip bounded by
two vertical lines, and , and a collection of
disks. Let be a point in above all disks of , and let
a point in below all disks of . The task is to find a curve
from to that lies in and that intersects as few disks of
as possible. Using our improved algorithm for minimum cuts in
disk graphs, we can solve the barrier resilience problem in
expected time.Comment: 11 pages, 4 figure
Predicting tipping points in mutualistic networks through dimension reduction
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1714958115/-/DCSupplemental.Peer reviewedPublisher PD
Robustness and modular structure in networks
Complex networks have recently attracted much interest due to their
prevalence in nature and our daily lives [1, 2]. A critical property of a
network is its resilience to random breakdown and failure [3-6], typically
studied as a percolation problem [7-9] or by modeling cascading failures
[10-12]. Many complex systems, from power grids and the Internet to the brain
and society [13-15], can be modeled using modular networks comprised of small,
densely connected groups of nodes [16, 17]. These modules often overlap, with
network elements belonging to multiple modules [18, 19]. Yet existing work on
robustness has not considered the role of overlapping, modular structure. Here
we study the robustness of these systems to the failure of elements. We show
analytically and empirically that it is possible for the modules themselves to
become uncoupled or non-overlapping well before the network disintegrates. If
overlapping modular organization plays a role in overall functionality,
networks may be far more vulnerable than predicted by conventional percolation
theory.Comment: 14 pages, 9 figure
Network Sensitivity of Systemic Risk
A growing body of studies on systemic risk in financial markets has
emphasized the key importance of taking into consideration the complex
interconnections among financial institutions. Much effort has been put in
modeling the contagion dynamics of financial shocks, and to assess the
resilience of specific financial markets - either using real network data,
reconstruction techniques or simple toy networks. Here we address the more
general problem of how shock propagation dynamics depends on the topological
details of the underlying network. To this end we consider different realistic
network topologies, all consistent with balance sheets information obtained
from real data on financial institutions. In particular, we consider networks
of varying density and with different block structures, and diversify as well
in the details of the shock propagation dynamics. We confirm that the systemic
risk properties of a financial network are extremely sensitive to its network
features. Our results can aid in the design of regulatory policies to improve
the robustness of financial markets
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