24 research outputs found
Fast and simple decycling and dismantling of networks
Decycling and dismantling of complex networks are underlying many important
applications in network science. Recently these two closely related problems
were tackled by several heuristic algorithms, simple and considerably
sub-optimal, on the one hand, and time-consuming message-passing ones that
evaluate single-node marginal probabilities, on the other hand. In this paper
we propose a simple and extremely fast algorithm, CoreHD, which recursively
removes nodes of the highest degree from the -core of the network. CoreHD
performs much better than all existing simple algorithms. When applied on
real-world networks, it achieves equally good solutions as those obtained by
the state-of-art iterative message-passing algorithms at greatly reduced
computational cost, suggesting that CoreHD should be the algorithm of choice
for many practical purposes
Compressing networks with super nodes
Community detection is a commonly used technique for identifying groups in a
network based on similarities in connectivity patterns. To facilitate community
detection in large networks, we recast the network to be partitioned into a
smaller network of 'super nodes', each super node comprising one or more nodes
in the original network. To define the seeds of our super nodes, we apply the
'CoreHD' ranking from dismantling and decycling. We test our approach through
the analysis of two common methods for community detection: modularity
maximization with the Louvain algorithm and maximum likelihood optimization for
fitting a stochastic block model. Our results highlight that applying community
detection to the compressed network of super nodes is significantly faster
while successfully producing partitions that are more aligned with the local
network connectivity, more stable across multiple (stochastic) runs within and
between community detection algorithms, and overlap well with the results
obtained using the full network
Network dismantling
We study the network dismantling problem, which consists in determining a
minimal set of vertices whose removal leaves the network broken into connected
components of sub-extensive size. For a large class of random graphs, this
problem is tightly connected to the decycling problem (the removal of vertices
leaving the graph acyclic). Exploiting this connection and recent works on
epidemic spreading we present precise predictions for the minimal size of a
dismantling set in a large random graph with a prescribed (light-tailed) degree
distribution. Building on the statistical mechanics perspective we propose a
three-stage Min-Sum algorithm for efficiently dismantling networks, including
heavy-tailed ones for which the dismantling and decycling problems are not
equivalent. We also provide further insights into the dismantling problem
concluding that it is an intrinsically collective problem and that optimal
dismantling sets cannot be viewed as a collection of individually well
performing nodes.Comment: Source code and data can be found at
https://github.com/abraunst/decycle
Community Detection Boosts Network Dismantling on Real-World Networks
Network dismantling techniques have gained increasing interest during the last years caused by the need for protecting and strengthening critical infrastructure systems in our society. We show that communities play a critical role in dismantling, given their inherent property of separating a network into strongly and weakly connected parts. The process of community-based dismantling depends on several design factors, including the choice of community detection method, community cut strategy, and inter-community node selection. We formalize the problem of community attacks to networks, identify critical design decisions for such methods, and perform a comprehensive empirical evaluation with respect to effectiveness and efficiency criteria on a set of more than 40 community-based network dismantling methods. We compare our results to state-of-the-art network dismantling, including collective influence, articulation points, as well as network decycling. We show that community-based network dismantling significantly outperforms existing techniques in terms of solution quality and computation time in the vast majority of real-world networks, while existing techniques mainly excel on model networks (ER, BA) mostly. We additionally show that the scalability of community-based dismantling opens new doors towards the efficient analysis of large real-world networks.We acknowledge financial support from FEDER/Ministerio de Ciencia, Innovación y Universidades Agencia Estatal de Investigación/ SuMaEco Project (RTI2018-095441-B-C22) and the María de Maeztu Program for Units of Excellence in R&D (No. MDM-2017-0711). D.R.-R. also acknowledges the Fellowship No. BES-2016-076264 under the FPI program of MINECO, Spain.Peer reviewe
Generalized Network Dismantling
Finding the set of nodes, which removed or (de)activated can stop the spread
of (dis)information, contain an epidemic or disrupt the functioning of a
corrupt/criminal organization is still one of the key challenges in network
science. In this paper, we introduce the generalized network dismantling
problem, which aims to find the set of nodes that, when removed from a network,
results in a network fragmentation into subcritical network components at
minimum cost. For unit costs, our formulation becomes equivalent to the
standard network dismantling problem. Our non-unit cost generalization allows
for the inclusion of topological cost functions related to node centrality and
non-topological features such as the price, protection level or even social
value of a node. In order to solve this optimization problem, we propose a
method, which is based on the spectral properties of a novel node-weighted
Laplacian operator. The proposed method is applicable to large-scale networks
with millions of nodes. It outperforms current state-of-the-art methods and
opens new directions in understanding the vulnerability and robustness of
complex systems.Comment: 6 pages, 5 figure
Network higher-order structure dismantling
Diverse higher-order structures, foundational for supporting a network's
"meta-functions", play a vital role in structure, functionality, and the
emergence of complex dynamics. Nevertheless, the problem of dismantling them
has been consistently overlooked. In this paper, we introduce the concept of
dismantling higher-order structures, with the objective of disrupting not only
network connectivity but also eradicating all higher-order structures in each
branch, thereby ensuring thorough functional paralysis. Given the diversity and
unknown specifics of higher-order structures, identifying and targeting them
individually is not practical or even feasible. Fortunately, their close
association with k-cores arises from their internal high connectivity. Thus, we
transform higher-order structure measurement into measurements on k-cores with
corresponding orders. Furthermore, we propose the Belief Propagation-guided
High-order Dismantling (BPDH) algorithm, minimizing dismantling costs while
achieving maximal disruption to connectivity and higher-order structures,
ultimately converting the network into a forest. BPDH exhibits the explosive
vulnerability of network higher-order structures, counterintuitively showcasing
decreasing dismantling costs with increasing structural complexity. Our
findings offer a novel approach for dismantling malignant networks, emphasizing
the substantial challenges inherent in safeguarding against such malicious
attacks.Comment: 14 pages, 5 figures, 2 table
Statistical analysis of articulation points in configuration model networks
An articulation point (AP) in a network is a node whose deletion would split
the network component on which it resides into two or more components. APs are
vulnerable spots that play an important role in network collapse processes,
which may result from node failures, attacks or epidemics. Therefore, the
abundance and properties of APs affect the resilience of the network to these
collapse scenarios. We present analytical results for the statistical
properties of APs in configuration model networks. In order to quantify their
abundance, we calculate the probability , that a random
node, i, in a configuration model network with P(K=k), is an AP. We also obtain
the conditional probability that a random node of degree
k is an AP, and find that high degree nodes are more likely to be APs than low
degree nodes. Using Bayes' theorem, we obtain the conditional degree
distribution, , over the set of APs and compare it to P(K=k).
We propose a new centrality measure based on APs: each node can be
characterized by its articulation rank, r, which is the number of components
that would be added to the network upon deletion of that node. For nodes which
are not APs the articulation rank is , while for APs . We obtain
a closed form expression for the distribution of articulation ranks, P(R=r).
Configuration model networks often exhibit a coexistence between a giant
component and finite components. To examine the distinct properties of APs on
the giant and on the finite components, we calculate the probabilities
presented above separately for the giant and the finite components. We apply
these results to ensembles of configuration model networks with a Poisson,
exponential and power-law degree distributions. The implications of these
results are discussed in the context of common attack scenarios and network
dismantling processes.Comment: 53 pages, 16 figures. arXiv admin note: text overlap with
arXiv:1804.0333
Underestimated cost of targeted attacks on complex networks
The robustness of complex networks under targeted attacks is deeply connected
to the resilience of complex systems, i.e., the ability to make appropriate
responses to the attacks. In this article, we investigated the state-of-the-art
targeted node attack algorithms and demonstrate that they become very
inefficient when the cost of the attack is taken into consideration. In this
paper, we made explicit assumption that the cost of removing a node is
proportional to the number of adjacent links that are removed, i.e., higher
degree nodes have higher cost. Finally, for the case when it is possible to
attack links, we propose a simple and efficient edge removal strategy named
Hierarchical Power Iterative Normalized cut (HPI-Ncut).The results on real and
artificial networks show that the HPI-Ncut algorithm outperforms all the node
removal and link removal attack algorithms when the cost of the attack is taken
into consideration. In addition, we show that on sparse networks, the
complexity of this hierarchical power iteration edge removal algorithm is only
.Comment: 14 pages, 7 figure