The critical node detection problem (CNDP) aims to fragment a graph G=(V,E) by removing a set of vertices R with cardinality |R|≤k, such that the residual graph has minimum pairwise connectivity for user-defined value k. Existing optimization algorithms are incapable of finding a good set R in graphs with many thousands or millions of vertices due to the associated computational cost. Hence, there exists a need for a time- and space-efficient approach for evaluating the impact of removing any v∈V in the context of the CNDP. In this paper, we propose an algorithm based on a modified depth-first search that requires O(k(|V|+|E|)) time complexity. We employ the method within in a greedy algorithm for quickly identifying R. Our experimental results consider small- (≤250 nodes) and medium-sized (≤25,000 nodes) networks, where it is possible to compare to known optimal solutions or results obtained by other heuristics. Additionally, we show results using six real-world networks. The proposed algorithm can be easily extended to vertex- and edge-weighted variants of the CNDP.

We examine the robustness of networks under attack when the attacker sequentially selects from a number of different attack strategies, each of which removes one node from the network. Network robustness refers to the ability of a network to maintain functionality under attack, and the problem-dependent context implies a number of robustness measures exist. Thus, we analyse four measures: (1) entropy, (2) efficiency, (3) size of largest network component, and suggest to also utilize (4) pairwise connectivity. Six network centrality measures form the set of strategies at the disposal of the attacker. Our study examines the utility of greedy strategy selection versus random strategy selection for each attack, whereas previous studies focused on greedy selection but limited to only one attack strategy. Using a set of common complex network benchmarks in addition to real-world networks, we find that randomly selecting an attack strategy often performs well when the attack strategies are of high quality. We also examine defense against the attacks by adding $$k$$ edges after each node attack and find that the greedy strategy is most useful in this context. We also observed that a betweenness-based attack often outperforms both random and greedy strategy selection.

Complex networks can model a wide range of complex systems in nature and society, and many algorithms (network generators) capable of synthesizing networks with few and very specific structural characteristics (degree distribution, average path length, etc.) have been developed. However, there remains a significant lack of generators capable of synthesizing networks with strong resemblance to those observed in the real-world, which can subsequently be used as a null model, or to perform tasks such as extrapolation, compression and control. In this paper, a robust new approach we term Action-based Modeling is presented that creates a compact probabilistic model of a given target network, which can then be used to synthesize networks of arbitrary size. Statistical comparison to existing network generators is performed and results show that the performance of our approach is comparable to the current state-of-the-art methods on a variety of network measures, while also yielding easily interpretable generators. Additionally, the action-based approach described herein allows the user to consider an arbitrarily large set of structural characteristics during the generator design process.

This study proposes a new methodology for selecting renewal plans for sewer networks based on their impacts on the behavior of the networks over their whole lifecycle. The proposed approach combines a multiobjective genetic algorithm and Monte Carlo simulation to maximize network condition and serviceability while minimizing network risk of failure and total lifecycle cost for the entire planning period. The algorithm was applied to a sewer network in Sahab City, Jordan, in 16 different analysis scenarios that consider the uncertainty in the model variables. These different analysis scenarios varied the network age, deterioration rate, and available budget at each time step throughout the planning period. The model was then validated by statistically comparing its performance to an existing prioritization model that does not consider the long-term impact behavior of the wastewater system. The results show that the proposed algorithm outperforms the existing prioritization model because it results in statistically significant improvement in the network condition, risk of failure, serviceability, and the total lifecycle cost at the end of the planning period.

Communication processes within the human brain at different cognitive states are neither well understood nor completely characterized. We assess communication processes in the human connectome using ant colony-inspired cooperative learning algorithm, starting from a source with no a priori information about the network topology, and cooperatively searching for the target through a pheromone-inspired model. This framework relies on two parameters, namely ph-perception and edge-perception, to define the cognizance and subsequent behaviour of the ants on the network and, overall, the communication processes happening between source and target nodes. Simulations obtained through different configurations allow the identification of path-ensembles that are involved in the communication between node pairs. These path-ensembles may contain different number of paths depending on the perception parameters and the node pair. In order to assess the different communication regimes displayed on the simulations and their associations with functional connectivity, we introduce two network measurements, effective path-length and arrival rate. These communication features are tested as individual as well as combined predictors of functional connectivity during different tasks. Finally, different communication regimes are found in different specialized functional networks. Overall, this framework may be used as a test-bed for different communication regimes on top of an underlaying topology.