Related papers: Network dismantling
Effectively preserving both the structural and dynamical properties during the reduction of complex networks remains a significant research topic. Existing network reduction methods based on renormalization group or sampling often face…
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 heterogeneous structure implies that a very few nodes may play the critical role in maintaining structural and functional properties of a large-scale network. Identifying these vital nodes is one of the most important tasks in network…
We study a large family of graph covering problems, whose definitions rely on distances, for graphs of bounded cyclomatic number (that is, the minimum number of edges that need to be removed from the graph to destroy all cycles). These…
In distributed networks, it is often useful for the nodes to be aware of dense subgraphs, e.g., such a dense subgraph could reveal dense subtructures in otherwise sparse graphs (e.g. the World Wide Web or social networks); these might…
An artificial neural network is usually treated as a whole system, being characterized by its ground state (the global minimum of the energy functional), the set of fixed points, their basins of attraction, etc. However, it is quite natural…
Our aim here is to address the problem of decomposing a whole network into a minimal number of ego-centered subnetworks. For this purpose, the network egos are picked out as the members of a minimum dominating set of the network. However,…
A hedge graph is a graph whose edge set has been partitioned into groups called hedges. Here we consider a generalization of the well-known \textsc{Cluster Deletion} problem, named \textsc{Hedge Cluster Deletion}. The task is to compute the…
Finding a maximum independent set is a fundamental NP-hard problem that is used in many real-world applications. Given an unweighted graph, this problem asks for a maximum cardinality set of pairwise non-adjacent vertices. Some of the most…
Networks are a popular tool for representing elements in a system and their interconnectedness. Many observed networks can be viewed as only samples of some true underlying network. Such is frequently the case, for example, in the…
Decompositions of networks are useful not only for structural exploration. They also have implications and use in analysis and computational solution of processes (such as the Ising model, percolation, SIR model) running on a given network.…
Many real-world networks describe systems in which interactions decay with the distance between nodes. Examples include systems constrained in real space such as transportation and communication networks, as well as systems constrained in…
We introduce the cycle intersection graph of a graph, an adaptation of the cycle graph of a graph, and use the structure of these graphs to prove an upper bound for the decycling number of all even graphs. This bound is shown to be…
We propose and study a set of algorithms for discovering community structure in networks -- natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative…
A set $V$ is said to be separated by subsets $V_1,\ldots,V_k$ if, for every pair of distinct elements of $V$, there is a set $V_i$ that contains exactly one of them. Imposing structural constraints on the separating subsets is often…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
We state a combinatorial optimization problem whose feasible solutions define both a decomposition and a node labeling of a given graph. This problem offers a common mathematical abstraction of seemingly unrelated computer vision tasks,…
The mincut graph bisection problem involves partitioning the n vertices of a graph into disjoint subsets, each containing exactly n/2 vertices, while minimizing the number of "cut" edges with an endpoint in each subset. When considered over…
Minimum Bisection denotes the NP-hard problem to partition the vertex set of a graph into two sets of equal sizes while minimizing the width of the bisection, which is defined as the number of edges between these two sets. We first consider…
Many real-world networks are prohibitively large for data retrieval, storage and analysis of all of its nodes and links. Understanding the structure and dynamics of these networks entails creating a smaller representative sample of the full…