Related papers: An O(m) Algorithm for Cores Decomposition of Netwo…
From physics to engineering, biology and social science, natural and artificial systems are characterized by interconnected topologies whose features - e.g., heterogeneous connectivity, mesoscale organization, hierarchy - affect their…
The CUR decomposition of an $m \times n$ matrix $A$ finds an $m \times c$ matrix $C$ with a subset of $c < n$ columns of $A,$ together with an $r \times n$ matrix $R$ with a subset of $r < m$ rows of $A,$ as well as a $c \times r$ low-rank…
By moving to millimeter wave (mmWave) frequencies, base stations (BSs) will be densely deployed to provide seamless coverage in sixth generation (6G) mobile communication systems, which, unfortunately, leads to severe cell-edge problem. In…
Multilayer networks provide a powerful framework for modeling complex systems that capture different types of interactions between the same set of entities across multiple layers. Core-periphery detection involves partitioning the nodes of…
(Hyper)Graph decomposition is a family of problems that aim to break down large (hyper)graphs into smaller sub(hyper)graphs for easier analysis. The importance of this lies in its ability to enable efficient computation on large and complex…
We present a data structure that, given a graph $G$ of $n$ vertices and $m$ edges, and a suitable pair of nested $r$-divisions of $G$, preprocesses $G$ in $O(m+n)$ time and handles any series of edge-deletions in $O(m)$ total time while…
Network robustness is a measure a network's ability to survive adversarial attacks. But not all parts of a network are equal. K-cores, which are dense subgraphs, are known to capture some of the key properties of many real-life networks.…
Network compression is crucial to making the deep networks to be more efficient, faster, and generalizable to low-end hardware. Current network compression methods have two open problems: first, there lacks a theoretical framework to…
Seeding then expanding is a commonly used scheme to discover overlapping communities in a network. Most seeding methods are either too complex to scale to large networks or too simple to select high-quality seeds, and the non-principled…
Many real-world networks are so large that we must simplify their structure before we can extract useful information about the systems they represent. As the tools for doing these simplifications proliferate within the network literature,…
A new general decomposition theory inspired from modular graph decomposition is presented. This helps unifying modular decomposition on different structures, including (but not restricted to) graphs. Moreover, even in the case of graphs,…
We provide a framework for the design and analysis of dynamic programming algorithms for surface-embedded graphs on n vertices and branchwidth at most k. Our technique applies to general families of problems where standard dynamic…
This paper investigates the problem of decomposition with respect to outputs for Boolean control networks (BCNs). First, with the linear expression of BCNs and the matrix semi-tensor product, some algebraic equivalent conditions for the…
Inspired by social networks and complex systems, we propose a core-periphery network architecture that supports fast computation for many distributed algorithms and is robust and efficient in number of links. Rather than providing a…
Graphs are an essential data structure that can represent the structure of social networks. Many online companies, in order to provide intelligent and personalized services for their users, aim to comprehensively analyze a significant…
This paper studies the problem of embedding very large information networks into low-dimensional vector spaces, which is useful in many tasks such as visualization, node classification, and link prediction. Most existing graph embedding…
Mutually connected components (MCCs) play an important role as a measure of resilience in the study of interdependent networks. Despite their importance, an efficient algorithm to obtain the statistics of all MCCs during the removal of…
A significant problem in analysis of complex network is to reveal community structure, in which network nodes are tightly connected in the same communities, between which there are sparse connections. Previous algorithms for community…
When analyzing temporal networks, a fundamental task is the identification of dense structures (i.e., groups of vertices that exhibit a large number of links), together with their temporal span (i.e., the period of time for which the high…
A typical theme for many well-known decomposition problems is to show that some obvious necessary conditions for decomposing a graph $G$ into copies $H_1, \ldots, H_m$ are also sufficient. One such problem was posed in 1987, by Alavi,…