Related papers: K-Core Maximization through Edge Additions
The concept of k-core, which indicates the largest induced subgraph where each node has k or more neighbors, plays a significant role in measuring the cohesiveness and the engagement of a network, and it is exploited in diverse…
Massive network exploration is an important research direction with many applications. In such a setting, the network is, usually, modeled as a graph $G$, whereas any structural information of interest is extracted by inspecting the way…
Due to the increasing discovery and implementation of networks within all disciplines of life, the study of subgraph connectivity has become increasingly important. Motivated by the idea of community (or sub-graph) detection within a…
The $k$-core decomposition in a graph is a fundamental problem for social network analysis. The problem of $k$-core decomposition is to calculate the core number for every node in a graph. Previous studies mainly focus on $k$-core…
We consider the \emph{$k$-edge connected spanning subgraph} (kECSS) problem, where we are given an undirected graph $G = (V, E)$ with nonnegative edge costs $\{c_e\}_{e\in E}$, and we seek a minimum-cost \emph{$k$-edge connected} subgraph…
On an evolving graph that is continuously updated by a high-velocity stream of edges, how can one efficiently maintain if two vertices are connected? This is the connectivity problem, a fundamental and widely studied problem on graphs. We…
We consider the optimisation problem of adding $k$ links to a given network, such that the resulting effective graph resistance is as small as possible. The problem was recently proven to be NP-hard, such that optimal solutions obtained…
The behavior of users in social networks is often observed to be affected by the actions of their friends. Bhawalkar et al. \cite{bhawalkar-icalp} introduced a formal mathematical model for user engagement in social networks where each…
We study two related problems: finding a set of k vertices and minimum number of edges (kmin) and finding a graph with at least m' edges and minimum number of vertices (mvms). Goldschmidt and Hochbaum \cite{GH97} show that the mvms problem…
The k-core of a graph is its maximal subgraph with minimum degree at least k. In this paper, we address robustness questions about k-cores. Given a k-core, remove one edge uniformly at random and find its new k-core. We are interested in…
We study the following two fixed-cardinality optimization problems (a maximization and a minimization variant). For a fixed $\alpha$ between zero and one we are given a graph and two numbers $k \in \mathbb{N}$ and $t \in \mathbb{Q}$. The…
Closeness is a widely-studied centrality measure. Since it requires all pairwise distances, computing closeness for all nodes is infeasible for large real-world networks. However, for many applications, it is only necessary to find the k…
Given a sparse undirected graph G with weights on the edges, a k-plex partition of G is a partition of its set of nodes such that each component is a k-plex. A subset of nodes S is a k-plex if the degree of every node in the associated…
In signed networks, each edge is labeled as either positive or negative. The edge sign captures the polarity of a relationship. Balance of signed networks is a well-studied property in graph theory. In a balanced (sub)graph, the vertices…
We generalize the theory of k-core percolation on complex networks to k-core percolation on multiplex networks, where k=(k_a, k_b, ...). Multiplex networks can be defined as networks with a set of vertices but different types of edges, a,…
The densest $k$-subgraph problem is the problem of finding a $k$-vertex subgraph of a graph with the maximum number of edges. In order to solve large instances of the densest $k$-subgraph problem, we introduce two algorithms that are based…
Graph analytics attract much attention from both research and industry communities. Due to the linear time complexity, the $k$-core decomposition is widely used in many real-world applications such as biology, social networks, community…
We consider the densest $k$-subgraph problem, which seeks to identify the $k$-node subgraph of a given input graph with maximum number of edges. This problem is well-known to be NP-hard, by reduction to the maximum clique problem. We…
In a vertex-colored graph, an edge is happy if its endpoints have the same color. Similarly, a vertex is happy if all its incident edges are happy. Motivated by the computation of homophily in social networks, we consider the algorithmic…
A signed graph is a graph where each edge receives a sign, positive or negative. The signed graph model has been used in many real applications, such as protein complex discovery and social network analysis. Finding cohesive subgraphs in…