Related papers: Finding $k$-community structures in special graph …
We give the first almost-linear time algorithm for computing the \emph{maximal $k$-edge-connected subgraphs} of an undirected unweighted graph for any constant $k$. More specifically, given an $n$-vertex $m$-edge graph $G=(V,E)$ and a…
Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that…
We show two results related to the Hamiltonicity and $k$-Path algorithms in undirected graphs by Bj\"orklund [FOCS'10], and Bj\"orklund et al., [arXiv'10]. First, we demonstrate that the technique used can be generalized to finding some…
We consider a random sparse graph with bounded average degree, in which a subset of vertices has higher connectivity than the background. In particular, the average degree inside this subset of vertices is larger than outside (but still…
Let $G$ be a graph on $n$ vertices. For $i\in \{0,1\}$ and a connected graph $G$, a spanning forest $F$ of $G$ is called an $i$-perfect forest if every tree in $F$ is an induced subgraph of $G$ and exactly $i$ vertices of $F$ have even…
Many algorithms have been developed for NP-hard problems on graphs with small treewidth $k$. For example, all problems that are expressable in linear extended monadic second order can be solved in linear time on graphs of bounded treewidth.…
We consider the problem of finding the smallest graph that contains two input trees each with at most $n$ vertices preserving their distances. In other words, we look for an isometric-universal graph with the minimum number of vertices for…
Community detection in networks is a key exploratory tool with applications in a diverse set of areas, ranging from finding communities in social and biological networks to identifying link farms in the World Wide Web. The problem of…
Network structures, consisting of nodes and edges, have applications in almost all subjects. A set of nodes is called a community if the nodes have strong interrelations. Industries (including cell phone carriers and online social media…
We propose a novel graph clustering method guided by additional information on the underlying structure of the clusters (or communities). The problem is formulated as the matching of a graph to a template with smaller dimension, hence…
The connected $k$-median problem is a constrained clustering problem that combines distance-based $k$-clustering with connectivity information. The problem allows to input a metric space and an unweighted undirected connectivity graph that…
We study space and time efficient quantum algorithms for two graph problems -- deciding whether an $n$-vertex graph is a forest, and whether it is bipartite. Via a reduction to the s-t connectivity problem, we describe quantum algorithms…
Social networks are often modeled using signed graphs, where vertices correspond to users and edges have a sign that indicates whether an interaction between users was positive or negative. The arising signed graphs typically contain a…
We consider the problem of detecting a community of densely connected vertices in a high-dimensional bipartite graph of size $n_1 \times n_2$. Under the null hypothesis, the observed graph is drawn from a bipartite Erd\H{o}s-Renyi…
Finding communities in graphs is one of the most well-studied problems in data mining and social-network analysis. In many real applications, the underlying graph does not have a clear community structure. In those cases, selecting a single…
Let $\mathcal{H}$ be a graph class and $k\in\mathbb{N}$. We say a graph $G$ admits a \emph{$k$-identification to $\mathcal{H}$} if there is a partition $\mathcal{P}$ of some set $X\subseteq V(G)$ of size at most $k$ such that after…
The discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community, but most methods proposed so far are unsuitable for very large networks because of their computational…
Given an undirected graph G = (V, E) and an integer k, the s-Club asks if Gcontains a vertex subset S of at least k vertices such that G[S] has diameter at most s. Recently, Vertex r-Triangle s-Club, and Edge r-Triangle s-Club that…
Given a connected graph $G$ on $n$ vertices and a positive integer $k\le n$, a subgraph of $G$ on $k$ vertices is called a $k$-subgraph in $G$. We design combinatorial approximation algorithms for finding a connected $k$-subgraph in $G$…
A popular way to define or characterize graph classes is via forbidden subgraphs or forbidden minors. These characterizations play a key role in graph theory, but they rarely lead to efficient algorithms to recognize these classes. In…