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Vertex connectivity is a well-studied concept in graph theory with numerous applications. A graph is $k$-connected if it remains connected after removing any $k-1$ vertices. The vertex connectivity of a graph is the maximum $k$ such that…
The median of a set of vertices $P$ of a graph $G$ is the set of all vertices $x$ of $G$ minimizing the sum of distances from $x$ to all vertices of $P$. In this paper, we present a linear time algorithm to compute medians in median graphs,…
Measures of complex network analysis, such as vertex centrality, have the potential to unveil existing network patterns and behaviors. They contribute to the understanding of networks and their components by analyzing their structural…
A random intersection graph is constructed by independently assigning a subset of a given set of objects $W,$ to each vertex of the vertex set $V$ of a simple graph $G.$ There is an edge between two vertices of $V,$ iff their respective…
With the growing significance of graphs as an effective representation of data in numerous applications, efficient graph analysis using modern machine learning is receiving a growing level of attention. Deep learning approaches often…
We propose novel recommendation algorithms to improve fairness in networks. Fairness is measured by how close different nodes are to influencers in the network. To allow for easy comparison of fairness across graphs of different sizes, our…
Finding a maximum-cardinality or maximum-weight matching in (edge-weighted) undirected graphs is among the most prominent problems of algorithmic graph theory. For $n$-vertex and $m$-edge graphs, the best known algorithms run in…
In modern applications of graphs algorithms, where the graphs of interest are large and dynamic, it is unrealistic to assume that an input representation contains the full information of a graph being studied. Hence, it is desirable to use…
Graph similarity search is a common and fundamental operation in graph databases. One of the most popular graph similarity measures is the Graph Edit Distance (GED) mainly because of its broad applicability and high interpretability.…
We consider the problem of graph generation guided by network statistics, i.e., the generation of graphs which have given values of various numerical measures that characterize networks, such as the clustering coefficient and the number of…
Estimating influential nodes in large scale networks including but not limited to social networks, biological networks, communication networks, emerging smart grids etc. is a topic of fundamental interest. To understand influences of nodes…
We revisit the problem of designing sublinear algorithms for estimating the average degree of an $n$-vertex graph. The standard access model for graphs allows for the following queries: sampling a uniform random vertex, the degree of a…
This paper presents a graph signal processing algorithm to uncover the intrinsic low-rank components and the underlying graph of a high-dimensional, graph-smooth and grossly-corrupted dataset. In our problem formulation, we assume that the…
Accurate routing network status estimation is a key component in Software Defined Networking. However, existing deep-learning-based methods for modeling network routing are not able to extrapolate towards unseen feature distributions. Nor…
Vertex connectivity and its variants are among the most fundamental problems in graph theory, with decades of extensive study and numerous algorithmic advances. The directed variants of vertex connectivity are usually solved by manually…
The average distance of a vertex $v$ of a connected graph $G$ is the arithmetic mean of the distances from $v$ to all other vertices of $G$. The proximity $\pi(G)$ and the remoteness $\rho(G)$ of $G$ are the minimum and the maximum of the…
We propose a fast approximate algorithm for large graph matching. A new projected fixed-point method is defined and a new doubly stochastic projection is adopted to derive the algorithm. Previous graph matching algorithms suffer from high…
We consider the maximum vertex-weighted matching problem (MVM) for non-bipartite graphs. In earlier work we have described a 2/3-approximation algorithm for the MVM on bipartite graphs (Dobrian, Halappanavar, Pothen and Al-Herz, SIAM J.…
Parallel betweenness computation algorithms are proposed and implemented in a graph database for power system contingency selection. Principles of the graph database and graph computing are investigated for both node and edge betweenness…
We consider the maximum vertex-weighted matching problem (MVM), in which non-negative weights are assigned to the vertices of a graph, the weight of a matching is the sum of the weights of the matched vertices, and we are required to…