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In graph-based applications, a common task is to pinpoint the most important or ``central'' vertex in a (directed or undirected) graph, or rank the vertices of a graph according to their importance. To this end, a plethora of so-called…
Graph matching is the process of computing the similarity between two graphs. Depending on the requirement, it can be exact or inexact. Exact graph matching requires a strict correspondence between nodes of two graphs, whereas inexact…
Kemeny's constant quantifies a graph's connectivity by measuring the average time for a random walker to reach any other vertex. We introduce two concepts of the directional derivative of Kemeny's constant with respect to an edge and use…
Many networks, such as transportation, power, and water distribution, can be represented as graphs. Crucial challenge in graph representations is identifying the importance of graph edges and their influence on overall network efficiency…
Betweenness centrality (BC) was proposed as an indicator of the extent of an individual's influence in a social network. It is measured by counting how many times a vertex (i.e., an individual) appears on all the shortest paths between…
This paper considers a joint multi-graph inference and clustering problem for simultaneous inference of node centrality and association of graph signals with their graphs. We study a mixture model of filtered low pass graph signals with…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
As relational datasets modeled as graphs keep increasing in size and their data-acquisition is permeated by uncertainty, graph-based analysis techniques can become computationally and conceptually challenging. In particular, node centrality…
Given a network G, edge centrality is a metric used to evaluate the importance of edges in G, which is a key concept in analyzing networks and finds vast applications involving edge ranking. In spite of a wealth of research on devising edge…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
Identifying central entities and interactions is a fundamental problem in network science. While well-studied for graphs (pairwise relations), many biological and social systems exhibit higher-order interactions best modeled by hypergraphs.…
Knowledge graphs play a central role for linking different data which leads to multiple layers. Thus, they are widely used in big data integration, especially for connecting data from different domains. Few studies have investigated the…
There has been significant recent interest in parallel graph processing due to the need to quickly analyze the large graphs available today. Many graph codes have been designed for distributed memory or external memory. However, today even…
Centrality rankings such as degree, closeness, betweenness, Katz, PageRank, etc. are commonly used to identify critical nodes in a graph. These methods are based on two assumptions that restrict their wider applicability. First, they assume…
In complex networks, especially social networks, networks could be divided into disjoint partitions that the ratio between the number of internal edges (the edges between the vertices within same partition) to the number of outer edges…
We consider the maintenance of maximal bicliques from a dynamic bipartite graph that changes over time due to the addition or deletion of edges. When the set of edges in a graph changes, we are interested in knowing the change in the set of…
Graph clustering is an important algorithmic technique for analysing massive graphs, and has been widely applied in many research fields of data science. While the objective of most graph clustering algorithms is to find a vertex set of low…
This paper initiates the study of the classic balanced graph partitioning problem from an online perspective: Given an arbitrary sequence of pairwise communication requests between $n$ nodes, with patterns that may change over time, the…
A bridge in a graph is an edge whose removal disconnects the graph and increases the number of connected components. We calculate the fraction of bridges in a wide range of real-world networks and their randomized counterparts. We find that…