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Researchers developing implementations of distributed graph analytic algorithms require graph generators that yield graphs sharing the challenging characteristics of real-world graphs (small-world, scale-free, heavy-tailed degree…
Graph sampling via crawling has become increasingly popular and important in the study of measuring various characteristics of large scale complex networks. While powerful, it is known to be challenging when the graph is loosely connected…
We consider the edge-triangle model (or Strauss model), and focus on the asymptotic behavior of the triangle density when the size of the graph increases to infinity. This random graph belongs to the class of exponential random graphs,…
One of the simplest problems on directed graphs is that of identifying the set of vertices reachable from a designated source vertex. This problem can be solved easily sequentially by performing a graph search, but efficient parallel…
Spanning Centrality is a measure used in network analysis to determine the importance of an edge in a graph based on its contribution to the connectivity of the entire network. Specifically, it quantifies how critical an edge is in terms of…
Using random walks for sampling has proven advantageous in assessing the characteristics of large and unknown social networks. Several algorithms based on random walks have been introduced in recent years. In the practical application of…
This work considers clustering nodes of a largely incomplete graph. Under the problem setting, only a small amount of queries about the edges can be made, but the entire graph is not observable. This problem finds applications in…
Graph labelling is a key activity of network science, with broad practical applications, and close relations to other network science tasks, such as community detection and clustering. While a large body of work exists on both unsupervised…
The application of network analysis has found great success in a wide variety of disciplines; however, the popularity of these approaches has revealed the difficulty in handling networks whose complexity scales rapidly. One of the main…
We propose a universal approach to a range of enumeration problems in graphs. The key point is in contracting suitably chosen symmetric tensors placed at the vertices of a graph along the edges. In particular, this leads to an algorithm…
This paper describes Census, a protocol for data aggregation and statistical counting in MANETs. Census operates by circulating a set of tokens in the network using biased random walks such that each node is visited by at least one token.…
We give a randomized algorithm that approximates the number of independent sets in a dense, regular bipartite graph -- in the language of approximate counting, we give an FPRAS for #BIS on the class of dense, regular bipartite graphs.…
A tessellation of a graph is a partition of its vertices into vertex disjoint cliques. A tessellation cover of a graph is a set of tessellations that covers all of its edges. The $t$-tessellability problem aims to decide whether there is a…
Random graph generation is an important tool for studying large complex networks. Despite abundance of random graph models, constructing models with application-driven constraints is poorly understood. In order to advance state-of-the-art…
We revisit the problem of counting the number of copies of a fixed graph in a random graph or multigraph, including the case of constrained degrees. Our approach relies heavily on analytic combinatorics and on the notion of patchwork to…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
The potential for machine learning systems to amplify social inequities and unfairness is receiving increasing popular and academic attention. Much recent work has focused on developing algorithmic tools to assess and mitigate such…
In statistical mechanical investigations on complex networks, it is useful to employ random graphs ensembles as null models, to compare with experimental realizations. Motivated by transcription networks, we present here a simple way to…
Quasi-cliques are dense incomplete subgraphs of a graph that generalize the notion of cliques. Enumerating quasi-cliques from a graph is a robust way to detect densely connected structures with applications to bio-informatics and social…
We study the problem of finding large cuts in $d$-regular triangle-free graphs. In prior work, Shearer (1992) gives a randomised algorithm that finds a cut of expected size $(1/2 + 0.177/\sqrt{d})m$, where $m$ is the number of edges. We…