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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…
In the course of the growth of the Internet and due to increasing availability of data, over the last two decades, the field of network science has established itself as an own area of research. With quantitative scientists from computer…
A $k$-motif (or graphlet) is a subgraph on $k$ nodes in a graph or network. Counting of motifs in complex networks has been a well-studied problem in network analysis of various real-word graphs arising from the study of social networks and…
Subgraph counting is a fundamental task that underpins several network analysis methodologies, including community detection and graph two-sample tests. Counting subgraphs is a computationally intensive problem. Substantial research has…
Many real world networks contain a statistically surprising number of certain subgraphs, called network motifs. In the prevalent approach to motif analysis, network motifs are detected by comparing subgraph frequencies in the original…
Subgraphs such as cliques, loops and stars form crucial connections in the topologies of real-world networks. Random graph models provide estimates for how often certain subgraphs appear, which in turn can be tested against real-world…
We introduce a new model of indeterminacy in graphs: instead of specifying all the edges of the graph, the input contains all triples of vertices that form a connected subgraph. In general, different (labelled) graphs may have the same set…
We develop a full theoretical approach to clustering in complex networks. A key concept is introduced, the edge multiplicity, that measures the number of triangles passing through an edge. This quantity extends the clustering coefficient in…
Conventionally, pairwise relationships between nodes are considered to be the fundamental building blocks of complex networks. However, over the last decade the overabundance of certain sub-network patterns, so called motifs, has attracted…
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…
Networks provide a popular representation of complex data. Often, different types of relational measurements are taken on the same subjects. Such data can be represented as a \textit{multislice network}, a collection of networks on the same…
Networks are a fundamental model of complex systems throughout the sciences, and network datasets are typically analyzed through lower-order connectivity patterns described at the level of individual nodes and edges. However, higher-order…
Designing algorithms that generate networks with a given degree sequence while varying both subgraph composition and distribution of subgraphs around nodes is an important but challenging research problem. Current algorithms lack control of…
Community detection has arisen as one of the most relevant topics in the field of graph data mining due to its importance in many fields such as biology, social networks or network traffic analysis. The metrics proposed to shape communities…
This article introduces a new class of models for multiple networks. The core idea is to parametrize a distribution on labelled graphs in terms of a Fr\'{e}chet mean graph (which depends on a user-specified choice of metric or graph…
Graph clustering (or community detection) has long drawn enormous attention from the research on web mining and information networks. Recent literature on this topic has reached a consensus that node contents and link structures should be…
The distance of a graph from being triangle-free is a fundamental graph parameter, counting the number of edges that need to be removed from a graph in order for it to become triangle-free. Its corresponding computational problem is the…
We consider the problem of estimating undirected triangle-free graphs of high dimensional distributions. Triangle-free graphs form a rich graph family which allows arbitrary loopy structures but 3-cliques. For inferential tractability, we…
Graph analytics for large scale graphs has gained interest in recent years. Many graph algorithms have been designed for vertex-centric distributed graph processing frameworks to operate on large graphs with 100 M vertices and edges, using…
Sampling random nodes is a fundamental algorithmic primitive in the analysis of massive networks, with many modern graph mining algorithms critically relying on it. We consider the task of generating a large collection of random nodes in…