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Not all nodes in a network are created equal. Differences and similarities exist at both individual node and group levels. Disentangling single node from group properties is crucial for network modeling and structural inference. Based on…

While network science has become an indispensable tool for studying complex systems, the conventional use of pairwise links often shows limitations in describing high-order interactions properly. Hypergraphs, where each edge can connect…

We propose and study a set of algorithms for discovering community structure in networks -- natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative…

The structural balance of a signed graph is known to be necessary and sufficient to obtain a bipartite consensus among agents with friend-foe relationships. In the real world, relationships are multifarious, and the coexistence of different…

Structure inference is an important task for network data processing and analysis in data science. In recent years, quite a few approaches have been developed to learn the graph structure underlying a set of observations captured in a data…

In this paper, we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups. Specifically,…

As the popularity of graph data increases, there is a growing need to count the occurrences of subgraph patterns of interest, for a variety of applications. Many graphs are massive in scale and also fully dynamic (with insertions and…

Motivated by the problem of inferring the graph structure of functional connectivity networks from multi-level functional magnetic resonance imaging data, we develop a valid inference framework for high-dimensional graphical models that…

In this work, we consider hypothesis testing and anomaly detection on datasets where each observation is a weighted network. Examples of such data include brain connectivity networks from fMRI flow data, or word co-occurrence counts for…

Understanding spreading dynamics will benefit society as a whole in better preventing and controlling diseases, as well as facilitating the socially responsible information while depressing destructive rumors. In network-based spreading…

Graphical Gaussian models have proven to be useful tools for exploring network structures based on multivariate data. Applications to studies of gene expression have generated substantial interest in these models, and resulting recent…

The vast majority of network datasets contains errors and omissions, although this is rarely incorporated in traditional network analysis. Recently, an increasing effort has been made to fill this methodological gap by developing network…

Nonlinear networked systems are of interest in several areas of research, such as multi-agent systems and social networks. In this paper, we examine the controllability of several classes of nonlinear networked dynamics on which the…

In the early days of gene expression data, researchers have focused on gene-level analysis, and particularly on finding differentially expressed genes. This usually involved making a simplifying assumption that genes are independent, which…

Multi-label network classification is a well-known task that is being used in a wide variety of web-based and non-web-based domains. It can be formalized as a multi-relational learning task for predicting nodes labels based on their…

Signed networks appear naturally in contexts where conflict or animosity is apparent. In this book chapter we review some of the literature on signed networks, especially in the context of partitioning. Most of the work is founded in what…

Detailed network models of social, biological and other complex systems are often dense, which increases their computational complexity in simulations and analysis. To address this challenge, graph sparsification is used to remove edges…

Community structure is common in many real networks, with nodes clustered in groups sharing the same connections patterns. While many community detection methods have been developed for networks with binary edges, few of them are applicable…

Scale-free (SF) networks and small world networks have been found to occur in very diverse contexts. It is this striking universality which makes one look for widely applicable mechanisms which lead to the formation of such networks. In…

Signed graph clustering is a critical technique for discovering community structures in graphs that exhibit both positive and negative relationships. We have identified two significant challenges in this domain: i) existing signed spectral…