Related papers: Triadic structures in multislice networks

A typical complex system should be described by a supernetwork or a network of networks, in which the networks are coupled to some other networks. As the first step to understanding the complex systems on such more systematic level,…

Redundancy needs more precise characterization as it is a major factor in the evolution and robustness of networks of multivariate interactions. We investigate the complexity of such interactions by inferring a connection transitivity that…

Counting the frequencies of 3-, 4-, and 5-node undirected motifs (also know as graphlets) is widely used for understanding complex networks such as social and biology networks. However, it is a great challenge to compute these metrics for a…

Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…

Link prediction plays an important role in network analysis and applications. Recently, approaches for link prediction have evolved from traditional similarity-based algorithms into embedding-based algorithms. However, most existing…

We define a new measure of network symmetry that is capable of capturing approximate global symmetries of networks. We apply this measure to different networks sampled from several classic network models, as well as several real-world…

Pattern counting in graphs is a fundamental primitive for many network analysis tasks, and a number of methods have been developed for scaling subgraph counting to large graphs. Many real-world networks carry a natural notion of strength of…

The connectivity of a network contains information about the relationships between nodes, which can denote interactions, associations, or dependencies. We show that this information can be analyzed by measuring the uncertainty (and…

We introduce a novel representation of structured polynomial ideals, which we refer to as chordal networks. The sparsity structure of a polynomial system is often described by a graph that captures the interactions among the variables.…

Graph-theoretic tools and techniques have seen wide use in the multi-agent systems literature, and the unpredictable nature of some multi-agent communications has been successfully modeled using random communication graphs. Across both…

Many real-world network are multilayer, with nontrivial correlations across layers. Here we show that these correlations amplify geometry in networks. We focus on mutual clustering--a measure of the amount of triangles that are present in…

The graph structure is a commonly used data storage mode, and it turns out that the low-dimensional embedded representation of nodes in the graph is extremely useful in various typical tasks, such as node classification, link prediction ,…

Algorithms for search of communities in networks usually consist discrete variations of links. Here we discuss a flow method, driven by a set of differential equations. Two examples are demonstrated in detail. First is a partition of a…

The large size of multiscale, distribution and transmission, power grids hinder fast system-wide estimation and real-time control and optimization of operations. This paper studies graph reduction methods of power grids that are favorable…

Finding, counting and/or listing triangles (three vertices with three edges) in large graphs are natural fundamental problems, which received recently much attention because of their importance in complex network analysis. We provide here a…

D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a…

High triangle density -- the graph property stating that a constant fraction of two-hop paths belong to a triangle -- is a common signature of social networks. This paper studies triangle-dense graphs from a structural perspective. We prove…

Let G = (V,E) be an n-vertex graph and M_d a d-vertex graph, for some constant d. Is M_d a subgraph of G? We consider this problem in a model where all n processes are connected to all other processes, and each message contains up to O(log…

Real-world networks exhibit prominent hierarchical and modular structures, with various subgraphs as building blocks. Most existing studies simply consider distinct subgraphs as motifs and use only their numbers to characterize the…

Motif counting plays a crucial role in understanding the structural properties of networks. By computing motif frequencies, researchers can draw key insights into the structural properties of the underlying network. As networks become…