Related papers: Approximate Network Symmetry

Asymmetry of in/out-degree distribution is a widespread phenomenon in real-world complex networks. This paper put forward the concept of Edge Asymmetry(EA) to quantify this feature. We designed an EA-based strategy to attack six kinds of…

We describe a new method for the random sampling of connected networks with a specified degree sequence. We consider both the case of simple graphs and that of loopless multigraphs. The constraints of fixed degrees and of connectedness are…

We propose a consistent approach to the statistics of the shortest paths in random graphs with a given degree distribution. This approach goes further than a usual tree ansatz and rigorously accounts for loops in a network. We calculate the…

The geometric renormalization technique for complex networks has successfully revealed the multiscale self-similarity of real network topologies and can be applied to generate replicas at different length scales. In this letter, we extend…

An increasing abstraction has marked some recent investigations in network science. Examples include the development of algorithms that map time series data into networks whose vertices and edges can have different interpretations, beyond…

Common measures of neural representational (dis)similarity are designed to be insensitive to rotations and reflections of the neural activation space. Motivated by the premise that the tuning of individual units may be important, there has…

The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of…

In this paper, we consider the problem of approximately aligning/matching two graphs. Given two graphs $G_{1}=(V_{1},E_{1})$ and $G_{2}=(V_{2},E_{2})$, the objective is to map nodes $u, v \in G_1$ to nodes $u',v'\in G_2$ such that when $u,…

Consider the continuum of points along the edges of a network, i.e., an undirected graph with positive edge weights. We measure distance between these points in terms of the shortest path distance along the network, known as the network…

We develop a statistical theory to characterize correlations in weighted networks. We define the appropriate metrics quantifying correlations and show that strictly uncorrelated weighted networks do not exist due to the presence of…

Random networks are a powerful tool in the analytical modeling of complex networks as they allow us to write approximate mathematical models for diverse properties and behaviors of networks. One notable shortcoming of these models is that…

We consider a Gaussian statistical model whose parameter space is given by the variances of random variables. Underlying this model we identify networks by interpreting random variables as sitting on vertices and their correlations as…

Asymptotic properties of random graph sequences, like occurrence of a giant component or full connectivity in Erd\H{o}s-R\'enyi graphs, are usually derived with very specific choices for defining parameters. The question arises to which…

Directed networks are ubiquitous and are necessary to represent complex systems with asymmetric interactions---from food webs to the World Wide Web. Despite the importance of edge direction for detecting local and community structure, it…

Over the last two decades, network theory has shown to be a fruitful paradigm in understanding the organization and functioning of real-world complex systems. One technique helpful to this endeavor is identifying functionally influential…

Networks in nature possess a remarkable amount of structure. Via a series of data-driven discoveries, the cutting edge of network science has recently progressed from positing that the random graphs of mathematical graph theory might…

Real-world networks are often complex and large with millions of nodes, posing a great challenge for analysts to quickly see the big picture for more productive subsequent analysis. We aim at facilitating exploration of node-attributed…

Assessing whether a given network is typical or atypical for a random-network ensemble (i.e., network-ensemble comparison) has widespread applications ranging from null-model selection and hypothesis testing to clustering and classifying…

Analogous to biological sequence comparison, comparing cellular networks is an important problem that could provide insight into biological understanding and therapeutics. For technical reasons, comparing large networks is computationally…

We explore pseudometrics for directed graphs in order to better understand their topological properties. The directed flag complex associated to a directed graph provides a useful bridge between network science and topology. Indeed, it has…