Related papers: Structural measures of similarity and complementar…
Revealing the structural features of a complex system from the observed collective dynamics is a fundamental problem in network science. In order to compute the various topological descriptors commonly used to characterize the structure of…
Comparing networks is essential for a number of downstream tasks, from clustering to anomaly detection. Despite higher-order interactions being critical for understanding the dynamics of complex systems, traditional approaches for network…
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…
We study homomorphism polynomials, which are polynomials that enumerate all homomorphisms from a pattern graph $H$ to $n$-vertex graphs. These polynomials have received a lot of attention recently for their crucial role in several new…
Networks are often characterized by node heterogeneity for which nodes exhibit different degrees of interaction and link homophily for which nodes sharing common features tend to associate with each other. In this paper, we propose a new…
Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of…
Homophily is the principle whereby "similarity breeds connections". We give a quantitative formulation of this principle within networks. Given a network and a labeled partition of its vertices, the vector indexed by each class of the…
Many complex systems can be represented as networks, and the problem of network comparison is becoming increasingly relevant. There are many techniques for network comparison, from simply comparing network summary statistics to…
The observation that individuals tend to be friends with people who are similar to themselves, commonly known as homophily, is a prominent and well-studied feature of social networks. Many machine learning methods exploit homophily to…
Clustering is indispensable for data analysis in many scientific disciplines. Detecting clusters from heavy noise remains challenging, particularly for high-dimensional sparse data. Based on graph-theoretic framework, the present paper…
Most models of complex systems have been homogeneous, i.e., all elements have the same properties (spatial, temporal, structural, functional). However, most natural systems are heterogeneous: few elements are more relevant, larger,…
We study the structure of social networks of students by examining the graphs of Facebook "friendships" at five American universities at a single point in time. We investigate each single-institution network's community structure and employ…
This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…
The purpose of this study is to investigate how homophily, memory constraints, and adversarial disruptions collectively shape the resilience and adaptability of complex networks. To achieve this, we develop a new framework that integrates…
We characterize structures such as monotonicity, convexity, and modality in smooth regression curves using persistent homology. Persistent homology is a key tool in topological data analysis that detects higher-dimensional topological…
Networks play a prominent role in the study of complex systems of interacting entities in biology, sociology, and economics. Despite this diversity, we demonstrate here that a statistical model decomposing networks into matching and…
Motivation: The study of diverse enzyme superfamilies can provide important insight into the relationships between protein sequence, structure and function. It is often challenging, however, to discover these relationships across a large…
The concept of nestedness, in particular for ecological and economical networks, has been introduced as a structural characteristic of real interacting systems. We suggest that the nestedness is in fact another way to express a mesoscale…
In recent years, social media has become a ubiquitous and integral part of social networking. One of the major attentions made by social researchers is the tendency of like-minded people to interact with one another in social groups, a…
The new concept of multilevel network is introduced in order to embody some topological properties of complex systems with structures in the mesoscale which are not completely captured by the classical models. This new model, which…