Related papers: The Generalized Friendship Paradox for Spectral Ce…
Information flow, opinion, and epidemics spread over structured networks. When using individual node centrality indicators to predict which nodes will be among the top influencers or spreaders in a large network, no single centrality has…
Group interactions occur frequently in social settings, yet their properties beyond pairwise relationships in network models remain unexplored. In this work, we study homophily, the nearly ubiquitous phenomena wherein similar individuals…
Centrality measures such as the degree, k-shell, or eigenvalue centrality can identify a network's most influential nodes, but are rarely usefully accurate in quantifying the spreading power of the vast majority of nodes which are not…
Core-satellite graphs (sometimes referred to as generalized friendship graphs) are an interesting class of graphs that generalize many well known types of graphs. In this paper we show that two popular clustering measures, the average…
In Hazra, den Hollander and Parvaneh (2025) we analysed the friendship paradox for sparse random graphs. For four classes of random graphs we characterised the empirical distribution of the friendship biases between vertices and their…
Let $G_n$ be an undirected finite graph on $n\in\mathbb{N}$ vertices labelled by $[n] = \{1,\ldots,n\}$. For $i \in [n]$, let $\Delta_{i,n}$ be the friendship bias of vertex $i$, defined as the difference between the average degree of the…
Social behaviors are often contagious, spreading through a population as individuals imitate the decisions and choices of others. A variety of global phenomena, from innovation adoption to the emergence of social norms and political…
Given a social network, which of its nodes are more central? This question has been asked many times in sociology, psychology and computer science, and a whole plethora of centrality measures (a.k.a. centrality indices, or rankings) were…
Spectral graph theory gives an algebraical approach to analyze the dynamics of a network by using the matrix that represents the network structure. However, it is not easy for social networks to apply the spectral graph theory because the…
Centrality is an important notion in complex networks; it could be used to characterize how influential a node or an edge is in the network. It plays an important role in several other network analysis tools including community detection.…
We determine all graphs whose adjacency matrix has at most two eigenvalues (multiplicities included) different from $\pm 1$ and decide which of these graphs are determined by their spectrum. This includes the so-called friendship graphs,…
The study of complex networks has been one of the most active fields in science in recent decades. Spectral properties of networks (or graphs that represent them) are of fundamental importance. Researchers have been investigating these…
Graph is an abstract representation commonly used to model networked systems and structure. In problems across various fields, including computer vision and pattern recognition, and neuroscience, graphs are often brought into comparison (a…
Centrality indices are used to rank the nodes of a graph by importance: this is a common need in many concrete situations (social networks, citation networks, web graphs, for instance) and it was discussed many times in sociology,…
Spectral clustering is a technique that clusters elements using the top few eigenvectors of their (possibly normalized) similarity matrix. The quality of spectral clustering is closely tied to the convergence properties of these principal…
Many natural and social systems develop complex networks, that are usually modelled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semi-circle law is known to…
Social networks are discrete systems with a large amount of heterogeneity among nodes (individuals). Measures of centrality aim at a quantification of nodes' importance for structure and function. Here we ask to which extent the most…
Complex networks are characterized by heterogeneous distributions of the degree of nodes, which produce a large diversification of the roles of the nodes within the network. Several centrality measures have been introduced to rank nodes…
We introduce a new centrality measure that characterizes the participation of each node in all subgraphs in a network. Smaller subgraphs are given more weight than larger ones, which makes this measure appropriate for characterizing network…
There are several applications that benefit from a definition of centrality which is applicable to sets of vertices, rather than individual vertices. However, existing definitions might not be able to help us in answering several network…