When Can Two Unlabeled Networks Be Aligned Under Partial Overlap?

Network alignment refers to the problem of matching the vertex sets of two unlabeled graphs, which can be viewed as a generalization of the classic graph isomorphism problem. Network alignment has applications in several fields, including social network analysis, privacy, pattern recognition, computer vision, and computational biology. A number of heuristic algorithms have been proposed in these fields. Recent progress in the analysis of network alignment over stochastic models sheds light on the interplay between network parameters and matchability. In this paper, we consider the alignment problem when the two networks overlap only partially, i.e., there exist vertices in one network that have no counterpart in the other. We define a random bigraph model that generates two correlated graphs $G_{1,2}$; it is parameterized by the expected node overlap $t^2$ and by the expected edge overlap $s^2$. We define a cost function for structural mismatch under a particular alignment, and we identify a threshold for perfect matchability: if the average node degrees of $G_{1,2}$ grow as $\omega\left( (s^{-2}t^{-1} \log(n) \right)$, then minimization of the proposed cost function results in an alignment which (i) is over exactly the set of shared nodes between $G_1$ and $G_2$, and (ii) agrees with the true matching between these shared nodes. Our result shows that network alignment is fundamentally robust to partial edge and node overlaps

A Comprehensive Bibliometric Analysis on Social Network Anonymization: Current Approaches and Future Directions

In recent decades, social network anonymization has become a crucial research field due to its pivotal role in preserving users' privacy. However, the high diversity of approaches introduced in relevant studies poses a challenge to gaining a profound understanding of the field. In response to this, the current study presents an exhaustive and well-structured bibliometric analysis of the social network anonymization field. To begin our research, related studies from the period of 2007-2022 were collected from the Scopus Database then pre-processed. Following this, the VOSviewer was used to visualize the network of authors' keywords. Subsequently, extensive statistical and network analyses were performed to identify the most prominent keywords and trending topics. Additionally, the application of co-word analysis through SciMAT and the Alluvial diagram allowed us to explore the themes of social network anonymization and scrutinize their evolution over time. These analyses culminated in an innovative taxonomy of the existing approaches and anticipation of potential trends in this domain. To the best of our knowledge, this is the first bibliometric analysis in the social network anonymization field, which offers a deeper understanding of the current state and an insightful roadmap for future research in this domain.Comment: 73 pages, 28 figure

Network Alignment: Theory, Algorithms, and Applications

Networks are central in the modeling and analysis of many large-scale human and technical systems, and they have applications in diverse fields such as computer science, biology, social sciences, and economics. Recently, network mining has been an active area of research. In this thesis, we study several related network-mining problems, from three different perspectives: the modeling and theory perspective, the computational perspective, and the application perspective. In the bulk of this thesis, we focus on network alignment, where the data provides two (or more) partial views of the network, and where the node labels are sometimes ambiguous. Network alignment has applications in social-network reconciliation and de-anonymization, protein-network alignment in biology, and computer vision. In the first part of this thesis, we investigate the feasibility of network alignment with a random-graph model. This random-graph model generates two (or several) correlated networks, and lets the two networks to overlap only partially. For a particular alignment, we define a cost function for structural mismatch. We show that the minimization of the proposed cost function (assuming that we have access to infinite computational power), with high probability, results in an alignment that recovers the set of shared nodes between the two networks, and that also recovers the true matching between the shared nodes. The most scalable network-alignment approaches use ideas from percolation theory, where a matched node-couple infects its neighboring couples that are additional potential matches. In the second part of this thesis, we propose a new percolation-based network-alignment algorithm that can match large networks by using only the network structure and a handful of initially pre-matched node-couples called seed set. We characterize a phase transition in matching performance as a function of the seed-set size. In the third part of this thesis, we consider two important application areas of network mining in biology and public health. The first application area is percolation-based network alignment of protein-protein interaction (PPI) networks in biology. The alignment of biological networks has many uses, such as the detection of conserved biological network motifs, the prediction of protein interactions, and the reconstruction of phylogenetic trees. Network alignment can be used to transfer biological knowledge between species. We introduce a new global pairwise-network alignment algorithm for PPI networks, called PROPER. The PROPER algorithm shows higher accuracy and speed compared to other global network-alignment methods. We also extend PROPER to the global multiple-network alignment problem. We introduce a new algorithm, called MPROPER, for matching multiple networks. Finally, we explore IsoRank, one of the first and most referenced global pairwise-network alignment algorithms. Our second application area is the control of epidemic processes. We develop and model strategies for mitigating an epidemic in a large-scale dynamic contact network. More precisely, we study epidemics of infectious diseases by (i) modeling the spread of epidemics on a network by using many pieces of information about the mobility and behavior of a population; and by (ii) designing personalized behavioral recommendations for individuals, in order to mitigate the effect of epidemics on that network

Impact of Clustering on the Performance of Network De-anonymization

Recently, graph matching algorithms have been successfully applied to the problem of network de-anonymization, in which nodes (users) participating to more than one social network are identified only by means of the structure of their links to other members. This procedure exploits an initial set of seed nodes large enough to trigger a percolation process which correctly matches almost all other nodes across the different social networks. Our main contribution is to show the crucial role played by clustering, which is a ubiquitous feature of realistic social network graphs (and many other systems). Clustering has both the effect of making matching algorithms more vulnerable to errors, and the potential to dramatically reduce the number of seeds needed to trigger percolation, thanks to a wave-like propagation effect. We demonstrate these facts by considering a fairly general class of random geometric graphs with variable clustering level, and showing how clever algorithms can achieve surprisingly good performance while containing matching error