We perform an extensive analysis of how sampling impacts the estimate of several relevant network measures.
In particular, we focus on how a sampling strategy optimized to recover a particular spectral centrality measure impacts other topological quantities. Our goal is on one hand to extend the analysis of the behavior of TCEC [Ruggeri2019], a theoretically-grounded sampling method for eigenvector centrality estimation.
On the other hand, to demonstrate more broadly how sampling can impact the estimation of relevant network properties like centrality measures different than the one aimed at optimizing, community structure and node attribute distribution.
Finally, we adapt the theoretical framework behind TCEC for the case of PageRank centrality and propose a sampling algorithm aimed at optimizing its estimation. We show that, while the theoretical derivation can be suitably adapted to cover this case, the resulting algorithm suffers of a high computational complexity that requires further approximations compared to the eigenvector centrality case.
We develop a new sampling method to estimate eigenvector centrality on incomplete networks. Our goal is to estimate this global centrality measure having at disposal a limited amount of data. This is the case in many real-world scenarios where data collection is expensive, the network is too big for data storage capacity or only partial information is available. The sampling algorithm is theoretically grounded by results derived from spectral approximation theory. We studied the problem on both synthetic and real data and tested the performance comparing with traditional methods, such as rando…
Complex networks have gained more attention from the last few years. The size of real-world complex networks, such as online social networks, WWW network, collaboration networks, is increasing exponentially with time. It is not feasible to collect the complete data and store and process it. In the present work, we propose a method to estimate the degree centrality rank of a node without having the complete structure of the graph. The proposed algorithm uses the degree of a node and power-law exponent of the degree distribution to calculate the ranking. Simulation results on the Barabasi-Albert…
Most network studies rely on an observed network that differs from the underlying network which is obfuscated by measurement errors. It is well known that such errors can have a severe impact on the reliability of network metrics, especially on centrality measures: a more central node in the observed network might be less central in the underlying network. We introduce a metric for the reliability of centrality measures -- called sensitivity. Given two randomly chosen nodes, the sensitivity means the probability that the more central node in the observed network is also more central in the und…
Betweenness centrality is a popular centrality measure with applications in several domains, and whose exact computation is impractical for modern-sized networks. We present SILVAN, a novel, efficient algorithm to compute, with high probability, accurate estimates of the betweenness centrality of all nodes of a graph and a high-quality approximation of the top-k betweenness centralities. SILVAN follows a progressive sampling approach, and builds on novel bounds based on Monte-Carlo Empirical Rademacher Averages, a powerful and flexible tool from statistical learning theory. SILVAN relies on a …
Understanding the importance of links in transmitting information in a network can provide ways to hinder or postpone ongoing dynamical phenomena like the spreading of epidemic or the diffusion of information. In this work, we propose a new measure based on stochastic diffusion processes, the \textit{transmission centrality}, that captures the importance of links by estimating the average number of nodes to whom they transfer information during a global spreading diffusion process. We propose a simple algorithmic solution to compute transmission centrality and to approximate it in very large n…
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 analysis questions. In this paper, we study generalizing aggregation of centralities of individual vertices, to the centrality of the set consisting of these vertices. In particular, we propose exclusive betweenness centrality, defined as the number of shortest paths passing over exactly one of the vertices in the set, and discuss how this can be useful in det…
Estimating influential nodes in large scale networks including but not limited to social networks, biological networks, communication networks, emerging smart grids etc. is a topic of fundamental interest. To understand influences of nodes in a network, a classical metric is centrality within which there are multiple specific instances including degree centrality, closeness centrality, betweenness centrality and more. As of today, existing algorithms to identify nodes with high centrality measures operate upon the entire (or rather global) network, resulting in high computational complexity. I…
This paper proposes an alternative way to identify nodes with high betweenness centrality. It introduces a new metric, k-path centrality, and a randomized algorithm for estimating it, and shows empirically that nodes with high k-path centrality have high node betweenness centrality. The randomized algorithm runs in time $O(κ^{3}n^{2-2α}\log n)$ and outputs, for each vertex v, an estimate of its k-path centrality up to additive error of $\pm n^{1/2+ α}$ with probability $1-1/n^2$. Experimental evaluations on real and synthetic social networks show improved accuracy in detecting high betweenness…
Robustness estimation is critical for the design and maintenance of resilient networks, one of the global challenges of the 21st century. Existing studies exploit network metrics to generate attack strategies, which simulate intentional attacks in a network, and compute a metric-induced robustness estimation. While some metrics are easy to compute, e.g. degree centrality, other, more accurate, metrics require considerable computation efforts, e.g. betweennes centrality. We propose a new algorithm for estimating the robustness of a network in sub-quadratic time, i.e., significantly faster than …
We consider the problem of estimating a network's eigenvector centrality only from data on the nodes, with no information about network topology. Leveraging the versatility of graph filters to model network processes, data supported on the nodes is modeled as a graph signal obtained via the output of a graph filter applied to white noise. We seek to simplify the downstream task of centrality ranking by bypassing network topology inference methods and, instead, inferring the centrality structure of the graph directly from the graph signals. To this end, we propose two simple algorithms for rank…
Network scientists have shown that there is great value in studying pairwise interactions between components in a system. From a linear algebra point of view, this involves defining and evaluating functions of the associated adjacency matrix. Recent work indicates that there are further benefits from accounting directly for higher order interactions, notably through a hypergraph representation where an edge may involve multiple nodes. Building on these ideas, we motivate, define and analyze a class of spectral centrality measures for identifying important nodes and hyperedges in hypergraphs, g…
Knowledge creation and dissemination in science and technology systems is perceived as a prerequisite for socio-economic development. The efficiency of creating new knowledge is considered to have a geographical component, i.e. some regions are more capable in scientific knowledge production than others. This article shows a method to use a network representation of scientific interaction to assess the relative efficiency of regions with diverse boundaries in channeling knowledge through a science system. In a first step, a weighted aggregate of the betweenness centrality is produced from empi…
This paper characterizes the difficulty of estimating a network's eigenvector centrality only from data on the nodes, i.e., with no information about the topology of the network. We model this nodal data as graph signals generated by passing white noise through generic (not necessarily low-pass) graph filters. Leveraging the spectral properties of graph filters, we estimate the eigenvectors of the adjacency matrix of the underlying network. To this end, a simple selection algorithm is proposed, which chooses the correct eigenvector of the signal covariance matrix with minimal assumptions on th…
This paper is concerned with distributed detection of central nodes in complex networks using closeness centrality. Closeness centrality plays an essential role in network analysis. Evaluating closeness centrality exactly requires complete knowledge of the network; for large networks, this may be inefficient, so closeness centrality should be approximated. Distributed tasks such as leader election can make effective use of centrality information for highly central nodes, but complete network information is not locally available. This paper refines a distributed centrality computation algorithm…
Betweenness centrality is a fundamental centrality measure in social network analysis. Given a large-scale network, how can we find the most central nodes? This question is of key importance to numerous important applications that rely on betweenness centrality, including community detection and understanding graph vulnerability. Despite the large amount of work on designing scalable approximation algorithms for betweenness centrality, estimating it on large-scale networks remains a computational challenge. In this paper, we study the Betweenness Centrality Maximization problem: given a graph …
In network analysis, the betweenness centrality of a node informally captures the fraction of shortest paths visiting that node. The computation of the betweenness centrality measure is a fundamental task in the analysis of modern networks, enabling the identification of the most central nodes in such networks. Additionally to being massive, modern networks also contain information about the time at which their events occur. Such networks are often called temporal networks. The temporal information makes the study of the betweenness centrality in temporal networks (i.e., temporal betweenness c…
User attributes, such as home location, are useful for many applications. Many researchers have been tackling how to estimate users' home locations using relationships among users. It is known that the home locations of certain users, such as celebrities, are hard to estimate using relationships. However, because estimating the home locations of all celebrities is not actually hard, it is important to clarify the characteristics of users whose home locations are hard to estimate. We analyze whether centralities, which represent users' characteristics, and the tendency to have the same home loc…
Unidistance（尤尼达朗斯大学）；Université Paris Saclay（巴黎萨克雷大学）；CNRS（法国国家科学研究中心）；Pompeu Fabra University（庞培法布拉大学）；ICREA（加泰罗尼亚研究与高级研究院）；Barcelona School of Economics（巴塞罗那经济学院）；Università de la Svizzera Italiana（瑞士意大利语大学）
The application of deep learning to symbolic domains remains an active research endeavour. Graph neural networks (GNN), consisting of trained neural modules which can be arranged in different topologies at run time, are sound alternatives to tackle relational problems which lend themselves to graph representations. In this paper, we show that GNNs are capable of multitask learning, which can be naturally enforced by training the model to refine a single set of multidimensional embeddings $\in \mathbb{R}^d$ and decode them into multiple outputs by connecting MLPs at the end of the pipeline. We …
Identifying key agents for the transmission of diseases (ideas, technology, etc.) across social networks has predominantly relied on measures of centrality on a static base network or a temporally flattened graph of agent interactions. Various measures have been proposed as the best trackers of influence, such as degree centrality, betweenness, and $k$-shell, depending on the structure of the connectivity. We consider SIR and SIS propagation dynamics on a temporally-extruded network of observed interactions and measure the conditional marginal spread as the change in the magnitude of the infec…
We introduce a new method to efficiently approximate the number of infections resulting from a given initially-infected node in a network of susceptible individuals. Our approach is based on counting the number of possible infection walks of various lengths to each other node in the network. We analytically study the properties of our method, in particular demonstrating different forms for SIS and SIR disease spreading (e.g. under the SIR model our method counts self-avoiding walks). In comparison to existing methods to infer the spreading efficiency of different nodes in the network (based on…
Finding the infection sources in a network when we only know the network topology and infected nodes, but not the rates of infection, is a challenging combinatorial problem, and it is even more difficult in practice where the underlying infection spreading model is usually unknown a priori. In this paper, we are interested in finding a source estimator that is applicable to various spreading models, including the Susceptible-Infected (SI), Susceptible-Infected-Recovered (SIR), Susceptible-Infected-Recovered-Infected (SIRI), and Susceptible-Infected-Susceptible (SIS) models. We show that under …
A rumor spreading in a social network or a disease propagating in a community can be modeled as an infection spreading in a network. Finding the infection source is a challenging problem, which is made more difficult in many applications where we have access only to a limited set of observations. We consider the problem of estimating an infection source for a Susceptible-Infected model, in which not all infected nodes can be observed. When the network is a tree, we show that an estimator for the source node associated with the most likely infection path that yields the limited observations is …
Collecting complete network data is expensive, time-consuming, and often infeasible. Aggregated Relational Data (ARD), which capture information about a social network by asking a respondent questions of the form ``How many people with trait X do you know?'' provide a low-cost option when collecting complete network data is not possible. Rather than asking about connections between each pair of individuals directly, ARD collects the number of contacts the respondent knows with a given trait. Despite widespread use and a growing literature on ARD methodology, there is still no systematic unders…
Department of Sociology, Cornell University（康奈尔大学社会学系）；Department of Sociology, Dartmouth College（达特茅斯学院社会学系）；Qatar Computing Research Institute（卡塔尔计算研究所）
In online social networks, it is common to use predictions of node categories to estimate measures of homophily and other relational properties. However, online social network data often lacks basic demographic information about the nodes. Researchers must rely on predicted node attributes to estimate measures of homophily, but little is known about the validity of these measures. We show that estimating homophily in a network can be viewed as a dyadic prediction problem, and that homophily estimates are unbiased when dyad-level residuals sum to zero in the network. Node-level prediction model…
