Complex networks vulnerability to module-based attacks

In the multidisciplinary field of Network Science, optimization of procedures for efficiently breaking complex networks is attracting much attention from practical points of view. In this contribution we present a module-based method to efficiently break complex networks. The procedure first identifies the communities in which the network can be represented, then it deletes the nodes (edges) that connect different modules by its order in the betweenness centrality ranking list. We illustrate the method by applying it to various well known examples of social, infrastructure, and biological networks. We show that the proposed method always outperforms vertex (edge) attacks which are based on the ranking of node (edge) degree or centrality, with a huge gain in efficiency for some examples. Remarkably, for the US power grid, the present method breaks the original network of 4941 nodes to many fragments smaller than 197 nodes (4% of the original size) by removing mere 164 nodes (~3%) identified by the procedure. By comparison, any degree or centrality based procedure, deleting the same amount of nodes, removes only 22% of the original network, i.e. more than 3800 nodes continue to be connected after thatComment: 8 pages, 8 figure

Learning Reputation in an Authorship Network

The problem of searching for experts in a given academic field is hugely important in both industry and academia. We study exactly this issue with respect to a database of authors and their publications. The idea is to use Latent Semantic Indexing (LSI) and Latent Dirichlet Allocation (LDA) to perform topic modelling in order to find authors who have worked in a query field. We then construct a coauthorship graph and motivate the use of influence maximisation and a variety of graph centrality measures to obtain a ranked list of experts. The ranked lists are further improved using a Markov Chain-based rank aggregation approach. The complete method is readily scalable to large datasets. To demonstrate the efficacy of the approach we report on an extensive set of computational simulations using the Arnetminer dataset. An improvement in mean average precision is demonstrated over the baseline case of simply using the order of authors found by the topic models

Analyzing the Facebook Friendship Graph

Online Social Networks (OSN) during last years acquired a\ud huge and increasing popularity as one of the most important emerging Web phenomena, deeply modifying the behavior of users and contributing to build a solid substrate of connections and relationships among people using the Web. In this preliminary work paper, our purpose is to analyze Facebook, considering a signi�cant sample of data re\ud ecting relationships among subscribed users. Our goal is to extract, from this platform, relevant information about the distribution of these relations and exploit tools and algorithms provided by the Social Network Analysis (SNA) to discover and, possibly, understand underlying similarities\ud between the developing of OSN and real-life social networks

Decremental All-Pairs ALL Shortest Paths and Betweenness Centrality

We consider the all pairs all shortest paths (APASP) problem, which maintains the shortest path dag rooted at every vertex in a directed graph G=(V,E) with positive edge weights. For this problem we present a decremental algorithm (that supports the deletion of a vertex, or weight increases on edges incident to a vertex). Our algorithm runs in amortized O(\vstar^2 \cdot \log n) time per update, where n=|V|, and \vstar bounds the number of edges that lie on shortest paths through any given vertex. Our APASP algorithm can be used for the decremental computation of betweenness centrality (BC), a graph parameter that is widely used in the analysis of large complex networks. No nontrivial decremental algorithm for either problem was known prior to our work. Our method is a generalization of the decremental algorithm of Demetrescu and Italiano [DI04] for unique shortest paths, and for graphs with \vstar =O(n), we match the bound in [DI04]. Thus for graphs with a constant number of shortest paths between any pair of vertices, our algorithm maintains APASP and BC scores in amortized time O(n^2 \log n) under decremental updates, regardless of the number of edges in the graph.Comment: An extended abstract of this paper will appear in Proc. ISAAC 201

The Minimum Wiener Connector

The Wiener index of a graph is the sum of all pairwise shortest-path distances between its vertices. In this paper we study the novel problem of finding a minimum Wiener connector: given a connected graph $G=(V,E)$ and a set $Q\subseteq V$ of query vertices, find a subgraph of $G$ that connects all query vertices and has minimum Wiener index. We show that The Minimum Wiener Connector admits a polynomial-time (albeit impractical) exact algorithm for the special case where the number of query vertices is bounded. We show that in general the problem is NP-hard, and has no PTAS unless $\mathbf{P} = \mathbf{NP}$. Our main contribution is a constant-factor approximation algorithm running in time $\widetilde{O}(|Q||E|)$. A thorough experimentation on a large variety of real-world graphs confirms that our method returns smaller and denser solutions than other methods, and does so by adding to the query set $Q$ a small number of important vertices (i.e., vertices with high centrality).Comment: Published in Proceedings of the 2015 ACM SIGMOD International Conference on Management of Dat

Robustness and Closeness Centrality for Self-Organized and Planned Cities

Street networks are important infrastructural transportation systems that cover a great part of the planet. It is now widely accepted that transportation properties of street networks are better understood in the interplay between the street network itself and the so called \textit{information} or \textit{dual network}, which embeds the topology of the street network navigation system. In this work, we present a novel robustness analysis, based on the interaction between the primal and the dual transportation layer for two large metropolis, London and Chicago, thus considering the structural differences to intentional attacks for \textit{self-organized} and planned cities. We elaborate the results through an accurate closeness centrality analysis in the Euclidean space and in the relationship between primal and dual space. Interestingly enough, we find that even if the considered planar graphs display very distinct properties, the information space induce them to converge toward systems which are similar in terms of transportation properties