Randomized algorithms
A fast randomized LOGSPACE algorithm for graph connectivity
ICALP '94 Selected papers from the 21st international colloquium on Automata, languages and programming
Search and replication in unstructured peer-to-peer networks
ICS '02 Proceedings of the 16th international conference on Supercomputing
Adaptive on-line page importance computation
WWW '03 Proceedings of the 12th international conference on World Wide Web
On unbiased sampling for unstructured peer-to-peer networks
Proceedings of the 6th ACM SIGCOMM conference on Internet measurement
The cover time of the preferential attachment graph
Journal of Combinatorial Theory Series B
Many random walks are faster than one
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Communications of the ACM
Centralities: capturing the fuzzy notion of importance in social graphs
Proceedings of the Second ACM EuroSys Workshop on Social Network Systems
Impact of local topological information on random walks on finite graphs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
A tight upper bound on the cover time for random walks on graphs
Random Structures & Algorithms
A tight lower bound on the cover time for random walks on graphs
Random Structures & Algorithms
Computing communities in large networks using random walks
ISCIS'05 Proceedings of the 20th international conference on Computer and Information Sciences
Evaluation of topological vulnerability of the internet under regional failures
ARES'11 Proceedings of the IFIP WG 8.4/8.9 international cross domain conference on Availability, reliability and security for business, enterprise and health information systems
Distributed assessment of the closeness centrality ranking in complex networks
Proceedings of the Fourth Annual Workshop on Simplifying Complex Networks for Practitioners
Ego network models for Future Internet social networking environments
Computer Communications
Distributed Assessment of Network Centralities in Complex Social Networks
ASONAM '12 Proceedings of the 2012 International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2012)
Scale-free topology evolution for wireless sensor networks
Computers and Electrical Engineering
DACCER: Distributed Assessment of the Closeness CEntrality Ranking in complex networks
Computer Networks: The International Journal of Computer and Telecommunications Networking
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A complex network can be modeled as a graph representing the ''who knows who'' relationship. In the context of graph theory for social networks, the notion of centrality is used to assess the relative importance of nodes in a given network topology. For example, in a network composed of large dense clusters connected through only a few links, the nodes involved in those links are particularly critical as far as the network survivability is concerned. This may also impact any application running on top of it. Such information can be exploited for various topological maintenance issues to prevent congestion and disruption. This can also be used offline to identify the most important actors in large social interaction graphs. Several forms of centrality have been proposed so far. Yet, they suffer from imperfections: initially designed for small social graphs, they are either of limited use (degree centrality), either incompatible in a distributed setting (e.g. random walk betweenness centrality). In this paper we introduce a novel form of centrality: the second order centrality which can be computed in a distributed manner. This provides locally each node with a value reflecting its relative criticity and relies on a random walk visiting the network in an unbiased fashion. To this end, each node records the time elapsed between visits of that random walk (called return time in the sequel) and computes the standard deviation (or second order moment) of such return times. The key point is that central nodes see regularly the random walk compared to other topology nodes. Both through theoretical analysis and simulation, we show that the standard deviation can be used to accurately identify critical nodes as well as to globally characterize graphs topology in a distributed way. We finally compare our proposal to well-known centralities to assess its competitivity.