scholarly journals Moebius function on the lattice of dense subgraphs

1960 ◽  
Vol 64B (1) ◽  
pp. 41 ◽  
Author(s):  
R.E. Nettleton ◽  
M.S. Green
Keyword(s):  
Dense Subgraphs ◽  
Moebius Function

Dense subgraphs of power-law random graphs

2021 ◽  
Vol 10 (1) ◽  
pp. 1-11
Author(s):  
Denis O. Lazarev ◽  
Nikolay N. Kuzyurin
Keyword(s):  
Random Graphs ◽  
Power Law ◽  
Dense Subgraphs

Finding dense subgraphs

1995 ◽  
pp. 102-111 ◽  
Author(s):  
Yuichi Asahiro ◽  
Kazuo Iwama
Keyword(s):  
Dense Subgraphs

scholarly journals Finding events in temporal networks: segmentation meets densest subgraph discovery

2019 ◽  
Vol 62 (4) ◽  
pp. 1611-1639
Author(s):  
Polina Rozenshtein ◽  
Francesco Bonchi ◽  
Aristides Gionis ◽  
Mauro Sozio ◽  
Nikolaj Tatti
Keyword(s):  
Optimization Problem ◽  
Approximate Dynamic Programming ◽  
Problem Formulation ◽  
Network Activity ◽  
Total Density ◽  
Temporal Networks ◽  
Time Intervals ◽  
Dense Subgraphs ◽  
Approximation Guarantee ◽  
Densest Subgraph

Abstract In this paper, we study the problem of discovering a timeline of events in a temporal network. We model events as dense subgraphs that occur within intervals of network activity. We formulate the event discovery task as an optimization problem, where we search for a partition of the network timeline into k non-overlapping intervals, such that the intervals span subgraphs with maximum total density. The output is a sequence of dense subgraphs along with corresponding time intervals, capturing the most interesting events during the network lifetime. A naïve solution to our optimization problem has polynomial but prohibitively high running time. We adapt existing recent work on dynamic densest subgraph discovery and approximate dynamic programming to design a fast approximation algorithm. Next, to ensure richer structure, we adjust the problem formulation to encourage coverage of a larger set of nodes. This problem is NP-hard; however, we show that on static graphs a simple greedy algorithm leads to approximate solution due to submodularity. We extend this greedy approach for temporal networks, but we lose the approximation guarantee in the process. Finally, we demonstrate empirically that our algorithms recover solutions with good quality.

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