Approximation Algorithms for Finding Highly Connected Subgraphs

(Also cross-referenced as UMIACS-TR-95-4

Parallel Adaptive Algorithms for Sampling Large Scale Networks

The study of real-world systems, represented as networks, has important application in many disciplines including social sciences [1], bioinformatics [2] and software engineering [3]. These networks are extremely large, and analyzing them is very expensive. Our research work involves developing parallel graph sampling methods for efficient analysis of gene correlation networks. Our sampling algorithms maintain important structural and informational properties of large unstructured networks. We focus on preserving the relative importance, based on combinatorial metrics, rather than the exact measures. We use a special subgraph technique, based on finding triangles called maximal chordal subgraphs, which maintains the highly connected portions of the network while increasing the distance between less connected regions. Our results show that even with significant reduction of the network we can obtain reliable subgraphs which conserve most of the relevant combinatorial and functional properties. Additionally, sampling reveals new functional properties which were previously undiscovered in the original system

Communities as Well Separated Subgraphs With Cohesive Cores: Identification of Core-Periphery Structures in Link Communities

Communities in networks are commonly considered as highly cohesive subgraphs which are well separated from the rest of the network. However, cohesion and separation often cannot be maximized at the same time, which is why a compromise is sought by some methods. When a compromise is not suitable for the problem to be solved it might be advantageous to separate the two criteria. In this paper, we explore such an approach by defining communities as well separated subgraphs which can have one or more cohesive cores surrounded by peripheries. We apply this idea to link communities and present an algorithm for constructing hierarchical core-periphery structures in link communities and first test results.Comment: 12 pages, 2 figures, submitted version of a paper accepted for the 7th International Conference on Complex Networks and Their Applications, December 11-13, 2018, Cambridge, UK; revised version at http://141.20.126.227/~qm/papers

Robust Group Linkage

We study the problem of group linkage: linking records that refer to entities in the same group. Applications for group linkage include finding businesses in the same chain, finding conference attendees from the same affiliation, finding players from the same team, etc. Group linkage faces challenges not present for traditional record linkage. First, although different members in the same group can share some similar global values of an attribute, they represent different entities so can also have distinct local values for the same or different attributes, requiring a high tolerance for value diversity. Second, groups can be huge (with tens of thousands of records), requiring high scalability even after using good blocking strategies. We present a two-stage algorithm: the first stage identifies cores containing records that are very likely to belong to the same group, while being robust to possible erroneous values; the second stage collects strong evidence from the cores and leverages it for merging more records into the same group, while being tolerant to differences in local values of an attribute. Experimental results show the high effectiveness and efficiency of our algorithm on various real-world data sets

The inhomogeneous evolution of subgraphs and cycles in complex networks

Subgraphs and cycles are often used to characterize the local properties of complex networks. Here we show that the subgraph structure of real networks is highly time dependent: as the network grows, the density of some subgraphs remains unchanged, while the density of others increase at a rate that is determined by the network's degree distribution and clustering properties. This inhomogeneous evolution process, supported by direct measurements on several real networks, leads to systematic shifts in the overall subgraph spectrum and to an inevitable overrepresentation of some subgraphs and cycles.Comment: 4 pages, 4 figures, submitted to Phys. Rev.