Community Detection in Social Networks

Social networks usually display a hierarchy of communities and it is the task of community detection algorithms to detect these communities and preferably also their hierarchical relationships. One common class of such hierarchical algorithms are the agglomerative algorithms. These algorithms start with one community per vertex in the network and keep agglomerating vertices together to form increasingly larger communities. Another common class of hierarchical algorithms are the divisive algorithms. These algorithms start with a single community comprising all the vertices of the network and then split the network into several connected components that are viewed as communities. We start this thesis by giving an introductory overview of the field of com- munity detection in part I, including complex networks, the basic groups of com- munity definitions, the modularity function, and a description of common com- munity detection techniques, including agglomerative and divisive algorithms. Then we proceed, in part II, with community detection algorithms that have been implemented and tested, with refined use of data structures, as part of this thesis. We start by describing, implementing and testing against benchmark graphs the greedy hierarchical agglomerative community detection algorithm proposed by Aaron Clauset, M. E. J. Newman, and Cristopher Moore in 2004 in the article Finding community structure in very large networks [5]. We continue with describing and implementing the hierarchical divisive algorithm proposed by Filippo Radicchi, Claudio Castellano, Federico Cecconi, Vittorio Loreto, and Domenico Parisi in 2004 in the article Defining and identifying communities in networks [28]. Instead of testing this algorithm against benchmark graphs we present a community detection web service that runs the algorithm by Radicchi et al. on the collaboration networks in the DBLP database of scientific publi- cations and co- authorships in the area of computer science. We allow the user to freely set the many parameters that we have defined for this algorithm. The final judgment on the results is measured by the modularity value or can be left to the knowledgeable user. A rough description of the design of the algorithms and of the web service is given, and all code is available at GitHub [10] [9]. Lastly, a few improvements both to the algorithm by Radicchi et al. and to the web service are presented.Master i InformatikkMAMN-INFINF39

Innovative approaches in investigating inter-beat intervals: Graph theoretical method suggests altered autonomic functioning in adolescents with ADHD

Cardiac inter-beat intervals (IBIs) are considered to reflect autonomic functioning and self-regulatory abilities and are often investigated by traditional time- and frequency domain analyses. These analyses investigate IBI fluctuations across relatively long time series. The similarity graph algorithm is a nonlinear method that analyzes segments of IBI time series (i.e., time windows)—possibly being more sensitive to transient and spontaneous IBI fluctuations. We hypothesized that the similarity graph algorithm would detect differences between Attention-Deficit/Hyperactivity Disorder (ADHD) and control groups. Resting electrocardiogram (ECG) recordings were collected in 10–18-year-olds with ADHD (n = 37) and controls (n = 36). IBIs were converted to graphs that were subsequently investigated for similarity. We varied the criterion for defining IBIs as similar, assessing which setting best distinguished ADHD and control groups. Using this setting, we applied the similarity graph algorithm to time windows of 2–5, 6–13 and 12–25 s, respectively. We also performed traditional IBI analyses. Independent samples t tests assessed group differences. Results showed that a 1.5% criterion of similarity and a time window of 2–5 s best distinguished adolescents with ADHD and controls. The similarity graph algorithm showed a higher number of edges, maximum edges and cliques, and lower edges10+10/edges2+2 in the ADHD group compared to controls. The results suggested more similar IBIs in the ADHD group compared to the controls, possibly due to altered vagal activity and less effective regulation of heart rate. Traditional analyses did not detect any group differences. Consequently, the similarity graph algorithm might complement traditional IBI analyses as a marker of psychopathology.publishedVersio

Diurnal variation of motor activity in adult ADHD patients analyzed with methods from graph theory

Attention-deficit /hyperactivity disorder (ADHD) is a common neurodevelopmental syndrome characterized by age-inappropriate levels of motor activity, impulsivity and attention. The aim of the present study was to study diurnal variation of motor activity in adult ADHD patients, compared to healthy controls and clinical controls with mood and anxiety disorders. Wrist-worn actigraphs were used to record motor activity in a sample of 81 patients and 30 healthy controls. Time series from registrations in the morning and evening were analyzed using measures of variability, complexity and a newly developed method, the similarity algorithm, based on transforming time series into graphs. In healthy controls the evening registrations showed higher variability and lower complexity compared to morning registrations, however this was evident only in the female controls. In the two patient groups the same measures were not significantly different, with one exception, the graph measure bridges. This was the measure that most clearly separated morning and evening registrations and was significantly different both in healthy controls and in patients with a diagnosis of ADHD. These findings suggest that actigraph registrations, combined with mathematical methods based on graph theory, may be used to elucidate the mechanisms responsible for the diurnal regulation of motor activity.publishedVersio

Community Detection in Social Networks

Social networks usually display a hierarchy of communities and it is the task of community detection algorithms to detect these communities and preferably also their hierarchical relationships. One common class of such hierarchical algorithms are the agglomerative algorithms. These algorithms start with one community per vertex in the network and keep agglomerating vertices together to form increasingly larger communities. Another common class of hierarchical algorithms are the divisive algorithms. These algorithms start with a single community comprising all the vertices of the network and then split the network into several connected components that are viewed as communities. We start this thesis by giving an introductory overview of the field of com- munity detection in part I, including complex networks, the basic groups of com- munity definitions, the modularity function, and a description of common com- munity detection techniques, including agglomerative and divisive algorithms. Then we proceed, in part II, with community detection algorithms that have been implemented and tested, with refined use of data structures, as part of this thesis. We start by describing, implementing and testing against benchmark graphs the greedy hierarchical agglomerative community detection algorithm proposed by Aaron Clauset, M. E. J. Newman, and Cristopher Moore in 2004 in the article Finding community structure in very large networks [5]. We continue with describing and implementing the hierarchical divisive algorithm proposed by Filippo Radicchi, Claudio Castellano, Federico Cecconi, Vittorio Loreto, and Domenico Parisi in 2004 in the article Defining and identifying communities in networks [28]. Instead of testing this algorithm against benchmark graphs we present a community detection web service that runs the algorithm by Radicchi et al. on the collaboration networks in the DBLP database of scientific publi- cations and co- authorships in the area of computer science. We allow the user to freely set the many parameters that we have defined for this algorithm. The final judgment on the results is measured by the modularity value or can be left to the knowledgeable user. A rough description of the design of the algorithms and of the web service is given, and all code is available at GitHub [10] [9]. Lastly, a few improvements both to the algorithm by Radicchi et al. and to the web service are presented

Results from actigraphic recordings for 300 min (one min sequences).

<p>Number of edges from each node. Undirected similarity graph.</p

Missing edges between direct neighbors from actigraphic recordings for 300 min (one min sequences), with both the directed and the undirected similarity graph, using 40 (20 + 20) neighbors.

<p>For the undirected similarity graph number of components are also given.</p

Results from horizontal visibility graph analyses.

<p>Number of edges from each node.</p

Results from actigraphic recordings for 12 days (288 hrs, 1 hr sequences).

<p>Number of edges from each node. Directed similarity graph.</p

Results from visibility graph analyses.

<p>Number of edges from each node.</p

The similarity graph algorithm used in the present study.

<p>The similarity graph algorithm used in the present study.</p