Estimating the resolution limit of the map equation in community detection

A community detection algorithm is considered to have a resolution limit if the scale of the smallest modules that can be resolved depends on the size of the analyzed subnetwork. The resolution limit is known to prevent some community detection algorithms from accurately identifying the modular structure of a network. In fact, any global objective function for measuring the quality of a two-level assignment of nodes into modules must have some sort of resolution limit or an external resolution parameter. However, it is yet unknown how the resolution limit affects the so-called map equation, which is known to be an efficient objective function for community detection. We derive an analytical estimate and conclude that the resolution limit of the map equation is set by the total number of links between modules instead of the total number of links in the full network as for modularity. This mechanism makes the resolution limit much less restrictive for the map equation than for modularity, and in practice orders of magnitudes smaller. Furthermore, we argue that the effect of the resolution limit often results from shoehorning multi-level modular structures into two-level descriptions. As we show, the hierarchical map equation effectively eliminates the resolution limit for networks with nested multi-level modular structures.Comment: 12 pages, 7 figure

Detecting Stable Communities In Large Scale Networks

A network is said to exhibit community structure if the nodes of the network can be easily grouped into groups of nodes, such that each group is densely connected internally but sparsely connected with other groups. Most real world networks exhibit community structure. A popular technique for detecting communities is based on computing the modularity of the network. Modularity reflects how well the vertices in a group are connected as opposed to being randomly connected. We propose a parallel algorithm for detecting modularity in large networks. However, all modularity based algorithms for detecting community structure are affected by the order in which the vertices in the network are processed. Therefore, detecting communities in real world graphs becomes increasingly difficult. We introduce the concept of stable community, that is, a group of vertices that are always partitioned to the same community independent of the vertex perturbations to the input. We develop a preprocessing step that identifies stable communities and empirically show that the number of stable communities in a network affects the range of modularity values obtained. In particular, stable communities can also help determine strong communities in the network. Modularity is a widely accepted metric for measuring the quality of a partition identified by various community detection algorithms. However, a growing number of researchers have started to explore the limitations of modularity maximization such as resolution limit, degeneracy of solutions and asymptotic growth of the modularity value for detecting communities. In order to address these issues we propose a novel vertex-level metric called permanence. We show that our metric permanence as compared to other standard metrics such as modularity, conductance and cut-ratio performs as a better community scoring function for evaluating the detected community structures from both synthetic networks and real-world networks. We demonstarte that maximizing permanence results in communities that match the ground-truth structure of networks more accurately than modularity based and other approaches. Finally, we demonstrate how maximizing permanence overcomes limitations associated with modularity maximization

Extension of Modularity Density for Overlapping Community Structure

Modularity is widely used to effectively measure the strength of the disjoint community structure found by community detection algorithms. Although several overlapping extensions of modularity were proposed to measure the quality of overlapping community structure, there is lack of systematic comparison of different extensions. To fill this gap, we overview overlapping extensions of modularity to select the best. In addition, we extend the Modularity Density metric to enable its usage for overlapping communities. The experimental results on four real networks using overlapping extensions of modularity, overlapping modularity density, and six other community quality metrics show that the best results are obtained when the product of the belonging coefficients of two nodes is used as the belonging function. Moreover, our experiments indicate that overlapping modularity density is a better measure of the quality of overlapping community structure than other metrics considered.Comment: 8 pages in Advances in Social Networks Analysis and Mining (ASONAM), 2014 IEEE/ACM International Conference o

Measuring Youth Program Quality: A Guide to Assessment Tools

Thanks to growing interest in the subject of youth program quality, many tools are now available to help organizations and systems assess and improve quality. Given the size and diversity of the youth-serving sector, it is unrealistic to expect that any one tool or process will fit all programs or circumstances. This report compares the purpose, history, structure, methodology, content and technical properties of nine different program observation tools

VALUING COMMUNITY DEVELOPMENT THROUGH THE SOCIAL INCLUSION PROGRAMME (SICAP) 2015–2017 TOWARDS A FRAMEWORK FOR EVALUATION. ESRI RESEARCH SERIES NUMBER 77 FEBRUARY 2019

The Social Inclusion and Community Activation Programme (SICAP) represents a major component of Ireland’s community development strategy, led by the Department of Rural and Community Development (DRCD). The vision of SICAP is to improve the opportunities and life chances of those who are marginalised in society, experiencing unemployment or living in poverty through community development approaches, targeted supports and interagency collaboration, where the values of equality and inclusion are promoted and human rights are respected. In 2016, total expenditure on SICAP amounted to approximately €36 million (Pobal, 2016a). Using a mixed methodology, this report examines the extent to which community development programmes can or should be subject to evaluation, with a particular focus on SICAP. In doing so, the report draws on a rich body of information – including desk-based research; consultation workshops with members of local community groups (LCGs), local community workers (LCWs) and other key policy stakeholders; and an analysis of administrative data held by Pobal – on the characteristics of LCGs that received direct support under SICAP. The findings in this report relate to the delivery of the SICAP 2015–2017 programme which ended in December 2017. The aim of the study is to inform policy by shedding light on a number of issues including the following. Can community development be evaluated? What are the current metrics and methodologies suggested in the literature for evaluating community development interventions? What possible metrics can be used to evaluate community development interventions and how do these relate to the SICAP programme? How can a framework be developed that could potentially be used by SICAP for monitoring evaluation of its community development programme

Comparison and validation of community structures in complex networks

The issue of partitioning a network into communities has attracted a great deal of attention recently. Most authors seem to equate this issue with the one of finding the maximum value of the modularity, as defined by Newman. Since the problem formulated this way is NP-hard, most effort has gone into the construction of search algorithms, and less to the question of other measures of community structures, similarities between various partitionings and the validation with respect to external information. Here we concentrate on a class of computer generated networks and on three well-studied real networks which constitute a bench-mark for network studies; the karate club, the US college football teams and a gene network of yeast. We utilize some standard ways of clustering data (originally not designed for finding community structures in networks) and show that these classical methods sometimes outperform the newer ones. We discuss various measures of the strength of the modular structure, and show by examples features and drawbacks. Further, we compare different partitions by applying some graph-theoretic concepts of distance, which indicate that one of the quality measures of the degree of modularity corresponds quite well with the distance from the true partition. Finally, we introduce a way to validate the partitionings with respect to external data when the nodes are classified but the network structure is unknown. This is here possible since we know everything of the computer generated networks, as well as the historical answer to how the karate club and the football teams are partitioned in reality. The partitioning of the gene network is validated by use of the Gene Ontology database, where we show that a community in general corresponds to a biological process.Comment: To appear in Physica A; 25 page