## 1 Introduction  
One of the most interesting and widely studied properties of complex networks is community structure. While an exact definition of a _community_ is difficult to find, communities or clusters are often interpreted as groups of nodes that are more connected to each other than to the rest of the network. Because of this, nodes in a community \"probably share common properties and/or play similar roles\" within the network [1]. Depending on the context, _community detection_ may also be referred to as _clustering_ or _graph partitioning_. Clustering is a very useful data exploratory machine learning tool that allows us to make better sense of heterogeneous data by grouping data with similar attributes based on some criteria. Popular graph partitioning methods such as the Girvan-Newman algorithm [2], sparsest-cuts [3], spectral partitioning [4], and general conductance based methods (related to spectral methods via Cheeger's inequality [5]) may be viewed as solving an _edge-based resilience_ problem on a graph while simultaneously outputting the components resulting from the removal of the _critical edge set_ as the set of clusters. In contrast to these graph-theoretic edge-based resilience methods, in preliminary work [6],we introduced a _node_-based resilience clustering approach using _vertex attack tolerance_ (VAT) [7; 8; 9; 10] with some unique applicability for noisy datasets. A node-based resilience measure by definition must express the relative size of a most critical set of target vertices whose removal, upon an attack, would be detrimental to the remaining network and attempt to quantify the amount of resulting damage [10]. We are the first to establish a relationship between combinatorial measures of node-based resilience and graph-theoretic clustering. The current work relies on this relationship to develop a clustering framework that can be used with many different resilience measures, the choice of which may depend upon the clustering objective and domain specific properties. To examine the relevance of different resilience measures to the problem of clustering, we perform extensive tests using the framework with the resilience measures discussed in [10], including VAT, integrity [11], toughness [12], tenacity [13], and scattering number [14]. A strength of the framework is that other resilience measures can also be used. Our focus on _node_-based resilience measures yields a number of unique advantages in the clustering context compared to _edge_-based approaches, along with some challenges as well. Measuring the resilience of a network against targeted node attacks naturally yields both a partial clustering with some outliers or noisy data points removed and a semi-clustering, targeting potential overlap nodes with multiple neighboring components. For a complete clustering in the traditional setting, an assignment of each critical attack set node to a unique cluster must additionally be made. The preliminary results of our node-based resilience clustering methodologies (NBR-Clust) [6; 15] have demonstrated their effectiveness for clustering native point-set data in the presence of noise as well as situations in which the number of clusters is not known a priori. Whereas our preliminary works examined applications of the NBR-Clust framework to point-set data, this paper exhaustively examines applications to several types of native _network_ data in addition to examining the applicability of the framework towards the important problem of overlapping community detection. In this paper, we formalize and extensively evaluate the efficacy of the NBR-Clust framework. Specifically, the key contributions of this work are as follows:  
* An empirical analysis of the robustness and accuracy of the results of NBR clustering is obtained by applying it to a diverse and rich set of data, including real and synthetically generated datasets with and without noise, as well as diverse graph networks with and without overlaps.