Several research studies have shown that Complex Networks modeling real-world phenomena are characterized by striking properties: (i) they are organized according to community structure and (ii) their structure evolves with time. Many researchers have worked on methods that can efficiently unveil substructures in complex networks, giving birth to the field of community discovery. A novel and fascinating problem started capturing researcher interest recently: the identification of evolving communities. Dynamic networks can be used to model the evolution of a system: nodes and edges are mutable and their presence, or absence, deeply impacts the community structure that composes them. This survey aims to present the distinctive features and challenges of dynamic community discovery and propose a classification of published approaches. As a "user manual", this work organizes state of the art methodologies into a taxonomy, based on their rationale, and their specific instantiation. Given a definition of network dynamics, desired community characteristics and analytical needs, this survey will support researchers to identify the set of approaches that best fit their needs. The proposed classification could also help researchers to choose in which direction to orient their future research.lated to the mathematical formalism used to describe them. In Figure 1 are shown four different conceptual Static Edge Weighted Snapshots Temporal Networks Model complexity Temporal impact FIG. 1 Network representations. Moving from static graph to interaction ones the model complexity increases while the grain of the temporal information available decreases (Rossetti, 2015).solutions that gradually introduce the temporal dimension in the network modelling process. At one hand we find the complete atemporal scenario (i.e., a single network snapshot capturing a static glimpse of a dynamic phenomenon): network dynamics can be gradually introduced by adopting labels that weights nodes and edges, thus capturing an aggregate network. Following this approach, weights models the number of occurrence of a given node/edge in a pre-determined observation window: with this little increment in the model complexity, several time-dependent analysis neglected before become possible (i.e., tie strength estimation). Aggregation strategies, however, suffer a severe limitation, they do not capture dynamics. For this reason several works model dynamic phenomena with temporally ordered series of network snapshots. This simple modeling choice allows to efficiently keep track of the perturbations occurring on the network topology. However, while the expressivity of the model is increased, the analytical complexity increases as well. When dealing with network snapshots to perform time-aware mining tasks, two issues need to be addressed: (i) how to keep track of multiple stages of the network life and (ii) how to harmonize the analytical results obtained in a snapshot with the outcome of subsequent ones. Dynamic network partition, as well as aggregation, suffe...

Community discovery in complex networks is the task of organizing a network’s structure by grouping together nodes related to each other. Traditional approaches are based on the assumption that there is a global-level organization in the network. However, in many scenarios, each node is the bearer of complex information and cannot be classified in disjoint clusters. The top-down global view of the partition approach is not designed for this. Here, we represent this complex information as multiple latent labels, and we postulate that edges in the networks are created among nodes carrying similar labels. The latent labels are the communities a node belongs to and we discover them with a simple local-first approach to community discovery. This is achieved by democratically letting each node vote for the communities it sees surrounding it in its limited view of the global system, its ego neighborhood, using a label propagation algorithm, assuming that each node is aware of the label it shares with each of its connections. The local communities are merged hierarchically, unveiling the modular organization of the network at the global level and identifying overlapping groups and groups of groups. We tested this intuition against the state-of-the-art overlapping community discovery and found that our new method advances in the chosen scenarios in the quality of the obtained communities. We perform a test on benchmark and on real-world networks, evaluating the quality of the community coverage by using the extracted communities to predict the metadata attached to the nodes, which we consider external information about the latent labels. We also provide an explanation about why real-world networks contain overlapping communities and how our logic is able to capture them. Finally, we show how our method is deterministic, is incremental, and has a limited time complexity, so that it can be used on real-world scale networks

Community discovery has emerged during the last decade as one of the most challenging problems in social network analysis. Many algorithms have been proposed to find communities on static networks, i.e. networks which do not change in time. However, social networks are dynamic realities (e.g. call graphs, online social networks): in such scenarios static community discovery fails to identify a partition of the graph that is semantically consistent with the temporal information expressed by the data. In this work we propose Tiles, an algorithm that extracts overlapping communities and tracks their evolution in time following an online iterative procedure. Our algorithm operates following a domino effect strategy, dynamically recomputing nodes community memberships whenever a new interaction takes place. We compare Tiles with state-of-the-art community detection algorithms on both synthetic and real world networks having annotated community structure: our experiments show that the proposed approach is able to guarantee lower execution times and better correspondence with the ground truth communities than its competitors. Moreover, we illustrate the specifics of the proposed approach by discussing the properties of identified communities it is able to identify

Nowadays the analysis of dynamics of and on networks represents a hot topic in the Social Network Analysis playground. To support students, teachers, developers and researchers in this work we introduce a novel framework, namely NDlib, an environment designed to describe diffusion simulations. NDlib is designed to be a multi-level ecosystem that can be fruitfully used by different user segments. For this reason, upon NDlib, we designed a simulation server that allows remote execution of experiments as well as an online visualization tool that abstracts its programmatic interface and makes available the simulation platform to non-technicians.

Community Discovery is among the most studied problems in complex network analysis. During the last decade, many algorithms have been proposed to address such task; however, only a few of them have been integrated into a common framework, making it hard to use and compare different solutions. To support developers, researchers and practitioners, in this paper we introduce a python library -namely CDLIB -designed to serve this need. The aim of CDLIB is to allow easy and standardized access to a wide variety of network clustering algorithms, to evaluate and compare the results they provide, and to visualize them. It notably provides the largest available collection of community detection implementations, with a total of 39 algorithms.

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Unveil the homophilic/heterophilic behaviors that characterize the wiring patterns of complex networks is an important task in social network analysis, often approached studying the assortative mixing of node attributes. Recent works underlined that a global measure to quantify node homophily necessarily provides a partial, often deceiving, picture of the reality. Moving from such literature, in this work, we propose a novel measure, namely Conformity, designed to overcome such limitation by providing a node-centric quantification of assortative mixing patterns. Differently from the measures proposed so far, Conformity is designed to be path-aware, thus allowing for a more detailed evaluation of the impact that nodes at different degrees of separations have on the homophilic embeddedness of a target. Experimental analysis on synthetic and real data allowed us to observe that Conformity can unveil valuable insights from node-attributed graphs.