Community structure

Abstract: We propose and study a set of algorithms for discovering community structure in networks-natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative removal of edges from the network to split it into communities, the edges removed being identified using any one of a number of possible "betweenness" measures, and second, these measures are, crucially, recalculated after each removal. We also propose a measure for the strength of the community structure found by our algorithms, which gives us an objective metric for choosing the number of communities into which a network should be divided. We demonstrate that our algorithms are highly effective at discovering community structure in both computer-generated and real-world network data, and show how they can be used to shed light on the sometimes dauntingly complex structure of networked systems.

Abstract: Strictly speaking, a community is composed of all the organisms that live together in a particular habitat. Community structure concerns all the various ways in which the members of such a community relate to and interact with one another, as well as community-level properties that emerge from these interactions, such as trophic structure, energy flow, species diversity, relative abundance, and community stabil­ ity. In practice, ecologists are usually unable to study entire communities, but instead interest is often focused on some convenient and tractable subset (usually taxonomic) of a particular community or series of communities. Thus one reads about plant communities, fish communities, bird communities, and so on. My topic here is the structure of lizard communities in this somewhat loose sense of the word (perhaps assemblage would be a more accurate description); my emphasis is on the niche relationships among such sympatric sets of lizard species, especially as they affect the numbers of species that coexist within lizard communities (species den­ sity). So defined, the simplest (and perhaps least interesting) lizard communities would be those that contain but a single species, as, for instance, northern populations of Eumeces msciatus. At the other extreme, probably the most complex lizard commu­ nities are those of the Australian sandridge deserts where as many as 40 different species occur in sympatry (20). Usually species densities of sympatric lizards vary from about 4 or 5 species to perhaps as many as 20. Lizard communities in arid regions are generally richer in species than those in wetter areas; therefore, because almost all ecological studies of entire saurofaunas have been in deserts (l8, 20, 25), this paper emphasizes the structure of desert lizard communities. As such, I review mostly my own work. Other studies on lizard communities in nondesert habitats are, however, cited where appropriate. Historical factors such as degree of isolation and available biotic stocks (particu­ larly the species pools of potential competitors and predators) have profoundly shaped lizard communities. Thus one reason the Australian deserts support such very rich lizard communities may be that competition with, and perhaps predation pressures from, snakes, birds, and mammals are reduced on that continent (20).

Abstract: Many networks in nature, society and technology are characterized by a mesoscopic level of organization, with groups of nodes forming tightly connected units, called communities or modules, that are only weakly linked to each other. Uncovering this community structure is one of the most important problems in the field of complex networks. Networks often show a hierarchical organization, with communities embedded within other communities; moreover, nodes can be shared between different communities. Here, we present the first algorithm that finds both overlapping communities and the hierarchical structure. The method is based on the local optimization of a fitness function. Community structure is revealed by peaks in the fitness histogram. The resolution can be tuned by a parameter enabling different hierarchical levels of organization to be investigated. Tests on real and artificial networks give excellent results.

Abstract: A large body of work has been devoted to defining and identifying clusters or communities in social and information networks, i.e., in graphs in which the nodes represent underlying social entities and the edges represent some sort of interaction between pairs of nodes. Most such research begins with the premise that a community or a cluster should be thought of as a set of nodes that has more and/or better connections between its members than to the remainder of the network. In this paper, we explore from a novel perspective several questions related to identifying meaningful communities in large social and information networks, and we come to several striking conclusions. Rather than defining a procedure to extract sets of nodes from a graph and then attempting to interpret these sets as "real" communities, we employ approximation algorithms for the graph-partitioning problem to characterize as a function of size the statistical and structural properties of partitions of graphs that could plausibly be i...