Behavior-related neural dynamics in the frontal cortex is an emergent property of network connectivity. The network structure at the level of individual neurons, and its relationship to neural coding are largely unknown. We developed an optical method for rapid (500k pairwise connections / 30 minutes) mapping of effective connectivity in the neocortex in vivo. To this end, we combined 2-photon optogenetic stimulation of individual excitatory neurons and measurement of responses in non-stimulated neurons (‘effective connection’) using 2-photon volumetric calcium imaging. We applied this method in anterior lateral motor cortex (ALM) in a novel behavioral task in which untrained mice performed multidirectional tongue-reaching for water rewards presented at multiple (up to 25) locations on a grid in front of the mouse face. A majority of ALM neurons were modulated by task variables with a subset of neurons (~25%) exhibited strong tuning to the reward location. Specifically, some neurons showed tuning to direction of the reward location with respect to the mouse face, whereas other neurons were selective for particular reward locations. We then mapped effective connectivity between 10,000,000 pairs of layer 2/3 neurons imaged in this task. Nearby neurons were more strongly connected and shared directional selectivity, revealing a fine-scale columnar architecture. We next analyzed effective connectivity between these neurons using methods borrowed from network science. The distribution of the number of out-degree connections could not be explained by random connectivity, but instead displayed a long tail – with a subset of neurons having unexpectedly large numbers of connections. These hub neurons had weak tuning to reward location, showed highly reliable responses on a trial-by-trial basis, and exhibited a strong influence on neighboring neurons. Hub neurons may act as local conductors of the neural orchestra.