Causal motifs and existence of endogenous cascades in directed networks with application to company defaults

Motivated by the problem of detection of cascades of defaults in economy, we developed a detection framework for an endogenous spreading based on causal motifs we define in this paper. We assume that the change of state of a vertex can be triggered either by an endogenous (related to the network) or an exogenous (unrelated to the network) event, that the underlying network is directed and that times when vertices changed their states are available. After simulating default cascades driven by different stochastic processes on different synthetic networks, we show that some of the smallest causal motifs can robustly detect endogenous spreading events. Finally, we apply the method to the data of defaults of Croatian companies and observe the time window in which an endogenous cascade was likely happening.

Remaining Agile and Adaptable

If a network has longevity, it will experience change. This chapter is about how networks reinvent themselves, mature, learn, grow, and dissolve. It uses a framework based on two distinctions: the goal-directedness of the network and the disruptiveness of the change. For serendipitous networks, or networks where organizations do not share goals, field-wide disruption and the accumulation of individual organizations’ actions drive change. In these circumstances, organizations manage changes by attending to their network portfolio and absorptive capacity. For goal-directed networks, change can be planned or unplanned. It can be incremental or radical. In each of these circumstances, the chapter recommends pathways for managing the degree and type of change. It uses case studies to illustrate how leaders manage the dilemmas caused by network change. It includes strategic planning, action learning team, and absorptive capacity tools.

The Influence of Funders and Resources

Generally, goal-directed networks are a more, not less, expensive way to coordinate organizational activity. This chapter describes the different types of resources typically required to achieve social impact, including financial resources, human resources, technology, and time. It describes the unique challenges in managing network resources, including when networks compete with their partners for resources and the significant time that networks require to achieve social impact. It includes recommendations for networks that lack the resources they need to make a social impact and funders that wish to forge a path for social impact. Throughout the chapter, case illustrations are used to describe both the types of resources networks require and the varied ways that they secure and manage those resources. It also includes recommendations for fiscal sponsorship and explains how to conduct a community asset inventory.